GMAT
®
7th Edition with Online Practice
by Lisa Zimmer Hatch, MA,
and Scott A.Hatch, JD
GMAT
®
For Dummies
®
, 7th Edition with Online Practice
Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com
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TM
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Library of Congress Control Number: 2017952681
ISBN 978-1-119-37414-5 (pbk); ISBN 978-1-119-37410-7 (ebk); ISBN 978-1-119-37408-4 (ebk)
Manufactured in the United States of America
10 9 8 7 6 5 4 3 2 1
Contents at a Glance
Introduction ......................................................................1
Part 1: Getting Started with the GMAT .......................................5
CHAPTER 1: Getting the Lowdown onthe GMAT ..............................................7
CHAPTER 2: Maximizing Your Score on the GMAT ...........................................17
CHAPTER 3: Mastering Business-School Admissions .........................................29
Part 2: Vanquishing the Verbal Section .....................................35
CHAPTER 4: Applying What You Learned (We Hope) in Grammar Class: Sentence Correction ......37
CHAPTER 5: Not as Enticing as a Bestseller: Reading Comprehension ..........................59
CHAPTER 6: Let’s Think This Through Logically: Critical Reasoning .............................79
CHAPTER 7: Bringing It Together: A Mini Practice Verbal Section ..............................103
Part 3: Acing the Analytical-Writing Section ..............................121
CHAPTER 8: Analyze This: What to Expect from the Analytical Writing Assessment ..............123
CHAPTER 9: Present Perfect Paragraphs: How to WriteaGMAT Essay .........................127
CHAPTER 10: Deconstructing Sample GMAT Essays ..........................................133
CHAPTER 11: Sampling a Series of Writing Prompts ..........................................143
Part 4: Conquering the Quantitative Section .............................151
CHAPTER 12: Getting Back to Basics: Numbers and Operations ...............................153
CHAPTER 13: Considering All the Variables: Algebra ..........................................175
CHAPTER 14: Getting the Angle on Geometry: Planes and Solids ...............................199
CHAPTER 15: Keeping in Step: Coordinate Geometry .........................................219
CHAPTER 16: Manipulating Numbers: Statistics and Sets .....................................233
CHAPTER 17: It’s All in the Presentation: GMAT Quantitative Question Types ....................249
CHAPTER 18: All Together Now: A Mini Practice Quantitative Section ...........................267
Part 5: Excelling on the Integrated-Reasoning Section ..................285
CHAPTER 19: Best of Both Worlds: The Integrated-Reasoning Section ..........................287
CHAPTER 20: Deciphering Data in Charts and Graphs ........................................303
Part 6: Practice Makes Perfect ...............................................315
CHAPTER 21: GMAT Practice Test ..........................................................317
CHAPTER 22: Practice Test Answers andExplanations ........................................347
Part 7: The Part of Tens .......................................................379
CHAPTER 23: Ten Question Types You’ve Got a Good Shot At .................................381
CHAPTER 24: Ten Writing Errors to Avoid ...................................................385
CHAPTER 25: Ten Ways to Increase Your Chances of Getting into Business School ...............387
Index .............................................................................391
Table of Contents v
Table of Contents
INTRODUCTION ..................................................................1
PART 1: GETTING STARTED WITH THE GMAT ...............................5
CHAPTER 1: Getting the Lowdown onthe GMAT .................................7
Knowing Why the GMAT Is Important .........................................7
Timing It Perfectly: When to Take the GMAT (And What to Bring) ..................8
When to register for and take the GMAT ....................................8
Things to take to the GMAT (and things to leave at home) ....................10
Forming First Impressions: The Format of the GMAT ...........................10
Getting familiar with what the GMAT tests .................................10
Understanding the computerized format ..................................11
Honing your computer skills for the GMAT .................................12
Knowing Where You Stand: Scoring Considerations ............................13
How the GMAT testers gure your score ...................................13
How the GMAT testers report your score ..................................13
Why you should (almost) never cancel your GMAT score .....................14
Repeating the Process: Retaking the GMAT ....................................15
CHAPTER 2: Maximizing Your Score on the GMAT ...............................17
Discovering Strategies for Successful Guessing ................................17
Forcing yourself to guess so you can move on ..............................18
Understanding the importance of completing each section ...................18
Winning the Race against the Clock ..........................................19
Giving each question equal treatment .....................................19
Making time for the last ten questions .....................................19
Keeping track of your pace ...............................................20
Getting Rid of Wrong Answers ...............................................20
Keeping track of eliminated answer choices for the computer test format ......20
Recognizing wrong answers ..............................................21
Playing It Smart: A Few Things You Shouldn’t Do When Taking the Test ...........25
Don’t lose your focus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Don’t read questions at lightning speed ...................................25
Don’t waste all your time on the hardest questions ..........................25
Don’t cheat ............................................................26
Tackling a Case of Nerves with Relaxation Techniques ..........................26
Devising a Plan of Attack ...................................................27
CHAPTER 3: Mastering Business-School Admissions ............................29
Choosing a Business School .................................................29
Lining Up Your Ducks— Applying to Business Schools ..........................31
When to apply .........................................................32
What to submit ........................................................32
Crafting Eective Business-School Essays .....................................33
vi GMAT For Dummies, 7th Edition with Online Practice
PART 2: VANQUISHING THE VERBAL SECTION ............................35
CHAPTER 4: Applying What You Learned (We Hope) in Grammar Class:
Sentence Correction
...................................................37
Building a Solid Foundation: Grammar Basics .................................38
Getting wordy: The parts of speech .......................................38
Pulling together: The parts of a sentence ..................................40
Pointing Out Mistakes: Common Sentence-Correction Errors ....................42
Can’t we all just get along? Errors in subject-verb and
noun-pronoun agreement ...............................................43
Building code violations: Faulty construction ...............................45
Follow the idiom: Correct use of standard expressions ......................49
Implementing an Approach to Sentence-Correction Questions ..................51
Spotting the error ......................................................52
Eliminating answers that don’t correct errors ...............................52
Eliminating choices that create new errors .................................53
Rereading the sentence .................................................53
Reviewing the process and guessing on sentence corrections. . . . . . . . . . . . . . . . . 53
Sentence-Correction Practice Problems with Answer Explanations ...............53
Practice problems ......................................................54
Answer explanations ....................................................56
CHAPTER 5: Not as Enticing as a Bestseller: Reading Comprehension ......59
Judging by Appearances: What Reading-Comprehension Questions Look Like .....59
Approaching Reading Passages ..............................................60
Mastering the message: The main point ...................................60
Absorbing the ambiance: Author’s tone ....................................61
Finding the framework: The passage’s outline ..............................61
Sticking to the Subject: Types of Passages .....................................62
Experimenting with natural science passages ..............................62
Gathering in social circles: Social science passages ..........................62
Getting down to business passages .......................................63
Approaching Reading-Comprehension Questions ..............................63
Identifying the question type .............................................63
Eliminating answer choices ..............................................66
Dealing with exception questions .........................................67
Reading-Comprehension Practice Questions with Answer Explanations ...........70
Reading-comprehension practice questions ................................70
Answer explanations ....................................................74
CHAPTER 6: Let’s Think This Through Logically: Critical Reasoning ..........79
Focusing on “Critical” Concepts: An Overview ..................................79
Understanding the structure of the questions ..............................80
Figuring out how to answer the questions .................................80
Making a Case: Essentials of Informal Logic ...................................81
Fighting fair: The elements of an argument ................................81
Getting from Point A to Point B: Types of reasoning .........................81
Thinking Inside the Box: Question Types ......................................83
Stalking Your Prey: How to Approach Each Question Type .......................84
Strengthening or weakening arguments ...................................84
Delving into drawing conclusions .........................................88
Spotting those sneaky assumptions .......................................89
Using your noggin to make inferences .....................................91
Making your way through method-of-reasoning questions ...................92
Table of Contents vii
Critical-Reasoning Practice Questions and Answer Explanations .................94
Critical-reasoning practice questions ......................................94
Answer explanations ....................................................98
CHAPTER 7: Bringing It Together: A Mini Practice Verbal Section ...........103
Working Through Verbal Reasoning Practice Questions ........................104
Understanding What’s Right with Answer Explanations ........................113
PART 3: ACING THE ANALYTICAL-WRITING SECTION ..................121
CHAPTER 8: Analyze This: What to Expect from the Analytical
Writing Assessment
..................................................123
Fitting in the AWA with the Rest of the GMAT .................................123
Calling 411: Your AWA Writing Tools ........................................124
Analyzing an Argument ....................................................124
Racking Up the Points: How the GMAT Scores Your Essay ......................125
Getting to know your readers ...........................................125
Interpreting the scores .................................................126
Requesting your essay be rescored ......................................126
CHAPTER 9: Present Perfect Paragraphs: How to WriteaGMAT Essay .....127
Avoiding Grammar, Punctuation, and Mechanics Errors .......................127
Punctuation errors ....................................................128
Sentence-structure problems ...........................................129
Faulty forming of possessives ...........................................129
Spelling issues ........................................................129
More dos and don’ts ...................................................130
Practice makes perfect! .................................................130
Building a Better Essay: Ten Steps to a Higher Score ...........................131
CHAPTER 10: Deconstructing Sample GMAT Essays .............................133
Dening GMAT AWA Scores ................................................133
Taking a Look at Sample Essays ............................................134
Sample essay #1 ......................................................135
Discussion of sample essay #1 ..........................................136
Sample essay #2 ......................................................136
Discussion of sample essay #2 ..........................................137
Sample essay #3 ......................................................138
Discussion of sample essay #3 ..........................................139
Sample essay #4 ......................................................139
Discussion of sample essay #4 ..........................................140
CHAPTER 11: Sampling a Series of Writing Prompts .............................143
Sample Prompt #1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Sample response to essay #1 ...........................................144
Dissection of essay #1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Sample Prompt #2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Sample response to essay #2 ...........................................145
Dissection of essay #2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Sample Prompt #3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Sample response to essay #3 ...........................................147
Dissection of essay #3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Sample Prompt #4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Sample response to essay #4 ...........................................148
Dissection of essay #4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
viii GMAT For Dummies, 7th Edition with Online Practice
PART 4: CONQUERING THE QUANTITATIVE SECTION ..................151
CHAPTER 12: Getting Back to Basics: Numbers and Operations ..............153
Just Your Type: Kinds of Numbers ..........................................153
It’s Not Brain Surgery: Basic Operations .....................................155
Adding, subtracting, multiplying, and dividing .............................155
Checking out the real estate: Properties of real numbers ....................157
Using Little Numbers for Big Values: Bases and Exponents .....................160
Adding and subtracting with exponents ..................................160
Multiplying and dividing with exponents ..................................160
Figuring out the powers of 0 and 1 .......................................161
Dealing with fractional exponents .......................................161
Working with negative exponents ........................................161
Checking Out the Ancestry: Roots ...........................................162
Order of Operations: Please Excuse My Dear Aunt Sally ........................164
Splitting Up: Fractions, Decimals, andPercentages ............................164
Dening numerators, denominators, and other stu
you need to know about fractions .......................................165
Adding and subtracting fractions ........................................167
Multiplying and dividing fractions ........................................167
Calculating percent change .............................................169
Taking it further: Repeated percent change ...............................170
Making Comparisons: Ratios and Proportions ................................171
Playing the Numbers: Scientic Notation ....................................172
CHAPTER 13: Considering All the Variables: Algebra ............................175
Dening the Elements: Algebraic Terms .....................................175
Braving the unknowns: Variables and constants ...........................175
Coming together: Terms and expressions .................................176
Knowing the nomials: Kinds of expressions ...............................176
Maintaining an Orderly Fashion: Algebraic Operations .........................177
Adding to and taking away ..............................................177
Multiplying and dividing expressions .....................................179
Extracting Information: Factoring Polynomials ................................181
Something in common: Finding common factors ...........................182
Two by two: Factoring quadratic polynomials ..............................182
Minding Your Ps and Qs: Functions .........................................183
Standing in: Understanding function terminology ..........................184
Taking it to the limit: Domain and range offunctions .......................185
Putting On Your Thinking Cap: Problem-Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Isolating the variable: Linear equations ...................................188
Bringing in the substitution: Simultaneous equations .......................189
Not playing fair: Inequalities ............................................191
Solving quadratic equations .............................................193
Reading between the lines: Word problems ...............................194
Burning the midnight oil: Work problems .................................196
Going the distance: Distance problems ...................................197
CHAPTER 14: Getting the Angle on Geometry: Planes and Solids .............199
Fishing for the Answers: Lines and Angles ....................................199
Trusting Triangles ........................................................202
Triple treat: Types of triangles ...........................................202
The area of a triangle ..................................................204
The Pythagorean theorem and other cool stu about right triangles ..........204
A striking resemblance: Similar triangles ..................................207
Table of Contents ix
Playing Four Square: Quadrilaterals .........................................208
Drawing parallels: Parallelograms ........................................209
Raising the roof: Trapezoids ............................................210
Showing Their Good Sides: Other Polygons ..................................211
Eating Up Pieces of Pi: Circles ..............................................212
Ring measurements: Radius, diameter, and circumference ..................212
Blueprints for Noah: Arcs ...............................................212
Line ’em up: Chords, inscribed and circumscribed gures, and tangents ......213
Getting a Little Depth Perception: Three-Dimensional Geometry ................215
Chipping o the old block: Rectangular solids .............................215
Sipping from soda cans and other cylinders ...............................217
CHAPTER 15: Keeping in Step: Coordinate Geometry ...........................219
Taking Flight: The Coordinate Plane .........................................219
Line dancing: Understanding coordinate geometry .........................219
What’s the point? Finding the coordinates .................................220
On all fours: Identifying quadrants .......................................220
Slip-Sliding Away: Slope and Linear Equations ................................221
Taking a peak: Dening the slope of a line ................................221
Using the slope-intercept form to graph lines .............................223
Meeting in the middle ..................................................225
Going the distance .....................................................226
Considering other shapes on the coordinate plane .........................227
Fully Functioning: Graphing Functions .......................................228
Passing the vertical line test .............................................228
Feeling at home with domain and range ..................................230
CHAPTER 16: Manipulating Numbers: Statistics and Sets ......................233
Joining a Clique: Groups ...................................................233
Setting Up Sets ...........................................................235
Set terminology .......................................................235
Getting a visual: Venn diagrams .........................................235
Making Arrangements: Permutations and Combinations .......................237
Positioning with permutations ..........................................237
Coming together: Combinations .........................................239
Meeting in the Middle: Mean, Median, and Mode .............................241
Straying from Home: Range and StandardDeviation ..........................243
Scouting out the range .................................................243
Watching out for wanderers: Standard deviation ...........................243
Predicting the Future: Probability ...........................................245
Finding the probability of one event ......................................245
Finding the probability of many events ...................................246
CHAPTER 17: It’s All in the Presentation: GMAT Quantitative
Question Types
........................................................249
Enough’s Enough: Data-Suciency Questions ................................249
You don’t need the solution to nd the answer ............................250
Steps to approaching data-suciency problems ...........................250
Taking a Look at Data-Suciency Practice Problems ...........................253
Practice questions .....................................................253
Answer explanations ...................................................255
Houston, We Have a Problem: Problem-Solving Questions .....................259
Trying Out Some Problem-Solving Practice Problems ..........................261
Practice questions .....................................................261
Answer explanations ...................................................263
x GMAT For Dummies, 7th Edition with Online Practice
CHAPTER 18: All Together Now: A Mini Practice Quantitative Section. . . . . . .267
Tackling GMAT Math Practice Questions .....................................267
Checking Out the Answer Explanations ......................................274
PART 5: EXCELLING ON THE INTEGRATED-
REASONING SECTION
.........................................................285
CHAPTER 19: Best of Both Worlds: The Integrated-Reasoning Section ......287
Understanding What the IR Section Is All About ...............................287
Skills tested ...........................................................288
Question format ......................................................288
Figuring Out How the IR Section Is Scored ...................................290
Making the Most of Your Time .............................................290
Approaching Each Question Type ...........................................291
Table analysis .........................................................291
Two-part analysis ......................................................294
Graphics interpretation ................................................297
Multi-source reasoning .................................................298
CHAPTER 20: Deciphering Data in Charts and Graphs ..........................303
Approaching Integrated-Reasoning Data in Five Easy Steps .....................303
Translating Information in Tables ...........................................304
Making Comparisons with Bar Graphs .......................................305
Simple bar graphs .....................................................305
Graphs with many bars .................................................305
Segmented bar graphs .................................................306
Evaluating Line Graphs ....................................................308
Basic line graphs ......................................................308
Scatter plots ..........................................................308
Complex scatter plots ..................................................309
Clarifying Circle Graphs (Also Known as Pie Charts) ............................310
Extracting Data from Venn Diagrams ........................................311
PART 6: PRACTICE MAKES PERFECT ........................................315
CHAPTER 21: GMAT Practice Test ...................................................317
CHAPTER 22: Practice Test Answers andExplanations .........................347
PART 7: THE PART OF TENS ..................................................379
CHAPTER 23: Ten Question Types You’ve Got a Good Shot At .................381
CHAPTER 24: Ten Writing Errors to Avoid .........................................385
CHAPTER 25: Ten Ways to Increase Your Chances of Getting
into Business School
..................................................387
INDEX ...........................................................................391
Introduction 1
Introduction
Y
ou’re merrily skimming through the admissions requirements for your favorite MBA
programs when all of a sudden, you’re dealt a shocking blow. Your absolute top choice
program—you’lldieifyoudon’tgetin—requiresthatyoutaketheGraduateManagement
AdmissionTest(GMAT).Andyouthoughtyourdaysofspeed-readingpassagesandsolvingfor
x were over.
ManyMBAprogramsincludetheGMATasanadmissionsrequirement,soyou’llbeingoodcom-
pany.Buthowdoyouprepareforsuchacomprehensivetest?Whatareyougoingtodo?Getout
your spiral notebooks from undergraduate courses and sift through years’ worth of doodles?
Many years may have gone by since you encountered a geometry problem, and we bet your gram-
mar skills have gotten a little rusty since English 101.
Clearly, you need a readable, concisely structured resource. Well, you’ve come to the right place.
GMAT For Dummies,7thEditionwithOnlinePractice,putsatyourngertipseverythingyouneed
toknowtoconquertheGMAT.Wegiveyoucompletemathandgrammarreviewsandprovide
insightsintohowtoavoidthepitfallsthattheGMATcreatorswantyoutofallinto.Wealsotryto
make this book as enjoyable as a book that devotes itself to setting up equations and critiquing
arguments can be.
About This Book
Wesuspectthatyouaren’teagerlyanticipatingsittingthroughtheGMAT,andyou’reprobably
not looking forward to studying for it, either. Therefore, we’ve attempted to make the study pro-
cess as painless as possible by giving you clearly written advice in a casual tone. We realize you
have a bunch of things you’d rather be doing, so we’ve broken down the information into easily
digested bites. If you have an extra hour before work or Pilates class, you can devour a chapter or
even a particular section within a chapter. (If these eating metaphors are making you hungry, feel
freetotakeasnackbreak.)
Inthisbook,youcannd
»
Plenty of sample questions so you can see just how the GMAT tests a particular concept. Our
sample questions read like the actual test questions, so you can get comfortable with the way
the GMAT phrases questions and expresses answer choices.
»
Detailed explanations of the strategies for mastering all four sections of the GMAT.Enjoy a
grammar review for the verbal-reasoning section, an extensive math lesson to help you with
the quantitative-reasoning section, a summary of good writing practices for the analytical
writing assessment, and a how-to on reading all kinds of charts and graphs for the integrated-
reasoning section.
»
Six practice tests. One appears in this book in Chapter21, and you’ll nd that one plus ve
others online. Ultimately, the best way to prepare for any standardized test is to practice on
lots of test questions, and this book, along with the accompanying online test bank, has more
than 600 of them.
2 GMAT For Dummies, 7th Edition with Online Practice
»
Time-tested techniques for improving your score. We show you how to quickly eliminate
incorrect answer choices and make educated guesses.
»
Tips on how to manage your time wisely.
»
Suggestions for creating a relaxation routine to employ if you start to panic during the test.
We’veincludedallkindsofinformationtohelpyoudoyourbestontheGMAT!
Youshouldndthisbookeasilyaccessible,butafewthingsmayrequireexplanation.Afewofthe
chaptersmaycontainsidebars(aparagraphortwoinashadedbox)withquirkybitsofinforma-
tionthatwethinkmayinterestyoubutaren’tessentialtoyourperformanceontheGMAT.If
you’re trying to save time, you can skip the sidebars.
Foolish Assumptions
Although we guess it’s possible that you picked up this book just because you have an insatiable
love for math, grammar, and argument analysis, we’re betting it’s more likely that you’re reading
thisbookparticularlybecauseyou’vebeentoldyouneedtotaketheGMAT.(Wehavebeenpraised
forourstartlingabilitytorecognizetheobvious!)Andbecausewe’reprettyastute,we’vegured
that this means that you intend to apply to MBA programs and probably are considering working
toward a masters of business administration.
Generally,MBAprogramsareprettyselective,sowe’rethinkingthatyou’reaprettymotivated
student. Some of you are fresh out of college and may have more recent experience with math and
grammar. Others of you probably haven’t stepped into a classroom in over a decade but possess
workskillsandlifeexperiencethatwillhelpyoumaximizeyourGMATscoredespitethetime
that’s passed since college.
If math and grammar are fresh in your mind and you just need to know what to expect when you
arrive at the test site, this book has that information for you. If you’ve been out of school for a
while, this book provides you with all the basics as well as advanced concepts to give you every-
thingyouneedtoknowtoexcelontheGMAT.
Icons Used in This Book
Oneexcitingfeatureofthisbookistheiconsthathighlightespeciallysignicantportionsofthe
text. These little pictures in the margins alert you to areas where you should pay particularly close
attention.
This icon highlights really important information that you should remember even after you close
the book.
Throughout the book, we give you insights into how you can enhance your performance on the
GMAT.Thetipsgiveyoujuicytimesaversandpointoutespeciallyrelevantconceptstokeepin
mind for the test.
Introduction 3
Yourworldwon’tfallapartifyouignoreourwarnings,butyourscoremaysuer.Heedthese
cautionary pointers to avoid making careless mistakes that can cost you points.
Whenever you see this icon in the text, you know you’re going to get to practice the particular
area of instruction covered in that section with a question like one you may see on the test. Our
examplesincludedetailedexplanationsofhowtomostecientlyanswerGMATquestionsand
avoid common pitfalls.
Beyond the Book
Be sure to check out the free Cheat Sheet for a handy guide that covers tips and tricks for answer-
ingquestionsineachsectionoftheGMAT.TogetthisCheatSheet,simplygoto
www.dummies.
com
andenter“GMATForDummiesCheatSheet”intheSearchbox.
Theonlinepracticethatcomesfreewiththisbookcontainssixfull-lengthpracticetests,sothat
youcanreallyhoneyourGMATskills!Togainaccesstotheonlinepractice,allyouhavetodois
register. Just follow these simple steps:
1. Find your PIN access code located on the inside front cover of this book.
2. Go to Dummies.com and click Activate Now.
3. Find your product (GMAT For Dummies, 7th Edition with Online Practice) and then follow
the on-screen prompts to activate your PIN.
Nowyou’rereadytogo!Youcangobacktotheprogramattestbanks.wiley.com as often as you
want—simplylogonwiththeusernameandpasswordyoucreatedduringyourinitiallogin.No
need to enter the access code a second time.
Tip:IfyouhavetroublewithyourPINorcan’tndit,contactWileyProductTechnicalSupportat
877-762-2974orgoto
support.wiley.com.
Where to Go from Here
Weknowthateveryonewhousesthisbookhasdierentstrengthsandweaknesses,sothisbook
is designed for you to read in the way that best suits you. If you’re a math whiz and need to brush
uponlyonyourverbalskills,youcanskimPart4andfocusonParts1,2,and3.Ifyou’vebeen
writingproposalseverydayforthelasttenyears,youcanprobablyscanPart3andfocusyour
attentiononthemathreviewinPart4.Becausetheintegrated-reasoningsectiondierssosig-
nicantlyfromotherstandardizedtestquestions,you’llbenetfromreadingPart5regardlessof
your math prowess or verbal genius.
Wesuggestthatyoutakeamorethoroughapproach,however.Familiarizeyourselfwiththegen-
eraltest-takingprocessinthersttwochaptersandthengothroughthecompleteGMATreview,
startingwiththeverbalsectionandworkingyourwaythroughtheanalytical-writing,math,and
integrated-reasoningsections.Youcanskimthroughinformationthatyouknowmoreaboutby
just reading the Tips and Warnings and working through the examples in those sections.
4 GMAT For Dummies, 7th Edition with Online Practice
Some of our students like to take a diagnostic test before they study. This is a fancy way of saying
thattheytakeoneofthefull-lengthpracticetestsbeforetheyreadtherestofthebook.Takinga
preview test shows you which questions you seem to cruise through and which areas need more
work. After you’ve taken a practice exam, you can focus your study time on the question types
thatgaveyouthemosttroubleduringtheexam.Then,whenyou’venishedreadingthroughthe
restofthebook(Parts1,2,3,4,and5),youcantakeanotherpracticetestandcompareyourscore
to the one you got on the rst test. This way, you can see just how much you improve with
practice.
This book provides you with a bunch of practice tests, but you can never get enough practice. So,
ifaftertakingallthepracticetestsprovidedatdummies.com,youstillcravemore,visittheo-
cialGMATwebsiteat
www.mba.comanddownloadthefreeGMATPrepsoftwarethere.Thissoft-
ware mimics the computerized format of the test and gives you practice on the types of
mouse-clickingandeye-straining skills youneedtosucceed on theexam.Thatway, you can
experience using the same software you’ll see on the exam.
We’recondentthatifyoudevoteafewhoursaweekforatleastsixweekstopracticingtheskills
and tips we provide for you in this book, you’ll do the best you can when you sit in front of that
computeronGMATtestday.WewishyouourbestforyourultimateGMATscore!
1
Getting Started
with the GMAT
IN THIS PART ...
Familiarize yourself with the format of the test.
Find out how to maximize your score by organizing
your time and streamlining your approach.
Discover what you can and should do to gain admission
to the business school of your choice.
CHAPTER1 Getting the Lowdown onthe GMAT 7
IN THIS CHAPTER
» Finding out how MBA programs
use your GMAT score
» Deciding when to take the GMAT
and knowing what to bring
» Figuring out the format of the
GMAT
» Understanding how the GMAT is
scored
» Considering whether you should
retake the GMAT
Getting the Lowdown
onthe GMAT
C
ongratulations on deciding to take a signicant step in your business career! More than
100 countries oer the Graduate Management Admission Test (GMAT), and according
to the Graduate Management Admission Council, 2,100 universities and organizations in
114 countries use GMAT to make admissions decisions. That said, you’re probably not taking the
GMAT because you want to. In fact, you may not be looking forward to the experience at all!
The GMAT need not be a daunting ordeal. A little knowledge can help calm your nerves, so this
chapter shows you how admissions programs use your test score and addresses the concerns you
may have about the GMAT’s format and testing and scoring procedures.
Knowing Why the GMAT Is Important
If you’re reading this book, you’re probably thinking about applying to an MBA program. And if
you’re applying to an MBA program, you probably need to take the GMAT.Many MBA programs
require that you submit a GMAT score for the admissions process. (Some may require other tests
or no test at all, so make sure you check each program’s admissions checklist.)
Your GMAT score gives the admissions committee another tool to use to assess your skills and
compare you with other applicants. But if you’re seeking a career in business, you’re probably
resigned to being continually assessed and compared. The GMAT doesn’t attempt to evaluate any
particular subject area that you may have studied, but instead it gives admissions ocers a reli-
able idea of how you’ll likely perform in the classes that make up a graduate business curriculum.
Although the GMAT doesn’t rate your experience or motivation, it does provide an estimate of
your academic preparation for graduate business studies.
Chapter1
8 PART 1 Getting Started with the GMAT
Not every MBA applicant has the same undergraduate experience, but most applicants take a
standardized test. Other admissions factors, like college grades, work experience, the admissions
essay or essays, and a personal interview are important, but the GMAT is an admissions tool that
admissions committees can use to directly compare you with other applicants.
The most selective schools primarily admit candidates with solid GMAT scores, and good scores
will certainly strengthen your application to any program, but you shouldn’t feel discouraged if
your practice tests don’t put you in the 90th percentile. Very few students achieve anything near
a perfect score on the GMAT.Even if you don’t score as high as you want to, you undoubtedly have
other strengths in your admissions prole, such as work experience, leadership ability, good col-
lege grades, motivation, and people skills. You may want to contact the admissions oces of the
schools you’re interested in to see how much they emphasize the GMAT.That said, the GMAT is
a very important factor in admissions, and because you’re required to take the test anyway, you
should do everything you can to perform your best!
Timing It Perfectly: When to Take
the GMAT (And What to Bring)
Which MBA programs to apply to isn’t the only decision you have to make. After you’ve gured out
where you want to go, you have to make plans for the GMAT.You need to determine the best time
to take the test and what to bring with you when you do. The following sections can help you out.
When to register for and take the GMAT
When is the best time to take the GMAT? With the computerized testing procedures, this question
has become more interesting than it was in the days of paper-based tests. When the exam was a
paper-and-pencil format with a test booklet and an answer sheet full of bubbles, you had a lim-
ited choice of possible test dates— about one every two months. Now you’ve got much more
exibility when choosing the date and time for taking the test. You can pick just about any time
to sit down and click answer choices with your mouse.
Registering when you’re ready
The rst step in the GMAT registration process is scheduling an appointment, but don’t put o
making this appointment the way you’d put o calling the dentist (even though you’d probably
like to avoid both!). Depending on the time of year, appointment times can go quickly. Usually,
you have to wait at least a month for an open time. To determine what’s available, you can go to
the ocial GMAT website at
www.mba.com. From there, you can choose a testing location and nd
out what dates and times are available at that location. When you nd a date and time you like,
you can register online, over the phone, or by mail or fax.
The best time to take the GMAT is after you’ve had about four to six weeks of quality study time
and during a period when you don’t have a lot of other things going on to distract you. Of course,
if your MBA program application is due in four weeks, put this book down and schedule an appoint-
ment right away! Be sure to come right back, though. You need to start studying— and now! If you
have more exibility, you should still plan to take the GMAT as soon as you think you’ve studied
suciently. All the following circumstances warrant taking the GMAT as soon as you can:
»
You want to start your MBA program right away. If you’re condent that you’d like to begin
business school within the next few semesters, you should consider taking the GMAT in the
CHAPTER 1 Getting the Lowdown onthe GMAT 9
near future. After you know your score, you’ll be better able to narrow down the business
schools you want to apply to. Then you can focus on the other parts of your application, and
you won’t have to worry about having an application due in four weeks and no GMAT score.
»
You’re considering attending business school. Maybe you don’t know whether you want to
pursue an MBA.Even so, now’s a good time to take the GMAT.Your GMAT score may help you
decide that you have the skills to succeed academically in graduate business school. You may
think that you don’t have what it takes, but your performance on the GMAT may surprise you!
If you do decide to apply to an MBA program, you’ll already have one key component of the
application under wraps.
»
You’re about to earn (or have just earned) your bachelor’s degree. If you’re nearing
graduation or have just graduated from college and you think you may want to get an MBA, it’s
better to take the GMAT now than wait until later. You’re used to studying. You’re used to tests.
And math and grammar concepts are probably as fresh on your mind as they’ll ever be.
You don’t have to start an MBA program right away. Your GMAT scores are generally valid for
up to ve years, so you can take the test now and take advantage of your current skills as a
student to get you into a great graduate program later.
Giving yourself about four to six weeks to study provides you with enough time to master the
GMAT concepts but not so much time that you forget what you’ve studied by the time you sit for
the test.
Scheduling for success
Whenever you register, you want to consider your own schedule when picking a test date and
time. Take advantage of the exibility allowed by the computer format. The GMAT is no longer
just an 8 a.m. Saturday morning option. You can take the test every day of the week except Sun-
day, and, depending on the test center, you may be able to start at a variety of times. Many centers
oer 8 a.m. testing times, but some have other options, even 6:30 at night— great for those night
owls who consider 8 a.m. a good bedtime rather than a good exam time. You have a little bit of
control over making the test t into your life instead of having to make your life t the test!
If you’re not a morning person, don’t schedule an early test if you can help it. If you’re better able
to handle a nonstop, two-and-a-half-hour barrage of questions— not to mention the analytical
essay— after the sun hits its highest point in the sky, schedule your test for the afternoon or
evening. By choosing the time that works for you, you’ll be able to comfortably approach the test
instead of worrying whether you set your alarm. We’re guessing that you have enough to worry
about in life as it is without the added stress of an inconvenient test time.
Check the GMAT website for the available testing times at the test centers near you. Then study
for the test at the dierent available times of the day to see when you’re at your best. Schedule
your test session for that time. Even if you have to take a few hours away from work or classes,
being able to take the test at a time that’s best for you is worth it. And you may end up picking a
test center based on its available times rather than its proximity to you.
While you’re thinking about the time that’s best for the test, you should think about days of the
week as well. For some people, Saturday may be a good day for a test. For others, the weekend is
the wrong time for that type of concentrated academic activity. If you’re used to taking the week-
ends o, scheduling the test during the week may make more sense for you.
Choosing the time and day to take the GMAT is primarily up to you. Be honest with yourself about
your habits, preferences, and schedule, and pick a time and day when you’ll excel.
10 PART 1 Getting Started with the GMAT
Things to take to the GMAT (and things
to leave at home)
The most important thing you can bring to the GMAT is a positive attitude and a willingness to
succeed. However, if you forget your admission voucher or your photo ID, you won’t get the
chance to apply those qualities! In addition to the voucher and ID, you may bring a list of ve
schools where you’d like to have your scores sent. You can send your scores to up to ve schools
for free if you select those schools when entering your pretest information at the test site. (You
can skip this step at the testing center if you provide your school information when you register
online.) You can, of course, list fewer than ve schools, but if you decide to send your scores to
additional schools later, you’ll have to pay. If you can come up with ve schools you’d like to
apply to, you may as well send your scores for free.
Because you can take two optional eight-minute breaks, we recommend you bring along a quick
snack, like a granola bar, and perhaps a bottle of water. You can’t take food or drink with you to
the testing area, but you’re given a little locker that you can access during a break.
That’s really all you need to bring. You can’t use a calculator, and the test center provides a book-
let of ve noteboards and a special black pen (but no eraser), which you’re required to use instead
of pencil and paper. You can ask for another booklet if you ll yours up.
Forming First Impressions:
The Format of the GMAT
The GMAT is a standardized test, and by now in your academic career, you’re probably familiar
with what that means: lots of questions to answer in a short period of time, no way to cram for or
memorize answers, and very little chance of scoring 100 percent. The skills tested on the GMAT
are those that leading business schools have decided are important for MBA students: analytical
writing, integrated reasoning, quantitative reasoning, and verbal reasoning.
The GMAT allows you to choose the order in which you take the four sections:
»
The original order of analytical writing assessment, integrated reasoning, quantitative,
and verbal
»
Quantitative, verbal, analytical writing assessment, and integrated reasoning
»
Verbal, quantitative, analytical writing assessment, and integrated reasoning
Pick the order that’s most comfortable for you. If you’re unsure, we suggest leaving the less
important writing and integrated reasoning sections for the end when you’re more fatigued.
Whether you take the quantitative or verbal rst depends on which section is easier for you. You
may want to lead with your strength or get the section you like least out of the way in the
beginning.
Getting familiar with what the GMAT tests
Standardized tests are supposed to test your academic potential, not your knowledge of specic
subjects. The GMAT focuses on the areas that admissions committees have found to be relevant
to MBA programs. The sections that follow are an introduction to the four GMAT sections. We
devote the majority of the rest of this book to telling you exactly how to approach each one.
CHAPTER 1 Getting the Lowdown onthe GMAT 11
Demonstrating your writing ability
You type an original analytical writing sample during the GMAT.The test gives you 30 minutes to
compose and type an essay that analyzes an argument. You’re expected to write this essay in
standard written English. Although you won’t know exactly the nature of the argument you’ll get
on test day, examining previous essay prompts gives you adequate preparation for the type of
task you’re bound to see.
The readers of your GMAT essay score you based on the overall quality of your ideas and your
ability to organize, develop, express, and support those ideas.
Integrating your reasoning skills
The second GMAT section is a 30-minute integrated-reasoning test that examines your ability to
read and evaluate charts, graphs, and other forms of presenting data. You’ll examine a variety of
data representation and answer 12 questions based on the information.
The GMAT categorizes the four basic question types in this section as graphics interpretation,
two-part analysis, table analysis, and multi-source reasoning. Graphics interpretation and table
analysis questions are self-explanatory: You interpret graphs and analyze tables— simple enough,
right? The two-part analysis questions present a problem and related data provided in two col-
umns. You choose a piece of information from each column to solve the problem. Multi-source
reasoning questions provide you with a bunch of information from which you have to decide what
piece or pieces of data actually give you what you need to know to solve the problem.
Quizzing your quantitative skills
The quantitative section is pretty similar to most standardized math sections except that it pres-
ents you with a dierent question format and tests your knowledge of statistics and probability.
In the 37-question section, the GMAT tests your knowledge of arithmetic, algebra, geometry, and
data interpretation with standard problem-solving questions. You’ll have to solve problems and
choose the correct answer from ve possible choices.
Additionally, GMAT data suciency questions present you with two statements and ask you to
decide whether the problem can be solved by using the information provided by the rst state-
ment only, the second statement only, both statements, or neither statement. We show you
exactly how to tackle these unusual math questions in Chapter15.
Validating your verbal skills
The GMAT verbal section consists of 41 questions of three general types: the ubiquitous reading-
comprehension problems, sentence-correction questions, and critical-reasoning questions.
Reading comprehension requires you to answer questions about written passages on a number of
dierent subjects. Sentence-correction questions test your ability to spot and correct writing
errors. Critical-reasoning questions require you to analyze logical arguments and understand
how to strengthen or weaken those arguments.
Understanding the computerized format
The quantitative-reasoning and verbal-reasoning sections on the computerized GMAT can be
taken only in computer-adaptive test (CAT) format. The CAT adapts to your ability level by present-
ing you with questions of various diculty, depending on how you answer previous questions. If
you’re answering many questions correctly, the computer gives you harder questions as it seeks
to nd the limits of your impressive intellect. If you’re having a tough day and many of your
12 PART 1 Getting Started with the GMAT
answers are wrong, the computer will present you with easier questions as it seeks to nd the
correct level of diculty for you.
With the CAT format, your score isn’t based solely on how many questions you get right and
wrong but rather on the average diculty of the questions you answer correctly. Theoretically,
you could miss several questions and still get a very high score, so long as the questions you
missed were among the most dicult available in the bank of questions. At the end of each sec-
tion, the computer scores you based on your level of ability.
Answering in an orderly fashion
With the CAT format, the question order in the verbal and quantitative sections is dierent from
the order on paper exams that have a test booklet and answer sheet. On the CAT, the rst ten
questions of the test are preselected for you, and the order of subsequent questions depends on
how well you’ve answered the previous questions. So if you do well on the rst ten questions,
Question 11 will reect your success by being more challenging. If you do poorly on the initial
questions, you’ll get an easier Question 11. The program continues to take all previous questions
into account as it feeds you question after question.
Perhaps the most important dierence of the CAT format is that because each question is based
on your answers to previous questions, you can’t go back to any question. You must answer each
question as it comes. After you conrm your answer, it’s nal. If you realize three questions later
that you made a mistake, try not to worry about it. After all, your score is based on not only your
number of right and wrong answers but also the diculty of the questions.
We’re guessing you’ve gured out that the analytical writing assessment isn’t in CAT format
because it’s not a multiple-choice test. But you may not know that the integrated-reasoning sec-
tion also isn’t a CAT section. You receive questions in a preordained order and that order doesn’t
change based on your answer selections. Like the CAT sections, though, after you’ve submitted an
answer to a question, you can’t change your answer.
Observing time limits
Both the verbal and quantitative sections have a 75-minute time limit. Because the quantitative
section has 37 questions, you have about two minutes to master each question. The verbal section
has 41 questions, so you have a little less time to ponder those, about a minute and three-quarters
per question. The integrated-reasoning section is shorter; you have 30 minutes to answer 12
questions, or about two and a half minutes per question. You don’t have unlimited time in the
analytical writing section, either; you have to write the essay within 30 minutes.
These time limits have important implications for your test strategy on the quantitative and ver-
bal sections. As we discuss later in this chapter, your GMAT score for these two sections depends
on the number of questions you’re able to answer. If you run out of time and leave questions
unanswered at the end of a section, you’ll essentially reduce your score by the number of ques-
tions you don’t answer. In Chapter2, we present you with an ecient, workable strategy for
managing your time and maximizing your score.
Honing your computer skills for the GMAT
Technically challenged, take heart! You need to have only minimal computer skills to take the
computerized GMAT.In fact, the skills you need for the test are far less than those you’ll need
while pursuing an MBA! Because you have to type your essays, you need basic word-processing
skills. For the multiple-choice sections, you need to know how to select answers by using either
the mouse or the keyboard.
CHAPTER 1 Getting the Lowdown onthe GMAT 13
Knowing Where You Stand:
Scoring Considerations
Okay, you know the GMAT’s format and how many questions it has and so on. But what about
what’s really important to you, the crucial nal score? Probably very few people take standardized
tests for fun, so we give you the lowdown on scoring in the following sections.
How the GMAT testers gure your score
Because the GMAT is a computer-adaptive test, your verbal and quantitative scores aren’t based
just on the number of questions you get right. The scores you earn are based on three factors:
»
The diculty of the questions you answer: The questions become more dicult as you
continue to answer correctly, so getting tough questions means you’re doing well on the test.
»
The number of questions you answer: If you don’t get to all the questions in the verbal and
quantitative sections, your score is reduced by the proportion of questions you didn’t answer.
So if you fail to answer 5 of the 37 quantitative questions, for example, your raw score would
be reduced by 13 percent: after converting the raw score to the scaled measure, this loss may
decrease your percentile rank from the 90th percentile to the 75th percentile.
»
The number of questions you answer correctly: In addition to scoring based on how
dicult the questions are, the GMAT score also reects your ability to answer those questions
correctly.
GMAT essay readers determine your analytical writing assessment (AWA) score. College and uni-
versity faculty members from dierent disciplines read your response to the essay prompt. How-
ever, one of your readers may be an automated essay-scoring machine programmed to evaluate
the important elements of your essay. Two independent readers separately score your writing
assignment on a scale from 0 to 6, with 6 being the top score. Your nal score is the average of
the scores from each of the readers.
If the two readers assigned to your writing task give you scores that dier by more than one
point, a third reader is assigned to adjudicate. For example, if one reader gives you a 6 and the
other gives you a 4, a third reader will also review your essay.
Your integrated-reasoning score ranges in whole numbers from 1 to 8, with 8 being the highest.
Scores of 1 and 2 are rare and unusually low, and very few GMAT-takers score as high as 7 or 8.
Generally, if you receive a score of 4, 5, or 6, you’ve done a respectable job answering the
integrated-reasoning questions.
How the GMAT testers report your score
Your nal GMAT score consists of separate verbal-reasoning, quantitative-reasoning,
integrated-reasoning, and analytical writing assessment scores and a combined verbal and quan-
titative score. When you’re nished with the test— or when your time is up— the computer
immediately calculates your verbal, quantitative, and integrated-reasoning scores and provides
them to you in an unocial score report. You’ll have a separate scaled score from 0 to 60 for the
verbal and quantitative sections. The two scores are added together and converted to a scaled
score ranging between 200 and 800. The mean total score falls slightly above 500.
14 PART 1 Getting Started with the GMAT
You won’t see your analytical writing assessment scores immediately after the test. These scores
are included in the ocial score report that’s either mailed to you or made available online about
20 days after you take the exam. So although you’ll be able to view your verbal, quantitative,
integrated-reasoning, and total scores immediately after the test, you’ll need to wait three weeks
to see how well you did on the AWA section.
When you do get your ocial score, the AWA score appears as a number between 0 and 6. This
number is a scaled score that’s the average of the scores for all the readings of your response. The
nal score is rounded to the nearest half point, so a 4.8 average is reported as 5. The integrated-
reasoning scaled score ranges between 1 and 8. Neither the AWA nor the integrated-reasoning
score aect your total GMAT score in any way. Both scores are reported separately, and each MBA
program decides how to use them in their admissions decisions.
Ocial scores, including the verbal-reasoning, quantitative-reasoning, total, integrated-
reasoning, and AWA scores, are sent to the schools that you’ve requested receive them. The score
reports they receive include all your scores, as well as a table showing the percentage of test-
takers who scored below you. (For example, if your total score is 670, then about 89 percent of
test-takers have a score lower than yours.) You don’t have to pay for the ve schools you select
before you take the test to receive your scores, and for a fee, you can request your scores be sent
to any other school at any time up to ve years after the test.
Why you should (almost) never
cancel your GMAT score
Immediately after you conclude the GMAT and before the computer displays your scores, you’re
given the option of canceling your scores. You may see this as a blessing if you’ve had a rough day
at the computer. You may jump at the chance to get rid of all evidence of your verbal, quantitative,
and writing struggles.
Canceling your scores is almost always a bad idea for several reasons:
»
People routinely overestimate or underestimate their performance on standardized
tests. The GMAT isn’t a test on state capitals or chemical symbols, so knowing how well you
did isn’t always easy. As long as you answer most of the questions and are able to focus
reasonably well during the test, you’ll probably earn scores that aren’t too dierent from the
average scores you’d get if you took the test repeatedly. People who retake the GMAT and
other standardized tests rarely see their scores change signicantly unless they’re initially
unprepared to take the exam and later attempt it with signicant preparation. You’re reading
this book, so you don’t fall into that category of test-taker.
»
You may not have time to reschedule. It may take a while to reschedule the test. If your
applications are due right away, you could miss an application deadline because you don’t
have GMAT scores to submit.
»
You’ll never know how you did. If you cancel your scores, you’ll never know how you did or
what areas you need to work on to improve your score if you decide to retake the test later.
A few circumstances exist in which you should consider canceling your scores. These situations
aren’t based on your estimation of how you did, which may be inaccurate, but on extenuating
factors:
»
You’re pretty darn ill during the test. Waking up on test day with a fever of 101 degrees or
getting sick during the test may warrant canceling a GMAT score.
CHAPTER 1 Getting the Lowdown onthe GMAT 15
»
You were unable to concentrate during the test. Unusual personal diculties, like a death
in the family or the demise of a close relationship, could distract you to the point where you
freeze up in the middle of the exam.
»
You left many questions unanswered. If you forget the time-management techniques we
discuss in Chapter2 and you leave quite a few questions unanswered in the verbal and
quantitative sections, you may consider canceling your scores.
Repeating the Process: Retaking the GMAT
Because most programs consider only your top scores, retaking the GMAT may be in your best
interest if you aren’t happy with your rst score. The GMAT administrators let you take the test
quite a few times if you want (that’s pretty big of them, considering you have to pay for it every
time). If you do retake the GMAT, make sure you take the process and test seriously. You should
show score improvement. A college will be much more impressed with a rising score than a fall-
ing one.
Many colleges may be turned o if they see that you’ve taken the GMAT more than two or three
times. The key is to prepare to do your best on the rst (or second) try.
Ocial GMAT reports contain scores for every time you take the test. So if you take the GMAT
twice, both scores appear on your report. It’s up to the business program to decide how to use
those scores. Some may take the higher score and some may take the average. Keep in mind that
your new scores won’t automatically be sent to the recipients of previous scores, so you’ll need to
reselect those programs when you retake the test.
CHAPTER2 Maximizing Your Score onthe GMAT 17
IN THIS CHAPTER
» Checking out guessing strategies
» Managing your time like a pro
» Knowing how to recognize a wrong
answer
» Avoiding worthless activities that
minimize your score
» Quieting your nerves with tried-
and-true relaxation techniques
Maximizing Your Score
onthe GMAT
Y
ou enter the test center and stare down the computer. For the next three and a half hours,
that machine is your adversary. The GMAT loaded on it is your nemesis. All you have to aid
you in this showdown is a booklet of noteboards and your intellect. The questions come
quickly, and your reward for answering a question correctly is another, usually more dicult
question! Why did you give up your precious free time for this torture?
By the time you actually take the GMAT, you’ll have already given up hours and hours of your free
time studying for the test, researching business schools, and planning for the future. Those three
and a half hours alone with a computer represent a rite of passage that you must complete to
accomplish the goals you’ve set for yourself. And because the test is a necessary evil, you may as
well get the highest score you’re capable of achieving!
This chapter contains the techniques you need to apply to pull together a winning strategy for the
GMAT.You already have the brains, and the test center provides the materials. In this chapter, we
share with you the other tools you need to maximize your score.
Discovering Strategies for Successful Guessing
You may be surprised that we start this chapter by discussing guessing strategies. Your ideal
GMAT test-day scenario probably involves knowing the answers to most of the questions right
away rather than randomly guessing! The reality is that almost no one is absolutely sure of every
answer to every question on the GMAT.Think back; did you have to guess at any questions on the
ACT or SAT? We bet you did! We provide a few guessing strategies in the following sections to
improve your chances of answering more questions correctly, even if you otherwise have no clue
of the correct answer.
Chapter2
18 PART 1 Getting Started with the GMAT
Forcing yourself to guess so you can move on
Remember that standardized tests aren’t like tests in your undergraduate college courses. If you
studied hard in college, you may not have had to do much guessing on your midterms and nals.
On the GMAT, however, the computer won’t allow you to skip questions. So if you stumble upon
some really dicult questions that you’re not sure how to answer, you have to guess and move
on. Don’t fall into thinking that you must know the correct answer for each question to do well
on the GMAT.The GMAT is designed to test the potential of a wide range of future MBA students,
so some of the questions have to be ridiculously dicult to challenge that one-in-a-million Ein-
stein who takes the GMAT.Almost everyone incorrectly answers a few questions in each section,
and almost everyone has to guess on those really dicult questions. Don’t worry if you have to
guess; just gure out how to guess eectively!
With the computer-adaptive test (CAT) format, developing a strategy for successful guessing in
the quantitative-reasoning and verbal-reasoning sections is actually more important than ever.
In these sections, as you answer questions correctly, the level of diculty continues to increase.
Although the integrated-reasoning section isn’t in the CAT format, you can’t skip the questions
in this section, either, so be sure to apply the guessing strategies we discuss in this chapter to that
section as well. Even if you do really, really well on the test, you’ll probably nd yourself guessing
on some questions. On the GMAT, almost everyone guesses!
Understanding the importance of completing
each section
To get the optimum score for the questions you answer correctly, you must respond to all the
questions in each section. If you don’t have time to complete the questions at the end of each sec-
tion, your score is reduced in proportion to the number of questions you didn’t answer. Therefore,
it’s important to move at a pace that allows you to get to all the questions.
One of the ways you can get into real trouble with the CAT format is by spending too much time
early on trying to correctly answer questions that are more dicult. If you’re reluctant to guess
and, therefore, spend more than a minute or two on several dicult questions, you may not have
time to answer the relatively easy questions at the end.
Answer every question in each section! If you notice that you have only three or four minutes
remaining in a section and more than ve questions left, spend the remaining minutes marking
an answer for every question, even if you don’t have time to read them. You always have a
20 percent chance of randomly guessing the correct answer to a verbal-reasoning or quantitative-
reasoning question, which is better than not answering the question at all. If you have to guess
randomly at the end of the section, mark the same bubble for each answer. For example, you may
choose to mark the second bubble from the bottom. Chances are that at least one in ve questions
will have a correct answer placed second to the end. Marking the same bubble also saves time
because you don’t have to choose which answer to mark for each question; you already have your
guessing strategy in mind, so you don’t have to think about it.
Even the GMAT folks warn of a severe penalty for not completing the test. They claim that if you
fail to answer just 5 questions out of the 41in the verbal section, your score could go from the 91st
percentile to the 77th percentile. That’s the kind of score reduction that could make a huge dif-
ference to your admissions chances!
CHAPTER 2 Maximizing Your Score onthe GMAT 19
Winning the Race against the Clock
Random guessing as the clock runs out serves you better than leaving the remaining questions in
a section unanswered, but it’s not a good way to approach the test in general. Instead, adopt a
strategy of good time management that combines proper pacing, an active approach to answering
questions, and appropriate guessing. We discuss all these time-management strategies in the
following sections.
Giving each question equal treatment
You may have heard that you should spend a lot of time on the rst ten questions because your
performance on them determines your ultimate score. Although your performance on the rst ten
questions does give the computer an initial estimate of your ability, in the end, these rst ques-
tions don’t carry greater signicance than any other questions. You’ll still encounter all the ques-
tions in the section eventually, so you really have no reason to spend an unreasonable length of
time on the rst ten.
If you spend too much time on the rst ten questions and answer them all correctly, you’ll have
a limited amount of time in which to answer the 27 remaining quantitative or 31 remaining verbal
questions. The computer program would give you a high estimated score after those rst ten
questions, but that initial estimate would then most likely fall steadily throughout the session as
you would hurry through questions and guess at those you didn’t have time to answer at the end.
The worst outcome of all would be if you were unable to nish the section and had your score
reduced in proportion to the questions you couldn’t answer. You can’t cheat the system by focus-
ing on the rst few questions. If you could, the very intelligent, highly paid test designers would
nd a way to adjust the format to thwart you.
Making time for the last ten questions
A much better approach than lavishing time on the rst ten questions is allowing ample time to
answer the last ten questions in both the verbal and quantitative sections. Because the best way
to score well is to give adequate time to each question, guess when necessary, and complete the
entire test, you shouldn’t spend a disproportionate amount of time answering the early
questions.
Here are the steps to follow for this approach:
1. Work through the rst 55 minutes of the quantitative and verbal sections at a good pace.
Plan to spend around two minutes per quantitative question and a little more than a minute
and a half per verbal question.
2. Don’t spend more than three minutes on any question during the rst 75 percent of the
quantitative and verbal sections.
3. When you have ten questions remaining in the section, check the time remaining and
adjust your pace accordingly.
Ten questions remain when you hit Question 27 of the quantitative section or Question 31 of
the verbal section.
For example, if you’ve answered the rst 27 quantitative questions in only 50 minutes, you have
a total of 25 minutes to work on the last ten questions. That means you can spend about two
and a half minutes on each of the last ten questions. That extra 30 seconds per question may
be what you need to answer a high percentage of those nal ten questions correctly. Avoid
random guesses on the last unanswered questions of either section.
20 PART 1 Getting Started with the GMAT
We’re not suggesting that you rush through the rst 55 minutes of each section so you can spend
lots of time on the last ten questions. Instead, you should stick to a pace that allows you to give
equal time to all the questions in a section. You can’t spend ve or six minutes on a single ques-
tion without sacricing your performance on the rest of the test, so stick to your pace.
If you happen to have additional time when you get to the last ten questions, by all means, use it.
There’s a severe penalty for not nishing a section but no prize for getting done early.
When you work steadily and carefully through the rst 75 percent of each section, you’re rewarded
with a score that stabilizes toward the higher end of the percentile and that may rise to an even
higher level at the end of the section as you spend any extra time you have getting the last ques-
tions right. Talk about ending on a high note!
Keeping track of your pace
You may think that keeping an even pace throughout the test means a lot of clock watching, but
this isn’t the case if you go into the test site with a plan. You can conceal the clock on the com-
puter to keep from becoming obsessed with time, but you should periodically reveal the clock to
check your progress. For example, you may plan to check your computer clock after every eight
questions you answer. This means revealing the feature about ve or six times during the verbal
and quantitative sections. You’ll spend a second or two clicking on the clock and glancing at it,
but knowing that you’re on pace will be worth it.
If you time yourself during practice tests you take at home, you’ll probably begin to know intui-
tively whether you’re falling behind. During the actual exam, you may not have to look at your
clock as frequently. However, if you suspect that you’re using too much time on a question (more
than three minutes), you should check the clock. If you’ve spent more than three minutes, mark
your best guess from the choices you haven’t already eliminated and move on.
Getting Rid of Wrong Answers
We’ve stressed that the key to success is to move through the test steadily so you can answer
every question and maximize your score. Keeping this steady pace will probably require you to
make some intelligent guesses, and intelligent guesses hang on your ability to eliminate incorrect
answers.
Eliminating answer choices is crucial on the verbal and quantitative sections of the GMAT.Most
questions come with ve answer choices, and usually one or two of the options are obviously
wrong (especially in the verbal section). As soon as you know an answer choice is wrong, elimi-
nate it. After you’ve eliminated that answer, don’t waste time reading it again. By quickly getting
rid of choices that you know are wrong, you’ll be well on your way to nding the right answer! In
the following sections, we show you a few elimination strategies that help you cross o wrong
answers so you can narrow in on the right ones.
Keeping track of eliminated answer choices
for the computer test format
You may be thinking that eliminating answer choices on a computerized test won’t work. In
truth, doing so is more dicult than on a paper test where you can actually cross o the entire
CHAPTER 2 Maximizing Your Score onthe GMAT 21
answer in your test booklet. However, you can achieve the same results on the computerized test
with a little practice. You must train your mind to look only at the remaining choices and not read
every word that your eyes fall upon. You can’t aord to waste time rereading a choice after you’ve
eliminated it. That’s why you need a system.
You can use the booklet of noteboards you’re given at the test site to help you eliminate answers.
The test administrators will replenish your noteboard supply if you ll them up, so don’t be afraid
to write all over your noteboards.
Here are some simple steps to help you keep track of which answers you’ve eliminated:
1. At the beginning of the section (especially the verbal one, where eliminating answer
choices is easier), quickly write down “A, B, C, D, and E” (or 1, 2, 3, 4, and 5 if you prefer
numbers) in a vertical row on your noteboard.
A stands for the rst answer choice, B for the second, C for the third, and so on, even though
these letters don’t appear on your computer screen.
2. When you eliminate an answer choice, cross out the corresponding letter on your
noteboard.
For example, if you’re sure that the second and fth answers are wrong, mark a line through B
and E on your noteboard.
3. If you look at your noteboard and see only one remaining answer letter, you’ve zeroed in
on the right answer.
You don’t need to reread the answer choices to remember which one was correct. It’s listed
right there on the noteboard.
4. If you can’t narrow down your choices to just one answer, eliminating three incorrect
choices gives you a good chance of guessing correctly between the two options that
remain.
5. Quickly rewrite the ve letters (or numbers) for the next question and repeat the process.
Practice this technique when you’re taking your practice tests. The hard part isn’t crossing out
the letters on your noteboard; it’s training your eyes to skip the wrong answers on the computer
screen. Your brain will want to read through each choice every time you look at the answers. With
the paper test booklet, you’d simply cross out the entire answer choice and then skip that choice
every time you came to it. With the computerized test, you have to mentally cross out wrong
answers. Developing this skill takes time. Mastering it is especially important for the verbal sec-
tion, which has some long answer choices.
Recognizing wrong answers
So maybe you’ve mastered the art of the noteboard answer-elimination system, but you may be
wondering how you know which answers to eliminate. Most of the verbal questions are best
answered by process of elimination because answers aren’t as clearly right or wrong as they may
be for the math questions. For many math questions, the correct answer is obvious after you’ve
performed the necessary calculations, but you may be able to answer some math questions with-
out performing complex calculations if you look through the answers rst and eliminate choices
that don’t make sense. So by using your common sense and analyzing all the information you
have to work with (we show you how to do both in the next sections), you can reach a correct
answer without knowing everything there is to know about a question.
22 PART 1 Getting Started with the GMAT
Using common sense
Reading carefully reveals a surprising number of answer choices that are obviously wrong. In the
quantitative- and integrated-reasoning sections, you may know before you even do a math calcu-
lation that one or two of the answers are simply illogical. In the verbal section, critical-reasoning
questions may have answer choices that don’t deal with the topic of the argument, or some
sentence-correction answer choices may obviously display poor grammar or faulty sentence
construction. You can immediately eliminate these eyesores from contention. If an answer is
outside the realm of possibility, you don’t ever have to read through it again. For example, consider
the following sample critical-reasoning question.
Most New Year’s resolutions are quickly forgotten. Americans commonly make resolutions to
exercise, lose weight, quit smoking, or spend less money. In January, many people take some
action, such as joining a gym, but by February, they are back to their old habits again.
Which of the following, if true, most strengthens the preceding argument?
(A) Some Americans do not make New Year’s resolutions.
(B) Americans who do not keep their resolutions feel guilty the rest of the year.
(C) Attempts to quit smoking begun at times other than the rst of the year are less success-
ful than those begun in January.
(D) Increased sports programming in January motivates people to exercise more.
(E) People who are serious about lifestyle changes usually make those changes immediately
and do not wait for New Year’s Day.
Chapter6 gives you a whole slew of tips on how to answer critical-reasoning questions, but with-
out even looking closely at this one, you can eliminate at least two choices immediately. The
argument states that people usually don’t live up to New Year’s resolutions and the question asks
you to strengthen that argument. Two of the answer choices have nothing to do with keeping
resolutions, so you can discard them right away: Choice (A) provides irrelevant information—
the argument is about people who make resolutions, not those who don’t — and Choice (D)
brings up a completely dierent topic (sports programming) and doesn’t mention resolutions.
Without even taxing your brain, you’ve gone from ve choices down to three. Psychologically,
dealing with three answer choices is much easier than dealing with all ve. Plus, if you were short
on time and had to quickly guess at this question, narrowing your choices to only three gives you
a much better chance of answering it correctly.
Relying on what you know
Before you attempt to solve a quantitative problem or begin to answer a sentence-correction
question, you can use what you know to eliminate answer choices.
For example, if a quantitative question asks for a solution that’s an absolute value, you can imme-
diately eliminate any negative answer choices, because absolute value is always positive. (For
more about absolute value, see Chapter12.) Even if you don’t remember how to solve the problem,
you can at least narrow down the choices and increase your chances of guessing correctly. If you
eliminate one or two choices and if you have the time, you may be able to plug the remaining
answer choices back into the problem and nd the correct answer that way. So if you approach
questions with a stash of knowledge, you can correctly answer more questions than you realize.
Letting the question guide you
If you’ve ever watched a popular TV game show, you know that the clue to the answer can some-
times be found in the question. Although the answers to most GMAT questions aren’t as obvious
CHAPTER 2 Maximizing Your Score onthe GMAT 23
as the answer to “in 1959, the U.S. said ‘aloha’ to this 50th state,” you can still use clues from the
GMAT questions themselves to answer them.
In the earlier critical-reasoning example on New Year’s resolutions, you were left with three
answer choices. Paying attention to the wording of the question can help you eliminate two more.
The question asks you to strengthen the argument that Americans quickly forget their New Year’s
resolutions. Choice (B) seriously weakens the argument by indicating that instead of forgetting
their resolutions, Americans are haunted by failed resolutions for the rest of the year. Likewise,
Choice (C) indicates that a resolution to quit smoking at the beginning of the New Year may be
more successful than the same resolution at other times. Because these answers weaken the
argument rather than strengthen it as the question asks, you can eliminate them, also. By process
of elimination, you know that Choice (E) is the correct answer to the question, and you haven’t
yet seriously considered the logic of the argument!
Quickly recognizing and eliminating wrong answers after only a few seconds puts you on the path
to choosing a right answer. This strategy works in the quantitative section as well. Consider this
problem-solving question example.
If
1
2
of the air in a balloon is removed every 10 seconds, what fraction of the air has been
removed from the balloon after 30 seconds?
(A)
1
8
(B)
1
6
(C)
1
4
(D)
5
6
(E)
7
8
You can immediately eliminate any choices with fractions smaller than one-half because the
problem tells you that half the air departs within the rst ten seconds. So you can discard Choices
(A), (B), and (C). Without performing any calculations at all, you’ve narrowed down your choices
to just two!
Another benet of eliminating obviously wrong answer choices is that you save yourself from
inadvertently making costly errors. The GMAT oers Choices (A), (B), and (C) to trap unsuspect-
ing test-takers. If you mistakenly tried to solve the problem by multiplying
1
2
1
2
1
2
, you’d come
up with
1
8
. But if you’ve already eliminated that answer, you know you’ve done something wrong.
By immediately getting rid of the answer choices that can’t be right, you may avoid choosing a
clever distracter. By the way,
1
8
is the amount of air remaining in the balloon after 30 seconds.
After the rst 10 seconds,
1
2
of the air remains. After 20 seconds,
1
2
of that, or
1
4
, remains. After
30 seconds, the balloon still has
1
2
of
1
4
of its air, which is
1
8
.
So the amount of air removed in 30 seconds is Choice (E),
7
8
, because
1
1
8
7
8
.
Dealing with questions that contain Roman numerals
The GMAT presents a special type of question that pops up from time to time. This question gives
you three statements marked with the Roman numerals I, II, and III and asks you to evaluate their
validity. You’ll nd these questions in the quantitative- and verbal-reasoning sections. You’re
supposed to select the answer choice that presents the correct list of either valid or invalid state-
ments, depending on what the question is looking for.
24 PART 1 Getting Started with the GMAT
To approach questions that contain statements with Roman numerals, follow these steps:
1. Evaluate the validity of the rst statement or the statement that seems easiest
to evaluate.
2. If the rst statement meets the qualications stated by the question, eliminate any
answer choices that don’t contain Roman numeral I; if it doesn’t, eliminate any choices
that have Roman numeral I in them.
3. Examine the remaining answer choices to see which of the two remaining statements is
best to evaluate next.
4. Evaluate another statement and eliminate answer choices based on your ndings.
You may nd that you don’t have to spend time evaluating the third statement.
Here’s an example to show how the approach works.
If x and y are dierent integers, each greater than 1, which of the following must be true?
I.
xy4
II.
xy0
III.
xy
results in an integer
(A) II only
(B) I and II
(C) I, II, and III
(D) I and III
(E) III only
Consider the statements one by one. Start with Statement I and determine whether the expres-
sion
xy4
is true. Because x and y are greater than 1, they must be positive. The smaller of the
two integers must be at least 2, and the other number can’t be less than 3. So because
2 35
,
xy5
, so their sum has to be greater than 4.
Don’t read Statement II yet. Instead, run through the answer choices and eliminate any that don’t
include Statement I.Choice (A) and Choice (E) don’t include Statement I, so cross out those letters
on your noteboard. The remaining choices don’t give you any indication which statement is best
to evaluate next, so proceed with your evaluation of Statement II, which states that
xy0
. This
statement can’t be correct because x and y have dierent values. The only way one number sub-
tracted from another number can result in 0 is when the two numbers are the same. The dier-
ence of two dierent integers will always be at least 1.
Because Statement II isn’t correct, eliminate choices that include Statement II.You can cross out
Choice (B) and Choice (C), which leaves you with Choice (D). By process of elimination, Choice (D)
has to be right. You don’t even need to read Statement III, because you know the correct answer.
Not all Roman numeral questions are so helpful, but many are, and in those cases, the strategy is
a real timesaver!
CHAPTER 2 Maximizing Your Score onthe GMAT 25
Playing It Smart: A Few Things You Shouldn’t
Do When Taking the Test
Most of this chapter focuses on what you should do to maximize your score on the GMAT.How-
ever, there are also a few things you shouldn’t do, which we discuss in the following sections.
Avoid these mistakes, and you’ll have an advantage over many other test-takers!
Don’t lose your focus
You may be used to the fast-paced world of business or the cooperative world of group presenta-
tions that is popular in many business classes. Don’t be surprised if 180 minutes of multiple-
choice questions peppered with 30 minutes of essay writing gets a little boring. We know the
prospect is shocking!
Don’t allow yourself to lose focus. Keep your brain on a tight leash, and don’t let your mind wan-
der. This test is too important. Just remind yourself how important these three and a half hours
are to your future. Teach yourself to concentrate and rely on the relaxation tips we give you later
in this chapter to avoid incessant mind wandering. You’ll need those powers of concentration in
that MBA program you’ll soon be starting!
Don’t read questions at lightning speed
We hate to break it to you, but you probably aren’t a superhero named “Speedy Reader.” You’ll be
anxious when the test begins, and you may want to blow through the questions at record speed.
Big mistake! You don’t get bonus points for nishing early, and you have plenty of time to answer
every question if you read at a reasonable pace. You may take pride in your ability to speed-read
novels, and that skill may help you with the reading-comprehension passages, but don’t use it to
read the questions. You need to read questions carefully to capture the nuances the GMAT oers
and understand exactly what it asks of you.
Many people who get bogged down on a few questions and fail to complete a section do so because
of poor test-taking techniques, not because of slow reading. Do yourself a favor: Relax, read at a
reasonable pace, and maximize your score!
Don’t waste all your time on the
hardest questions
Although you shouldn’t try to work at lightning speed, remember not to get held back by a few
hard questions, either. The diculty of a question depends on the person taking the test. For
everyone, even the high scorers, a few questions on a test are just harder than others. When you
confront a dicult question on the GMAT, do your best, eliminate as many wrong answers as you
can, and then make an intelligent guess. Even if you had all day, you might not be able to answer
that particular question. If you allow yourself to guess and move on, you can work on plenty of
other questions that you’ll answer correctly.
26 PART 1 Getting Started with the GMAT
Don’t cheat
We aren’t sure how you’d cheat on the computerized GMAT, and we won’t be wasting our time
thinking of ways! Spend your time practicing for the test and do your best. Cheating is futile.
Tackling a Case of Nerves with
Relaxation Techniques
All this talk about time management, distracting answer choices, blind guessing, and losing focus
may be making you nervous. Relax. After you’ve read this book, you’ll have plenty of techniques
for turning your quick intellect and that packet of noteboards into a high GMAT score. You may
feel a little nervous on the day of the test, but don’t worry about it, because a little nervous
adrenaline can actually keep you alert. Just don’t let anxiety ruin your performance.
You may be working along steadily when suddenly, from out of the blue, a question appears that
you don’t understand at all. Instead of trying to eliminate answer choices and solve the problem,
you may stare at the question as if it were written in a foreign language. You may start to second-
guess your performance on the test as a whole. You panic and think that maybe you’re just not cut
out for a graduate business degree. You’re on the verge of freaking out— help!
Because much of the GMAT is in CAT format, encountering a super-hard quantitative or verbal
question probably means you’re doing pretty well. Besides, if you do miss a question, you’ll just
get an easier question next— unless you’re on the last question, in which case you needn’t freak
out at all. Heck, you’re nearly done!
If you do nd yourself seizing up with anxiety partway through the test, and if these facts about
the CAT format don’t ease your tension, try these techniques to get back on track:
»
Inhale deeply. When you stress out, you take shallow breaths and don’t get the oxygen you
need to think straight. Breathing deeply can calm you and supply the air you need to get back
to doing your best.
»
Stretch a little. Anxiety causes tension, and so does working at a computer. Do a few simple
stretches to relax and get the blood owing. Try shrugging your shoulders toward your ears
and rolling your head from side to side. You can put your hands together and stretch your
arms above your head or stretch your legs out and move your ankles up and down (or both!).
Last, shake your hands as though you’ve just washed them and don’t have a towel.
»
Give yourself a mini massage. If you’re really tense, give yourself a little rubdown. The
shoulders and neck usually hold the most tension in your body, so rub your right shoulder
with your left hand and vice versa. Rub the back of your neck. It’s not as great as getting a full
rubdown from a professional, but you can book that appointment for after the test!
»
Think positive thoughts. Give yourself a quick break. The GMAT is tough, but don’t get
discouraged. Focus on the positive; think about the questions you’ve done well on. If you’re
facing a tough question, realize that it will get better.
»
Take a little vacation. If nothing else is working and you’re still anxious, picture a place in
your mind that makes you feel comfortable and condent. Visit that place for a few moments
and come back ready to take charge!
CHAPTER 2 Maximizing Your Score onthe GMAT 27
Devising a Plan of Attack
The best way to avoid freaking out on exam day is to be fully prepared. So make sure you have a
strategy. About two to three months before your test day, map out a regular study schedule that
includes these steps:
1. Use one of the online practice tests included with this book to take a full, timed exam.
2. Score your practice exam.
3. Based on your scores, read the chapters in this book that correspond to those areas
where you need the most improvement.
If your verbal score is lower than your math, focus on improving your reading and grammar
skills in Part 2. If your math score is closer to your total number of ngers and toes than the
measure of your height in inches, open up the math review in Part 4.
4. Once you’ve read through the appropriate chapters, practice what you’ve learned by
answering practice questions.
Use the questions provided in the remaining ve practice tests oered in this book and online.
Try to spend several hours each week involved in practice. After you score your eorts, examine
the questions you answer incorrectly to determine your error. Then check the answer explana-
tions for more insight.
5. Follow the same approach to studying your areas of strength.
If you’ve spent the previous month focusing on the math in Part 4, focus on the verbal approach
oered in Part 2. If you’ve concentrated on the verbal questions, set your sights on the math
chapters.
6. When you’ve mastered the verbal and math questions, work on the AWA approach
oered in Part 3 and the suggestions for integrated-reasoning practice in Part 5.
7. Test your skills on actual GMAT questions and get used to the online test format.
Supplement your practice with the most current ocial GMAT materials: The Ocial Guide for
GMAT Review, The Ocial Guide for GMAT Quantitative Review, and The Ocial Guide for GMAT
Verbal Review. Download the free GMATPrep software on
www.mba.com. After you work through
the initial practice questions in the program, reserve a three-hour block of time to take a
full-length GMAT practice exam. Review concepts and strategies in this book. Then take the
other full-length practice exam in the GMATPrep program.
Take the GMAT as soon as you’re ready. You’ll lose momentum and intensity if you prepare for
more than three or four months prior to your test date.
CHAPTER3 Mastering Business-School Admissions 29
IN THIS CHAPTER
» Selecting an MBA program
» Applying to business school
» Making your essay stand out
Mastering Business-School
Admissions
I
f you’re reading a book about the GMAT, you’re probably considering an MBA.Well, get ready
for a great adventure. Applying to business school can be a challenge, not to be attempted by
the lukewarm or ambivalent. If you’re truly committed to acquiring an MBA, though, the appli-
cation process may be sort of exciting. You may end up living someplace new and broadening your
opportunities in ways you never considered.
In this chapter, we discuss the ins and outs of evaluating business programs and applying for
admission, as well as the importance of the GMAT in this process.
Choosing a Business School
Choosing the right business school is not unlike choosing the right car or home— you’re faced
with numerous considerations, and what works best for, say, your sister or friend may not be the
best option for you. Just as cars and houses are major investments, so is a business-school educa-
tion, so just as you would likely test-drive a new car before buying it and have a home inspection
performed on a house before sinking your life savings into it, you ought to conduct extensive
research before deciding where to pursue that MBA.
Not all MBA programs are created equal. You may still be able to get a ne business education at
most of them, but understand that dierent programs have dierent characteristics. Some are
extremely competitive, while others are easier to get into. Most require attending classes on cam-
pus, but a growing number of colleges oer programs that can be completed entirely online or
through a blend of online and on-campus coursework. Some have excellent practical career-
oriented programs while others present a more theoretical approach to business. You need to
decide what you want in a school before you let schools decide whether they have the privilege of
accepting you.
Chapter3
30 PART 1 Getting Started with the GMAT
As you build your application list, consider the following factors:
»
Prestige: School prestige falls rst on this list, and that isn’t by accident. In a Forbes survey of
about 750 GMAT test-takers, prospective students were asked which consideration was most
important to them when selecting a business school. Prestige was the most common answer,
and the best measure of prestige at a given school was said to be the proven success of its
alumni. Why does prestige get so much credit? Primarily, because students believe that being
aliated with a particular high-ranked school will give them a foot up in many areas and help
them stand out from the crowd. To be more specic, students tend to associate higher-
prestige business schools with enhanced opportunities for career and business networking,
and in many ways the association is justied. For example, Wall Street rms generally recruit
from the top-ranked East Coast MBA programs, so if you desire to join one of these corpora-
tions, you need to apply to the programs they favor. Checking the top ve rankings of MBA
programs— Forbes, Businessweek, US News & World Reports, The Economist, and The
Financial Times— provides you with an indication of which programs are most prestigious.
An MBA school’s rank may not matter to you, however, if you’re already employed or are
self-employed and primarily desire to acquire skills to enhance your current profession.
»
Aordability: Obviously, it makes sense to borrow as little money as possible for business
school, as you’ll more than likely be committed to pay it all back, plus interest, somewhere
down the line. MBA programs generally aren’t cheap, however, so the trick is to not only nd a
school that you can aord, but uncover one that oers the biggest return on your investment
(ROI). To get a sense of what that ROI may ultimately be, you’ll want to take a comprehensive
look at all costs associated with attending a particular institution. In addition to tuition rates,
review any additional fees that contribute to the total cost of attendance, such as room and
board (if applicable), textbooks and technology needs (for example, laptops and so on) and
personal living expenses. Carefully assess the likelihood of receiving nancial aid and merit
scholarships to help oset expenses. Also, consider the wages you give up while you attend a
full-time program. Ultimately, ROI comes down to whether the amount you spend for your
MBA, including the lost wages, will be less than the salary increase you receive as a result of
enhancing your academic credentials.
»
Selectivity: You have to get into an MBA program before you can graduate from it. Check with
admissions to determine a school’s mid 50 percent and top 25 percent qualications regarding
accepted GPA and GMAT scores. Your application list should include at least one or two
programs where your numbers— grades and test scores— fall within the top 25 percent.
With that assurance, you can toss your hat in the ring for more selective schools.
»
Concentrations and specialties: As with undergraduate programs, some MBA programs
specialize in a particular business concentration. Do your research. If your focus is nance,
apply to programs with a strong nance curriculum. If your goal is to increase your manage-
ment opportunities, nd programs that specialize in business management. Some universities
oer dual degree programs. You can earn an MBA and a law degree in four years at some or
combine an MBA with an MD.Master’s degrees in a variety of areas, such as education, public
policy, journalism, and so on, may be paired with an MBA.If gaining more than one degree
excites you, look for schools that oer these options.
»
Special programs: While traditional MBA programs consist of a full-time, two-year commit-
ment, you’ll nd a variety of options that stray from this model. Some schools oer part-time
programs that allow you to work while you earn your degree. Other programs may integrate
online learning or may be oered entirely online to accommodate dierent schedules. You
may seek a program that oers more practical application opportunities, or you may be more
interested in a program with a more theoretical approach. Investigate programs to nd the
ones that best t your schedule and goals.
CHAPTER 3 Mastering Business-School Admissions 31
»
Location: Geography plays a big role in deciding where you pursue your MBA.Do you want to
be near your family? Do you want to be able to drive to the beach or the mountains to get a
break from your studies? Do you feel more comfortable on the East Coast or West Coast? Or
are you more at home in the Midwest or South? Location may also be a factor in overall cost;
living in Palo Alto, California, is more expensive than residing in Columbus, Ohio.
If you’re fresh out of college and don’t yet have a family, you may have more exibility choos-
ing a business school than you might if you own property and have children or other responsi-
bilities that require you to stay close to your home base. Additionally, it’s wise to think beyond
graduation when determining where to attend business school. Often, MBA programs have
tight links within their communities, meaning your best bet at landing a job through network-
ing, interning, or networking with alumni may be in the same neighborhood as the institution.
Choosing a business school may also mean choosing your future hometown.
»
Public or private: MBA programs may be found at state university systems or in private
universities. Many public schools charge less for tuition than private ones, especially for
in-state residents, but more nancial aid and scholarship possibilities may exist at private
universities.
»
Average starting salary: You’re probably considering business school at least in part because
you hope an MBA will boost your ability to secure gainful employment or command a higher
salary. All MBA programs are not created equal, and (here’s where “prestige” again factors in)
attending a big-name school really can help you bring home the bacon, so to speak. An MBA
from a highly ranked, selective business school, such as Stanford, Harvard, or Wharton, can
considerably boost your ability to earn a substantial income. The average MBA starting salary
is also important if you are accruing interest on student loans. Checking program rankings
based on starting salary may help give you a rough idea of how long you’ll be indebted.
»
Quality of life: Some business schools are known for being competitive, even cutthroat;
others embrace a more collaborative atmosphere. Examine your personality and be honest
with yourself. Does competition challenge you or defeat you? Are you more comfortable
working in groups or individually? Talk with current students and alumni to get an accurate
assessment of a program’s character to make sure it ts with yours.
»
Alumni network: You’re going to spend much more of your life as a business-school graduate
than as a business-school student. The connections you make as you earn your MBA may last
a lifetime, and a strong alumni network can be a valuable resource throughout your career.
Consider the depth and breadth of a program’s alumni when you draw up your application list.
When it comes to selecting a business school, there is no “one size ts all” approach. Do your due
diligence, therefore, to nd the programs that best t you. Once you have your list, your next step
is to create a memorable, eective application that leaves a lasting impression.
Lining Up Your Ducks— Applying
to Business Schools
Applying to MBA programs is an expensive and time-consuming process not to be entered into
lightly. Each school has its own admissions requirements and components you must gather and
submit according to instructions. Be sure to check each program’s admission web page thor-
oughly, and carefully follow the instructions. Despite slight dierences, most MBA admissions
expect to receive by a designated deadline the application, GMAT (or GRE) scores, college tran-
scripts, a personal essay, a list of activities and/or a resume, letters of recommendation, and the
application fee.
32 PART 1 Getting Started with the GMAT
When to apply
Most traditional MBA programs begin in the fall semester, and the application season begins the
fall prior. More exible schedules may accommodate entry at several times throughout the year,
each with its own application deadline. Some schools have rolling admissions, reviewing applica-
tions as they come in and cutting o applications after a certain date. A relatively common appli-
cation practice is to accept applications in two or three rounds with separate deadlines and
notication dates. This practice cuts down on the time it takes for you to receive a decision.
Whether your program has one deadline or three, rolling admissions or not, it’s best to get your
materials in as early as possible. Early applications cut down on your competition and may make
you eligible for additional scholarships and nancial aid. To ready yourself for early applying,
take the GMAT as soon as you decide to pursue an MBA.
What to submit
Most programs expect to see the following:
»
A completed, signed application form
»
GMAT (or GRE) score
»
Transcripts of prior academic record
»
Letters of recommendation, at least one from an immediate supervisor
»
A personal statement— an essay usually explaining why you want to earn an MBA
»
For some programs, additional essays, usually dening why you want to study at that
institution
»
A hefty application fee, which can vary from around $50 to $250 or so at some selective
universities
You may also have to send in documentation of state residency, nancial aid forms, or other rel-
evant information.
If one required component of your application isn’t in place by the deadline (or whenever the
admissions committee stops considering applications), no one will read any of it. So if one of your
recommenders forgets to send in a letter or you neglect to order an ocial transcript from a col-
lege you attended during the summer, your application may be jeopardized or thrown out.
TO GMAT OR TO GRE— THAT IS THE QUESTION
A growing trend among business schools is to accept either the GRE or the GMAT for admissions. This
practice may leave you wondering which to choose. The GRE is used for most graduate programs other
than the MBA, so if you aren’t sure whether you want an MBA or, say, a masters in finance, or you have
your heart set on a dual-degree program, it may seem that the GRE is a more efficient option. Be care-
ful, though; business schools may view your GRE score as a lack of surety on your part regarding your
dedication to an MBA.Choosing the GMAT over the GRE may help your admissions chances because it
indicates a commitment to the MBA path. If an MBA is your one and only goal, the GMAT is likely a better
option, and that choice may serve you well even after you graduate with potential employers who are
more familiar with GMAT results in job applications.
CHAPTER 3 Mastering Business-School Admissions 33
Crafting Eective Business-School Essays
More people apply to MBA programs than any other post-graduate degree, which results in a
large number of business-school graduates seeking positions. This fact poses a problem for
business-school administrators who want to boast about their alumni’s high employment rates.
Therefore, MBA programs are much more likely to accept you when they see evidence of your
future success. This support comes to them in your academic record, for sure, but it’s also con-
veyed in the case you make in your personal statement.
Before you sit down to write your essay, outline your future plans. Dene exactly why you want
to earn an MBA and clarify specic career goals. The personal statement should not only convey
what you’ve achieved so far, but it should also link your past accomplishments to concrete future
goals, ones that require an MBA to fulll. The essay is your chance to show admissions the unique
contributions you can make to their program. To this end, here is a summary of what an appro-
priate personal statement is not:
»
The essay isn’t a summary of your past education, activities, and accolades. Your resume
fullls this task. Use the personal statement to provide deeper insight into who you are as well
as what you do.
»
The essay isn’t a university fan letter. Resist the temptation to ll your personal statement
with boundless praise. Your discussion of the business school should reveal your knowledge of
its strengths as they relate to your particular goals. Don’t tell a school about its unique
concentrations and experiences; show how these opportunities align with your goals and
abilities.
»
The essay isn’t poetic license. The personal statement provides an opportunity for you to
convey your story in creative ways. By all means, use stories and sensory description to reveal
your qualities in a very real way. But avoid overstepping the boundaries. Observe word or
page limits and follow directions. An attempt to dazzle with dierence may just show admis-
sions that you have trouble following rules.
REVIEW OF APPLICATIONS
Many law schools receive far more applicants than they have spaces for in an entering class. Obviously
the first thing admissions committees look at is academic credentials and GMAT scores, but numbers
aren’t everything. Every year competitive business schools admit some students with comparatively low
scores and grades and reject some with stellar numbers.
MBA programs desire to create classes that represent a diversity of backgrounds and interests and have
the potential to bring them fame and fortune as successful alumni. Therefore, these factors may also
contribute to a successful application:
•
Geography (where students come from); schools like to get people from all over the world
•
Race and ethnicity
•
Unique activities or work experience
You can highlight your individual contributions in your personal statement, which is why this essay can
be a very important component of your application.
34 PART 1 Getting Started with the GMAT
»
The essay isn’t a philosophical treatise. Focus on what’s true for you rather than what’s true
for the world.
»
The essay isn’t a personality assessment. Perhaps the biggest mistake applicants make in
writing their personal essays is over-generalization and under-substantiation. You don’t
convince others of your personal characteristics by simply telling them you’re awesome or
hardworking. Show who you are through carefully chosen stories that unfold through specic
details. Allow the reader to draw conclusions about who you are from reading about how you
interact with the world.
»
The essay doesn’t have to sugarcoat. Don’t be afraid to express some vulnerability. You
aren’t good at everything. If you were, you wouldn’t need an advanced degree. Sometimes the
best way to endear your reader is to acknowledge a shortcoming.
2
Vanquishing the
Verbal Section
IN THIS PART ...
Put your grammar skills to work to catch and correct
sentence errors that GMAT writers are most fond of
throwing at you.
Discover techniques to help you move through reading
passages most eciently within the time limit.
Apply our time-tested strategy for approaching critical
reasoning arguments so that you get really good at
evaluating the arguments and answering the questions.
Tackle a short version of a GMAT verbal section to
get familiar with how all three question types come
together.
CHAPTER4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 37
IN THIS CHAPTER
» Grasping grammar basics
» Recognizing commonly tested
errors
» Mastering the approach to
sentence-correction questions
Applying What You
Learned (We Hope) in
Grammar Class: Sentence
Correction
B
usiness success depends on a number of diverse skills, and one of the most important of
these skills is the ability to communicate eectively. The GMAT can’t test your speaking
ability (not yet, anyway), so it focuses on your reading and writing skills. In fact, about
half of the GMAT is devoted to reading and writing. And, of course, knowing the rules of standard
written English is essential to good writing. The GMAT test-makers have developed diabolically
eective ways to use multiple-choice questions to test your knowledge of written English. They
present you with a sentence and underline a portion of it. Your job is to gure out whether the
underlined part is okay the way it is. If it needs to be changed, you have to pick the answer choice
that oers the proper correction.
Sentence-correction questions appear in the verbal-reasoning section along with reading-
comprehension and critical-reasoning questions. You have 75 minutes to answer the 41 questions
that appear in the entire section. So you have a little less than two minutes to answer each ques-
tion. You’ll likely need more time to ponder reading questions, so plan to spend no more than one
minute answering each sentence-correction question.
Punctuation, subject-verb agreement, parallel construction, and other keys to good grammar
may have you lying awake at night. Take heart. We won’t let your dream of attending the business
school of your choice die on the sentence-correction portion of the GMAT.Fortunately, the kinds
of sentence errors that crop up on the GMAT don’t change much, so you can focus your study on
the common ones.
In this chapter, we review the grammar basics you should have down before test day. We also
show you what sentence-correction questions look like, which common errors the GMAT likes to
test, and the best way to approach the questions.
Chapter4
38 PART 2 Vanquishing the Verbal Section
Building a Solid Foundation: Grammar Basics
Luckily, the rules of grammar are really pretty logical. After you understand the basic rules
regarding the parts of speech and the elements of a sentence, you’ve got it made. The following
sections provide what you need to know to do well on sentence-correction questions. As an added
bonus, this refresher can help you write the GMAT analytical-writing essay.
Getting wordy: The parts of speech
Sentence-correction questions consist of, well, sentences. Sentences are made up of words, and
each word in a sentence has a function. The parts of speech in the English language that are
important to know for GMAT grammar are verbs, nouns, pronouns, adjectives, adverbs, conjunc-
tions, and prepositions.
Acting out: Verbs
Every sentence has a verb, which means that a sentence isn’t complete without one. You should
be familiar with three types of verbs:
»
Action verbs: These verbs state what the subject of the sentence is doing. Run, jump, compile,
and learn are examples of action verbs.
»
To be: The verb to be (conjugated as am, is, are, was, were, been, and being) functions sort of like
an equal sign. It equates the subject with a noun or adjective. For example: Ben is successful
means Ben = successful. She is a CEO means she = CEO.
»
Linking verbs: These words join (or link) the subject to an adjective that describes the
condition of the subject. Like the verb to be, they express a state of the subject, but they
provide more information about the subject than to be verbs do. Common linking verbs are
feel, seem, appear, remain, look, taste, and smell.
Telling it like it is: Nouns
You’ve undoubtedly heard nouns dened as persons, places, or things. They provide the “what”
of the sentence. A noun can function in a sentence in dierent ways:
1. The subject plays the principal role in the sentence. It’s what the sentence is about or who is
doing the action.
2. A direct object receives the action of an action verb.
3. An indirect object receives the direct object. Sentences with direct objects don’t need indirect
objects, but you need a direct object before you can have an indirect object.
4. The object of a preposition receives a preposition. (See the “Joining forces: Conjunctions and
prepositions” section, later in this chapter.)
5. The object in a verbal phrase serves as the receiver of the gerund (which is a verb form that
functions as a noun, like singing).
6. An appositive claries or renames another noun.
7. A predicate noun follows the verb to be and regards the subject.
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 39
So you can see how these dierent types of nouns function, we’ve marked their appearances in
these two sentences with numbers that correspond to the preceding list:
Being a businesswoman (5) with great leadership abilities (4), Anna Arnold (1), an MBA (6), gave her
employees (3) the opportunity (2) to succeed. Anna (1) was a supportive supervisor (7).
The GMAT won’t ask you to dene the various noun functions, but being familiar with them helps
when we talk about the dierent types of sentence errors you may encounter.
One of the most important things to remember about nouns and verbs on the GMAT is that the
subject and verb of a sentence have to agree in number. See the later section “Pointing Out Mis-
takes: Common Sentence-Correction Errors” for details.
Standing in: Pronouns
Pronouns gure prominently in the sentence-correction portion of the GMAT.Pronouns rename
nouns and provide a means of avoiding the needless repetition of names and other nouns in a
sentence or paragraph. On the GMAT, pronoun errors are common. To correct these errors, you
need to be familiar with the three types of pronouns: personal, indenite, and relative:
»
Personal pronouns: These words rename specic nouns. They take two forms: subjective and
objective.
•
The subjective personal pronouns are I, you, he, she, it, we, and they. Subjective personal
pronouns are used when the pronoun functions as a subject or predicate noun (see the
preceding section for info on noun functions).
•
The objective personal pronouns are me, you, him, her, it, us, and them. Objective personal
pronouns are properly used when they function as an object in the sentence.
»
Indenite pronouns: These pronouns refer to general nouns rather than specic ones. Some
common examples are everyone, somebody, anything, each, one, none, and no one. It’s important
to remember that most indenite pronouns are singular, which means they require singular
verbs: One of the employees is being laid o.
»
Relative pronouns: These words, like that, which, and who, introduce adjective clauses that
describe nouns. Who refers to persons; which and that refer primarily to animals and things: He
is a manager who is comfortable leading. The consulting work that she does usually saves compa-
nies money, which makes her a very popular consultant.
Filling in the details: Adjectives
Adjectives describe and clarify nouns and pronouns. For example: The secretive culture of the corpo-
ration created discontented employees. Secretive denes the kind of culture and discontented describes
the feeling of the employees. Without the adjectives, the sentence is virtually meaningless: The
culture of the corporation created employees.
With sentence-correction questions, make sure adjectives are positioned correctly in the sentence
so each adjective modies the word it’s supposed to. For example, I brought the slides to the meeting
that I created makes it seem that the author of the sentence created the meeting rather than the
slides. The descriptive clause that I created is in the wrong place. The better composition is I
brought the slides that I created to the meeting.
40 PART 2 Vanquishing the Verbal Section
Describing the action: Adverbs
Adverbs are like adjectives because they add extra information to the sentence, but adjectives
usually modify nouns, and adverbs primarily dene verbs. Adverbs include all words and groups
of words (called adverb phrases) that answer the questions where, when, how, and why: The stock
market gradually recovered from the 1999 crash. Gradually denes how the stock market recovered.
Some adverbs modify adjectives or other adverbs: The extremely unfortunate plumber yodeled very well.
You’ll recognize many adverbs by the -ly ending. But not all adverbs end in -ly. For example, in
The company’s manufacturing moved overseas, the adverb overseas reveals where the manufacturing
is located. In The Human Resources director resigned today, today explains when the director resigned.
Positioning adverbs correctly is important on the GMAT.Separating adverbs from the words they
modify makes sentences imprecise.
Joining forces: Conjunctions and prepositions
Conjunctions and prepositions link the main elements of the sentence.
»
Conjunctions: This part of speech joins words, phrases, and clauses. The three types of
conjunctions are coordinating, correlative, and subordinating. Don’t worry about memorizing
these terms; just remember that the three types exist.
•
The seven coordinating conjunctions— and, but, for, nor, or, so, and yet— are the ones
most people think of when they consider conjunctions.
•
Correlative conjunctions always appear in pairs: either/or, neither/nor, not only/but also.
These conjunctions correlate two similar clauses in one sentence. Therefore, if you use
either as a conjunction, you have to include or.
•
Subordinating conjunctions introduce dependent clauses and connect them to indepen-
dent clauses. Although, because, if, when, and while are common examples of subordinating
conjunctions. We talk more about clauses in the section “In so many words: Phrases and
clauses.”
»
Prepositions: These words join nouns to the rest of a sentence. We’d need several pages to
list all the prepositions, but common examples are about, above, at, for, in, over, to, and with. A
preposition can’t function within a sentence unless the preposition is connected to a noun, so
prepositions always appear in prepositional phrases. These phrases consist of a preposition
and noun, which is called the object of the preposition: The woman in the suit went to the oce
to sit down. The preposition in relates its object, suit, to another noun, woman, so in the suit is a
prepositional phrase that works as an adjective to describe woman; to the oce is an adverbial
prepositional phrase that describes where the woman went. Note that the word to in to sit
down isn’t a preposition; rather, it’s part of the innitive form of the verb to sit — the phrase
doesn’t have an object, so you don’t have a prepositional phrase.
Prepositions often play a part in sentence-correction questions. The GMAT may provide you with
a sentence that contains an improper preposition construction. Here’s a simple example: He
watched the ood while sitting in the roof. The correct preposition is on, not in. Other types of prepo-
sition questions may not be so easy, but we highlight these for you in the section “Pointing Out
Mistakes: Common Sentence-Correction Errors.”
Pulling together: The parts of a sentence
The parts of speech work together to form sentences. And the thrust of the sentence’s informa-
tion is conveyed by three main elements: the subject, the verb, and the element that the verb links
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 41
to the subject. To locate the main idea of a sentence, you focus on these three elements. Other
information within the sentence is secondary.
Trouble comes in threes: Subject, verb, and third element
The subject is the main character of the sentence; it’s the noun that carries out the action of the
sentence or whose condition the sentence describes. The verb describes the action or links the
subject and predicate. Depending on the verb used, the third important part of the sentence could
be a direct object, an adverb, an adjective, or a predicate noun. The third element for a sentence
with a transitive verb (an action verb that must be followed by a direct object) is always a direct
object. Intransitive verbs (action verbs that can’t be followed by direct objects) may be completed
by adverbs. You can follow the verb to be with either an adjective or a predicate noun. Recognizing
the three main elements of the sentence helps you spot errors in the sentence-correction
questions.
In so many words: Phrases and clauses
In addition to the main elements, a sentence may contain single words, phrases, or clauses that
convey more information about the sentence’s main message. Phrases and clauses are groups of
words that work together to form a single part of speech, like an adverb or adjective. The dier-
ence between phrases and clauses is that clauses contain their own subjects and verbs, and
phrases don’t. A good understanding of both clauses and phrases can help you greatly on the
sentence-correction portion of the GMAT.
PHRASES
Phrases are groups of words that function together as a part of speech. Many tested errors on the
GMAT concern phrases, and we discuss them in more depth in the section “Pointing Out Mis-
takes: Common Sentence-Correction Errors.”
INDEPENDENT AND DEPENDENT CLAUSES
The distinguishing characteristic of clauses is that they contain subjects and verbs. The two types
of clauses are independent and dependent. Recognizing the dierence between independent and
dependent clauses can help you with many of the sentence-correction problems on the GMAT.
»
Independent clauses: These clauses express complete thoughts and could stand as sen-
tences by themselves. Here’s an example of a sentence that contains two independent clauses:
The rm will go public, and investors will rush to buy stock. Each clause is a complete sentence:
The rm will go public. Investors will rush to buy stock.
Punctuate two independent clauses in a sentence by joining them either with a semicolon or
with a comma and a coordinating conjunction.
»
Dependent clauses: These clauses express incomplete thoughts and are, therefore, sentence
fragments. Even though they contain a subject and verb, they can’t stand alone as sentences
without other information. For example, in the sentence After the two companies merge, they’ll
need only one board of directors, the dependent clause in the sentence is after the two compa-
nies merge. The clause has a subject, companies, and a verb, merge, but it still leaves the reader
needing more information. So the clause is dependent. To form a complete sentence, a
dependent clause must be paired with an independent clause.
Punctuate a beginning dependent clause by placing a comma between it and the independent
clause that comes after it. If the dependent clause follows the independent clause, you don’t
need any punctuation: They’ll need only one board of directors after the two companies merge.
42 PART 2 Vanquishing the Verbal Section
When you understand the dierence between independent and dependent clauses, you’ll be bet-
ter able to recognize sentence fragments and faulty modication errors (more about those appears
in the section “Pointing Out Mistakes: Common Sentence-Correction Errors”).
Before we talk about the most commonly tested errors in the sentence-correction questions, we
need to share one more thing about dependent clauses. Dependent clauses can be classied as
either restrictive or nonrestrictive. Distinguishing between the two can be tricky.
»
Restrictive clauses are vital to the meaning of the sentence. Without them, the sentence’s
original meaning is lost. For example, in She never wins her cases that involve the IRS, the
restrictive clause that involve the IRS provides essential information about the particular type of
cases she never wins. The point of the sentence is that she never wins IRS cases.
»
Nonrestrictive clauses provide clarifying information, but they aren’t mandatory for the
sentence to make sense. In the sentence She never wins her cases, which involve the IRS, the
nonrestrictive clause, which involve the IRS, makes a “by the way” statement. It provides
additional information about what type of cases she handles. The main point of the sentence
is that she never wins a case.
Note that in the preceding examples, the restrictive clause begins with that and the nonrestrictive
clause begins with which. You don’t use commas before clauses that begin with that because
they’re restrictive clauses and integral parts of the sentence. You should use commas to set non-
restrictive clauses apart from the rest of the sentence.
Pointing Out Mistakes: Common
Sentence-Correction Errors
Sentence-correction questions test your ability to edit written material so it follows the rules of
standard written English. The questions provide you with sentences that contain underlined parts.
From the ve provided answer choices, you have to choose the answer that expresses the under-
lined portion of the sentence in the way that conforms to the dictates of standard written English.
The rst answer choice is always the same as the underlined portion of the sentence. So if you
think the sentence is ne as is, select the rst answer. The other four choices present alternative
ways of expressing the idea in the underlined part. Your task is to determine whether the under-
lined portion of the statement contains an error and, if so, which of the four alternatives best
corrects the error.
NOT SO NEEDY: THE FUNCTIONS OF
DEPENDENT CLAUSES
Dependent clauses that function as adverbs begin with subordinating conjunctions and answer the ques-
tions how, when, where, or why. For example, The woman got the job because she was more qualied.
The bolded portion is a dependent clause explaining why the woman got the job. On the other hand, an
adjectival clause usually begins with a relative pronoun to provide more information about the noun it
modifies, like in this sentence: The judge is a man who requires a silent courtroom. The bolded clause
describes what type of man the judge is. Dependent clauses may also function as nouns: The insurance
company was focusing on how much money the hurricane would cost. The dependent clause in this sen-
tence is the object of the preposition on.
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 43
You correct errors in sentence-correction sentences by applying the basic rules of English gram-
mar. The good news is that you won’t be asked to dene or spell words or diagram sentences! And
no question expects you to correct specic punctuation errors, though knowing the rules for plac-
ing commas helps you eliminate answer choices in some cases.
The GMAT is a test for admission to business school. Therefore, sentence-correction questions
center on errors that adversely aect the quality of business writing, such as improper word
choices, incomplete or run-on sentences, and verb tense and agreement issues. The kind of errors
you’ll be asked to correct on the GMAT are the kind you should avoid if you want to write success-
fully in business.
Can’t we all just get along? Errors in subject-
verb and noun-pronoun agreement
One of the most fundamental skills in writing is the ability to make the elements of a sentence
agree. If your subject is singular but your verb is plural, you’ve got a problem! Even in less formal
kinds of communication, like quick emails, errors in subject-verb or noun-pronoun agreement
can obscure the message you hope to communicate. You can be sure that the GMAT sentence-
correction problems will contain some agreement errors.
Subject-verb agreement
When we say the subjects and verbs agree, we don’t mean they’re having a meeting of minds. We
mean that plural subjects pair with plural verbs and singular subjects require singular verbs.
Errors in simple constructions are pretty easy to spot. It just doesn’t sound right to say He attend
classes at the University of Michigan.
It’s when the subject isn’t simple or obvious that determining subject-verb agreement gets a
little more dicult. For example, take a look at this sentence: His xation with commodities markets
have grown into several prosperous ventures, including a consulting business. The subject is xation, but
the prepositional phrase with commodities markets may confuse you into thinking that markets is
the subject. Markets is a plural noun, so it would take a plural verb if it were the subject. But you
know that markets can’t be the subject of the sentence because markets is part of a prepositional
phrase. It’s the object of the preposition with, and a noun can’t be an object and a subject at the
same time. The subject has to be xation, so the singular verb has, rather than the plural have, is
proper.
Focus on the three main elements of any complex sentence by mentally eliminating words and
phrases that aren’t essential to the sentence’s point. Then you can check the subjects and verbs
to make sure they agree. For example, when you remove the prepositional phrase with commodi-
ties markets from the sample sentence we just discussed, you get His xation have grown, which
reveals an obvious disagreement in number between the subject and verb.
Noun-pronoun agreement
Another relationship you need to keep on track is the one between nouns and the pronouns that
refer to them. A pronoun must agree in number with the noun (or other pronoun) it refers to.
Plural nouns take plural pronouns, and singular nouns take singular pronouns. For example, this
sentence has improper noun-pronoun agreement: You can determine the ripeness of citrus by han-
dling them and noting their color. Citrus is a singular noun, so using plural pronouns to refer to it is
incorrect. It would be correct to say You can determine the ripeness of citrus by handling it and noting
its color.
44 PART 2 Vanquishing the Verbal Section
Another problem with pronouns is unclear references. To know whether a pronoun agrees with
its subject, you have to be clear about just what the pronoun refers to. For example, it’s not clear
which noun the pronoun in this sentence refers to: Bobby and Tom went to the store, and he pur-
chased a candy bar. Because the subject of the rst clause is plural, the pronoun he could refer to
either Bobby or Tom or even to a third person. To improve clarity in this case, you’d use the name
of the person who bought the candy bar rather than the ambiguous pronoun.
If a GMAT sentence-correction question contains a pronoun in the underlined portion, make sure
the pronoun clearly refers to a particular noun in the sentence and that it matches that noun in
number. Otherwise, you need to nd an answer choice that claries the reference or corrects the
number.
Here’s a sample question that contains both types of agreement errors:
Much work performed by small business owners, like managing human relations, keeping track
of accounts, and paying taxes, which are essential to its successful operation, have gone virtu-
ally unnoticed by their employees.
(A) which are essential to its successful operation, have gone virtually unnoticed by their
employees
(B) which are essential to successful operations, have gone virtually unnoticed by their
employees
(C) which is essential to its successful operation, have gone virtually unnoticed by its
employees
(D) which are essential to successful operation, has gone virtually unnoticed by their
employees
(E) which are essential to successful operation, has gone virtually unnoticed by its employees
The underlined portion contains several agreement errors, and your job is to locate and x all of
them. To accomplish this task, isolate the three main elements of this sentence:
»
The subject is work. None of the other nouns or pronouns or noun phrases in the sentence can
be the main subject because they’re all either objects (owners, managing, keeping, paying,
relations, accounts, taxes, operation, employees) or subjects of dependent clauses (which).
»
The main verb is have gone. The other verb (are) belongs to the dependent clause, so it can’t be
the main verb.
»
The third element is unnoticed.
So the essential sentence states that work have gone unnoticed. Well, that doesn’t sound right! You
know you have to change the verb to the singular has to make it agree with the singular subject
work. Eliminate any answer choices that don’t change have to has, which leaves you with Choices
(D) and (E).
You’ll notice that both Choice (D) and Choice (E) contain the verb are. So the pronoun which must
refer back to managing, keeping, and paying (which, together, are plural), so the verb that corre-
sponds to which has to be plural, too. Also, both choices eliminate its before successful operation
because it’s unclear what its refers to.
The dierence between the two choices is that Choice (E) changes their to its. Ask yourself which
noun the pronoun before employees refers to. Who or what has the employees? The only possibil-
ity is business owners, which is a plural noun. So the pronoun that refers to it must also be plural.
Their is plural; its is singular. Therefore, Choice (D) is the best answer: Much work performed by
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 45
small business owners, like managing human relations, keeping track of accounts, and paying taxes, which
are essential to successful operation, has gone virtually unnoticed by their employees.
Building code violations: Faulty construction
Errors in construction threaten the stability, readability, and even existence of a sentence! You
have, no doubt, been told to avoid incomplete and run-on sentences. It’s equally important to
avoid sentences that confuse your reader. Some sentences may not contain grammatical errors,
but they can be constructed so poorly that they obscure the point. Both grammatical and rhetori-
cal constructions rely on correct punctuation, proper ordering of clauses, and parallel sentence
structure.
The most commonly tested errors in grammatical construction are sentence fragments, run-on
sentences, and sentences that lack parallel structure. After you get used to them, these errors are
pretty easy to spot.
Sentence fragments
Sentence fragments on the GMAT usually show up as dependent clauses pretending to convey
complete thoughts or as a bunch of words with something that looks like a verb but doesn’t act
like one (technically, a verbal).
»
Dependent clauses standing alone are fragments because they don’t present complete
thoughts. For example, this clause comes complete with a subject and verb: Although many
companies have failed to maintain consistent prots with downsizing. However, it begins with a
subordinating conjunction, although, so it leaves you hanging.
»
Phrases with a verbal instead of a verb can appear to be complete if you don’t read
them carefully. The verbal phrases in this sentence look like verbs but don’t function as verbs:
The peacefulness of a morning warmed by the summer sun and the verdant pastures humming with
the sound of busy bees. Warmed and humming can function as verbs in other instances, but in
this sentence, they’re part of phrases that provide description but don’t tell what the subjects
(peacefulness and pastures) are like or what they’re doing.
You get the hang of recognizing sentence fragments with practice. If you read the sentence under
your breath, you should be able to tell whether it expresses a complete thought.
Correcting fragments is usually pretty simple. You just add the information that completes the
thought or change the verbal phrase to an actual verb. For example, you can make although many
companies have failed to maintain consistent prots with downsizing into a complete sentence by add-
ing a comma and some still try, like so: Although many companies have failed to maintain consistent
prots with downsizing, some still try. To complete the peacefulness of a morning warmed by the summer
sun and the verdant pastures humming with the sound of busy bees, you can change the verbal phrases:
The peacefulness of a morning is warmed by the summer sun, and the verdant pastures hum with the sound
of busy bees.
Run-on sentences
Run-on sentences occur when a sentence with multiple independent clauses is improperly punc-
tuated. Here’s an example: I had a job interview that morning so I wore my best suit. Both I had a job
interview and I wore my best suit are independent clauses. You can’t just stick a coordinating
46 PART 2 Vanquishing the Verbal Section
conjunction between them to make a sentence. Here are the two rules for punctuating multiple
independent clauses in a sentence:
»
Independent clauses may be joined with a comma and a coordinating conjunction. You
can correct the problem by adding a comma, like this: I had a job interview that morning, so I
wore my best suit.
»
Independent clauses may be joined by a semicolon. The sentence can look like this: I had a
job interview that morning; I wore my best suit.
Of course, you can change one of the independent clauses to a dependent clause, like this: Because
I had a job interview that morning, I wore my best suit. If you do that, remember to separate the
clauses with a comma when the dependent clause precedes the independent one.
The GMAT probably won’t give you a run-on sentence to correct, but it may give you an answer
choice that looks pretty good except that it makes the original sentence a run-on. Make sure the
answer you choose doesn’t create a run-on sentence.
Verb tense issues
In addition to checking for subject-verb agreement, make sure the verbs in the underlined por-
tion of the sentence-correction question are in the proper tense. The other verbs in the sentence
give you clues to what tense the underlined verbs should be in.
Lack of parallelism
You can count on several sentence-correction questions that test your ability to recognize a lack
of parallel structure. The basic rule of parallel structure is that all phrases joined by conjunctions
should be constructed in the same manner. For example, this sentence has a problem with paral-
lelism: Ann spent the morning emailing clients, responding to voice mails, and she wrote an article for the
newsletter.
The problem with the sentence is that the three phrases joined by the coordinating conjunction
(and) in this sentence are constructed in dierent ways. Emailing and responding both take the
gerund (or -ing) form, but she wrote initiates a clause. Changing wrote to its gerund form and
eliminating she gets rid of the clause and solves the problem: Ann spent the morning emailing clients,
responding to voice mails, and writing an article for the newsletter.
Parallel structure is also a factor when you make comparisons. The following sentence lacks par-
allel structure: To be physically healthy is as important as being prosperous in your work. The sentence
compares a phrase in the innitive form, to be physically healthy, with a phrase in the gerund form,
being prosperous in your work. Changing one of the constructions to match the other does the trick:
Being physically healthy is as important as being prosperous in your work.
When you see a sentence-correction question with an underlined list, check for lack of parallel-
ism. Look for phrases joined by coordinating conjunctions. If the phrases or sentence parts exhibit
dissimilar constructions, you have to correct the parallelism error.
Here’s how the GMAT may question you about parallel structure:
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 47
The consultant recommended that the company eliminate unneeded positions, existing depart-
ments should be consolidated, and use outsourcing when possible.
(A) eliminate unneeded positions, existing departments should be consolidated, and use out-
sourcing when possible
(B) eliminate unneeded positions, consolidate existing departments, and outsource when
possible
(C) eliminate unneeded positions, existing departments should be consolidated, and when
possible outsourcing used
(D) eliminate unneeded positions and departments and use outsourcing when possible
(E) eliminate unneeded positions, existing departments are consolidated, and outsourcing
used when possible
The underlined portion of this sentence contains a list joined by and, which is a pretty good clue
that you should be vigilant for any lack of parallelism. Because the three phrases joined by and are
not all constructed the same way, you know there’s an error, so eliminate Choice (A).
Next, eliminate the answers that don’t solve the problem. Choice (C) keeps the same faulty con-
struction as the original statement in the rst two recommendations, and it introduces even more
awkwardness by changing use to used and adding it to the end of the third recommendation. You
can clearly eliminate Choice (C). Get rid of Choice (E) because it’s also worse than the original.
Each of the three elements in Choice (E) has a completely dierent construction.
Both Choice (B) and Choice (D) seem to correct the error by introducing each recommendation
with a similar construction, but Choice (D) creates a new error because it changes the meaning of
the sentence. If you select Choice (D), you’re stating that some departments are also unneeded
and should be eliminated. The original, however, stated that departments should be consolidated.
An answer can’t be correct if it changes the meaning of the original sentence, so Choice (D) is
wrong.
Choice (B) solves the problem without changing the original meaning, so it’s the one to choose:
The consultant recommended that the company eliminate unneeded positions, consolidate existing depart-
ments, and outsource when possible.
Is that a rhetorical question? Other construction errors
It may surprise you to know that a GMAT sentence can be grammatically accurate and still need
correction. Sentences that exhibit awkward, wordy, imprecise, redundant, or unclear construc-
tions require xing. The GMAT calls these errors in rhetorical construction. The good news is that
you can often use your ear to correct these problems. The right answer will often simply sound
better to you.
»
Using passive instead of active voice makes a sentence seem weak and wordy. Passive
voice beats around the bush to make a point, so it lacks clarity. For example, this passive-voice
sentence masks the doer of an action: The speech was heard by most members of the corpora-
tion. The sentence isn’t technically incorrect, but it’s better to say it this way: Most members of
the corporation heard the speech. Notice also that the active voice sentence uses fewer words.
So if all else is equal, choose active voice over passive voice.
»
Using repetitive language adds unnecessary words and seems silly. A sentence shouldn’t
use more words than it needs to. For example, it’s a bit ridiculous to say the following: The
speaker added an additional row of chairs to accommodate the large crowd. The construction of
added an additional isn’t grammatically incorrect, but it’s needlessly repetitive. It’s more precise
and less wordy to say The speaker added a row of chairs to accommodate the large crowd.
48 PART 2 Vanquishing the Verbal Section
The bottom line is that any sentence that uses an excessive number of words to convey its mes-
sage probably has construction problems. Often, wordiness accompanies another type of error in
the underlined part. Look for the answer that uses the fewest words to correct the main error. Try
it out with this sample question.
Recently, the price of crude oil have been seeing uctuations with the demand for gasoline in
China.
(A) have been seeing uctuations with
(B) have uctuated with
(C) uctuate with
(D) has uctuated with
(E) has changed itself along with
The main error in the sentence concerns subject-verb agreement. The singular subject, price,
requires a singular verb. Additionally, the underlined portion is needlessly wordy. First, eliminate
answer choices that don’t correct the agreement problem. Then, focus on choices that clarify the
language.
Both Choices (B) and (C) perpetuate the agreement problem by providing plural verbs for the
singular subject. Eliminate those along with Choice (A), and you’re left with Choices (D) and (E).
Choice (E) is constructed even more awkwardly than the original sentence, so Choice (D) is the
best answer: Recently, the price of crude oil has uctuated with the demand for gasoline in China.
This sample question gives you practice recognizing redundancy:
A recent survey of American colleges reveal that among some of the most selective universities
the acceptance rates have lowered by at least a 2 percent decrease over the last two years.
(A) reveal that among some of the most selective universities the acceptance rates have low-
ered by at least a 2 percent decrease over the last two years
(B) reveals that among some of the most selective universities the acceptance rates have low-
ered by at least a 2 percent decrease over the last two years
(C) reveal that among some of the most selective universities acceptance rates have decreased
by at least 2 percent over the last two years
(D) reveals that among some of the most selective universities acceptance rates have
decreased by at least 2 percent over the last two years
(E) reveals that among some of the most selective universities the acceptance rates have
decreased by at least a 2 percent margin over the last two years
As you examine the possible answers, rst notice you have the option of either reveal or reveals.
The subject is survey, so you can eliminate answers that provide the plural verb reveal. So Choices
(A) and (C) are out.
In Choice (B), the verb lowered is sucient to let you know that the rates have gone down; you
don’t also need to know that the rate was a percent decrease. The redundancy makes this answer
incorrect. Choice (E) eliminates the repetition of the decrease, but it introduces another redun-
dancy. If the rate decreased by a percentage, you don’t also need to know it decreased by a
margin.
The answer that corrects the verb agreement and eliminates redundant wording is Choice (D).
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 49
Follow the idiom: Correct use of standard
expressions
Idiomatic expressions are constructions English speakers use because, well, those are the expres-
sions they use. In other words, we use certain words in certain ways for no particular reason other
than because that’s the way we do it. However, even native English speakers often fail to use idi-
omatic expressions correctly. It’s common to hear people use further instead of farther when they
mean distance or less instead of fewer when they’re talking about the number of countable items.
The GMAT tests you on your knowledge of idiomatic expressions because sentences that are idi-
omatically incorrect can damage your credibility and interfere with the clarity of your message.
The only way to know idiomatic constructions is to memorize them. Luckily, you probably know
most of them already. To help you along, Table4-1 lists some commonly tested idioms and how
to use them correctly.
TABLE4-1 Idiomatically Correct Constructions for the GMAT
Expression Rule Correct Use
among/between Use among for comparing three or more
things or persons, between for two things
or persons.
Between the two of us there are few problems,
but among the four of us there is much discord.
as...as When you use as in a comparison, use the
construction of as...as.
The dog is as wide as he is tall.
being Don’t use being after regard as. She is regarded as the best salesperson on the
team. (Not: She is regarded as being the best
salesperson.)
better/best and
worse/worst
Use better and worse to compare two things,
best and worst to compare more than
two things.
Of the two products, the rst is better known,
but this product is the best known of all 20 on
the market.
but Don’t use but after doubt or help. He could not help liking the chartreuse curtains
with the mauve carpet. (Not: He could not help
but like the curtains.)
dierent from Use dierent from rather than dierent than. This plan is dierent from the one we
implemented last year. (Not: This plan is
dierent than last year’s.)
eect/aect Generally, use eect as a noun and aect
as a verb.
No one could know how the eect of the
presentation would aect the client’s choice.
farther/further Use farther to refer to distance and further to
refer to time or quantity.
Carol walked farther today than she did
yesterday, and she vows to further study the
benets of walking.
hopefully Hopefully is an adverb meaning with hope
and should never be used to mean I hope or
it is hoped.
I hope they oer me the managerial position.
(Not: Hopefully, they’ll oer me the managerial
position.)
however However used at the beginning of a sentence
(without a comma) means to whatever extent.
However they try to discourage his antics, he
continues to engage in oce pranks.
imply/infer Use imply to mean to suggest or indicate,
infer to mean deduce.
From his implication that the car was packed, I
inferred that it was time to leave.
in regard to Use in regard to rather than in regards to. The memo was in regard to the meeting we had
yesterday. (Not: The memo was in regards to
the meeting.)
(continued)
50 PART 2 Vanquishing the Verbal Section
In addition to the expressions listed in Table 4-1, you should also memorize the correlative
expressions in Table4-2, which shows you words that must appear together in the same sen-
tence. To maintain parallel structure, the elements that follow each component of the correlative
should be similar. Thus, if not only precedes a verb and direct object, the but also that follows it
should also precede a verb and direct object.
Here are a couple of examples of how you may see idioms tested on the GMAT:
Never before had American businesses confronted so many challenges as they did during the
Great Depression.
(A) so many challenges as they did during the Great Depression
(B) so many challenges at one time as they confronted during the Great Depression
(C) at once so many challenges as they confronted during the Great Depression
(D) as many challenges as it did during the Great Depression
(E) as many challenges as they did during the Great Depression
You’ve memorized that the proper comparison construction is as...as, so you know that the sen-
tence contains an idiomatically improper construction (it also probably sounds strange to you!).
Start by eliminating all answers that don’t correct so many...as to as...as. Choices (A), (B), and
(C) retain the improper construction, so cross them out.
Now consider Choices (D) and (E). Both maintain the original verb, which is ne. The sentence
compares two dierent periods of time. The rst portion of the sentence refers to the period
TABLE4-2 Correlative Expressions
Expression Example
not only...but also He not only had his cake but also ate it.
either...or Either do it my way or take the highway.
neither...nor Neither steaming locomotives nor wild horses can persuade me to change my mind.
Expression Rule Correct Use
less/fewer Use less to refer to unmeasured quantity,
fewer to refer to number.
That oce building is less noticeable because it
has fewer oors.
less/least Use less to compare two things and least to
compare more than two things.
He is less educated than his brother is, but he is
not the least educated of his entire family.
like/as Use like before simple nouns and pronouns,
as before phrases and clauses.
Like Ruth, Steve wanted the oce policy to be
just as it had always been.
loan/lend Use loan as a noun, lend as a verb. Betty asked Julia to lend her a car until she
received her loan.
many/much Use many to refer to number, much to refer
to unmeasured quantity.
For many days I woke up feeling much anxiety,
but I’m better now that I’m reading GMAT
For Dummies.
more/most Use more to compare two things, most to
compare more than two things.
Of the two girls, the older is more educated, and
she is the most educated person in her family.
try/come Try and come take the innitive form of a
subsequent verb.
Try to le it by tomorrow. (Not: Try and le it by
tomorrow.)
TABLE4-1(continued)
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 51
before the Great Depression, which requires the past perfect verb had...confronted. The under-
lined part of the sentence simply requires the past tense verb did to maintain the proper tense.
Choice (D) creates a new error in pronoun agreement by using the singular pronoun it to refer to
the plural noun businesses. Choice (E) is the correct answer: Never before had American businesses
confronted as many challenges as they did during the Great Depression.
Experts agree that good health may result from following a regimen that includes consuming
less fat and calories.
(A) includes consuming less fat and calories
(B) includes the consumption of less fat and calories
(C) includes consuming less fat and fewer calories
(D) including the consumption of less fat and calories
(E) including consuming fewer fats and calories
For a single quantity, use less; use fewer for plural nouns. So the proper construction is less fat and
fewer calories. Choices (A), (B), and (D) are incorrect because they apply the singular less to the
plural calories. Choice (C) corrects the issue by adding fewer before calories, and Choice (E) changes
fat to fats, so fewer appropriately applies to both plural nouns. Choice (E) is wrong, however,
because including doesn’t properly follow that. The correct answer is Choice (C).
Implementing an Approach to Sentence-
Correction Questions
The key to performing well on sentence-correction questions is to approach them
systematically:
1. Determine the nature of the original sentence’s error (if one exists).
If a sentence has more than one error, focus on one error at a time. If you can, come up with a
quick idea of how to x the error before you look at the answers.
2. Skim through the answer choices and eliminate any choices that don’t correct the error.
3. Eliminate answer choices that correct the original error but add a new error or errors.
You should be left with only one answer that xes the original problem without creating new
errors.
4. Reread the sentence with the new answer choice inserted just to make sure that you
haven’t missed something and that the answer you’ve chosen makes sense.
To show you how this process works, we’ll refer to this example question throughout the next few
sections.
Because the company is disorganized, they will never reach their goal.
(A) they will never reach their goal
(B) it will never reach their goal
(C) it will never reach its goal
(D) their goal will never be reached
(E) its goal will never be reached
52 PART 2 Vanquishing the Verbal Section
Spotting the error
When you read the sentence-correction question, pay particular attention to the underlined por-
tion and look for at least one error.
»
If the underlined section contains verbs, make sure they agree with their subjects and are in
the proper tense.
»
Check any pronouns to determine whether they agree in number with the nouns they refer to.
»
Look at lists to conrm that their construction is parallel.
»
Note any tricky idiomatic phrases to verify that they’re used correctly.
»
Look for repetitive and otherwise wordy language.
If you don’t see any obvious errors, read through the answer choices just to make sure they don’t
reveal something you may have missed. If you still don’t see a problem, choose the rst answer
choice. About 20 percent of the sentence-correction sentences contain no errors.
Don’t look for errors in the portion of the sentence that isn’t underlined. Even if you nd some-
thing, you can’t correct it!
The underlined portion of the sample question contains a verb (will reach), but it agrees with its
subject and is in the proper tense. There’s also a pronoun, they. They refers to company, but com-
pany is a singular noun and they is a plural pronoun. You can’t have a plural pronoun refer to a
singular noun. Therefore, the underlined section denitely has a pronoun agreement error.
Eliminating answers that don’t correct errors
If you spot an error in the underlined portion, read through the answer choices and eliminate
those that don’t correct it. If you see more than one error in the underlined portion of the state-
ment, begin with the error that has the more obvious correction. For example, if the underlined
portion has both a rhetorical error and an error in subject-verb agreement, begin with the error
in subject-verb agreement. Eliminating answer choices that don’t address the agreement prob-
lem is quick and easy. After you’ve eliminated the choices that don’t x the obvious error, move
on to the other error or errors. Comparing rhetorical constructions in answer choices can take a
while, so eliminating choices before this step saves you time.
After you’ve eliminated an answer choice, don’t reread it! Chapter2 gives you tips on how to
“erase” wrong answer choices. Follow the guidelines in Chapter 2 to avoid wasting time on
answers you’ve already determined are wrong.
You know the example problem has an error, so you can eliminate Choice (A). Now eliminate any
choices that don’t correct the incorrect pronoun reference. Choice (D) doesn’t; it still uses a plural
pronoun (their) to refer to a singular subject. Eliminate Choice (D), and don’t look at it again. The
other three choices, Choices (B), (C), and (E), seem to x that particular pronoun error.
The underlined portion contains another problem with noun-pronoun agreement, though. Their
in the original sentence is also plural but refers to the singular noun company. Although Choice
(B) makes the rst plural pronoun singular, it retains the second problem pronoun, so you can
eliminate Choice (B). Only Choices (C) and (E) remain.
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 53
Eliminating choices that create new errors
The next step is to eliminate answers that create new errors.
A new error in an answer choice usually isn’t the same type of error as the original one. GMAT
writers know you’ll look for pronoun errors if a pronoun error occurs in the original sentence, so
the new error in an answer choice may be an improper expression or a verb-tense problem.
Check the remaining answer choices for new errors. Choice (E) doesn’t contain an agreement
error, but it changes the underlined portion of the sentence to a passive construction. On sentence
corrections, active voice is always better than passive voice. Choice (C) is the answer that corrects
the pronoun problem without creating new errors.
You should end up with only one answer choice that corrects the existing errors without creating
new ones. If you end up with two seemingly correct answer choices, read them both within the
context of the original sentence. One will have an error that you’ve overlooked.
Rereading the sentence
Don’t skip this step! Check your answer by replacing the underlined portion with your answer
choice and reading the new sentence in its entirety. Don’t just check to see whether the answer
sounds good in the sentence; also check for errors that you may not have noticed as you worked
through the question.
Missing errors is easy when you focus only on the underlined portion of the statement. After you
integrate your answer choice with the rest of the sentence, errors you’ve missed may suddenly
become obvious. Reading the statement with your answer choice inserted is the best way to check
your answer.
When you reread the sentence with Choice (C), you get this: Because the company is disorganized, it
will never reach its goal. The corrected sentence contains the proper noun-pronoun agreement.
Reviewing the process and guessing on
sentence corrections
The approach outlined in this section works well as long as you have time to determine the error
in the sentence or recognize that no error exists. If you’re running short on time or can’t tell
whether the statement is correct as written, you may need to guess. Eliminate the choices you
know are wrong because they contain their own errors. Then read each of the possible choices in
the context of the entire statement. You may nd errors that you didn’t notice before. If you still
can’t narrow down your choices to one answer, pick one from the remaining answers and move on.
Sentence-Correction Practice Problems
with Answer Explanations
After you master the approach to sentence-correction questions, they’ll seem a lot less daunting.
To help you solidify your plan of attack, answer the following ten practice questions. Try to
answer them in ten minutes or less. When you’re nished, check your answers with the explana-
tions that follow.
54 PART 2 Vanquishing the Verbal Section
Practice problems
1. Most state governors now have the power of line item veto, while the U.S.President does not.
(A) while the U.S.President does not
(B) a power which is not yet available to the U.S.President
(C) which the U.S.President has no such power
(D) the U.S.President does not
(E) they do not share that with the U.S.President
2. Although all six state governments faced budget problems after the economic downturn of 2007, the
problems were worse in California because much of it revenue came from a large number of high-tech
industries.
(A) worse
(B) worst
(C) more
(D) great
(E) worsening
3. The PTA held monthly meetings to discuss matters concerning the schoolchildren, determine what fun-
draisers to implement, and for coming up with ways to balance the budget.
(A) and for coming up with ways to balance the budget
(B) and to balance the budget in creative ways
(C) and discovering ways to balance the budget
(D) and to determine how to come up with ways the budget should be balanced
(E) and come up with ways to balance the budget
4. Many tourists seem to be avoiding the Tijuana/Rosarito Beach area because they are experiencing an
upsurge in the occurrence of border violence.
(A) seem to be avoiding the Tijuana/Rosarito Beach area because they are experiencing an upsurge in
the occurrence of border violence
(B) seem to avoid the Tijuana/Rosarito Beach area because they are experiencing an upsurge of vio-
lence on the border
(C) avoid the Tijuana/Rosarito Beach area because they are experiencing an upsurge of border violence
occurrence
(D) seem to be avoiding the Tijuana/Rosarito Beach area because it is experiencing an upsurge in the
occurrence of border violence
(E) seem to be avoiding the Tijuana/Rosarito Beach area because it experiences an upsurge in the
occurrence of border violence
5. Historians believe that roughly 600 deaths have occurred at the Grand Canyon since the 1870s; many
resulted from drowning, plane crashes into canyon walls, and the actions of overzealous hikers.
(A) many resulted from drowning, plane crashes into canyon walls
(B) many of these resulting from drowning deaths, planes crashing into canyon walls
(C) many of these deaths being the results of drowning, plane crashes into canyon walls
(D) many of these were drowning deaths, plane crash deaths
(E) with many as a result from drowning, planes crashing into canyon walls
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 55
6. After Great America Bank incited public outrage with its announcement of new debit-card fees, many
customers withdrew their funds and joined credit unions instead, which seems as if to indicate that
America’s mistrust of big banks is still widespread.
(A) as if to indicate that
(B) indicative of
(C) like an indication of
(D) like it is indicative that
(E) to indicate that
7. Despite arguments made by parent watch-dog groups, neither violent behavior or disruptiveness have
been directly linked to violent video games.
(A) neither violent behavior or disruptiveness have been directly linked to violent video games
(B) neither violent behavior nor disruptiveness has been directly linked to violent video games
(C) neither violent behavior or disruptiveness has been directly linked to violent video games
(D) neither violent behavior nor disruptiveness have been directly linked to violent video games
(E) neither violent behavior nor disruptiveness were directly linked to violent video games
8. Russell & Carmody, LLC, and Rutledge, Inc., merged in 2012 to create Russell, Carmody and Rutledge,
Inc., and they are now the most successful public relations rm in the metro area.
(A) and they are now the most successful public relations rm in the metro area
(B) it is now the most successful public relations rm in the metro area
(C) and they are now the most successful public relations rms in the metro area
(D) which is now the most successful public relations rm in the metro area
(E) and it is now the most successful public relations rms in the metro area
9. A transaction-broker assists the buyer or seller or both throughout a real estate transaction by per-
forming terms of any written or oral agreement, fully informing the parties, presenting all oers, and
assisting the parties with any contracts, including the closing of the transaction, without being an agent
or advocate for any of the parties.
(A) throughout a real estate transaction by performing
(B) throughout a real estate transaction by the performance of
(C) during a real estate transaction by the performance of
(D) with a real estate transaction by accomplishing the performing
(E) during a real estate transaction through the performance of
10. Although its policy for honorary doctorates was not dissimilar to Cambridge or Oxford— they gave
awards to the “distinguished” in particular elds, and the person had to be “widely recognized”— it is
clear that the universities were drawn to the entertainment industries to produce visible personalities
for their convocation ceremonies, and the idea of “widely recognized” trumped any other distinction.
(A) its policy for honorary doctorates was not dissimilar to
(B) their policies for awarding honorary doctorates were not dissimilar to those of
(C) their policies for honorary doctorates was not dissimilar from
(D) its policy for honorary doctorates was very similar to
(E) its policies for awarding honorary doctorates was very similar to that of
56 PART 2 Vanquishing the Verbal Section
Answer explanations
1. A. Always begin by trying to identify the error in the underlined portion of the statement.
The underlined words don’t contain any pronouns and the subject and verb agree, so you
don’t have any agreement errors. Parallel construction doesn’t seem to be an issue. The use
of while to mean although may have alerted you. However, while the primary purpose of
while is to indicate an event that happens at the same time as another, you may also use
while to mean although. In fact, we just used it that way in the previous sentence!
This question doesn’t seem to have an error. But just to be sure, read each answer choice to
make sure you haven’t missed something. Choice (B) is wrong because it uses which instead
of that to introduce a restrictive clause, and the pronoun which in Choice (C) has no clear
reference. You can’t use Choice (D) or Choice (E) because they’re independent clauses.
Plugging in either of these choices creates a comma splice. None of the answer choices oer
a better construction for the sentence.
Remember that about 20 percent of the time, the underlined part contains no error. Don’t
assume that the sentences always contain errors.
2. B. This example has only one underlined word, which is nice because you know just what to
focus on. If you simply go by what sounds right, you may think this example is ne the way
it is. You probably hear English speakers use worse like this in everyday conversations. But
the GMAT doesn’t test common spoken English; it tests standard written English.
You use worse to compare two entities and worst to compare three or more.
The sentence talks about a situation among several state governments. Worse would be
appropriate for a comparison between two states. But this sentence compares budget
problems in six states, so instead use the superlative form worst to single out poor Califor-
nia. That’s the answer you nd in Choice (B).
You can double-check your answer by reading through the other choices. You’ve found an
error, so Choice (A) can’t be right. Choices (C) and (D) aren’t superlatives, and Choice (E)
uses the progressive form were worsening, which changes the meaning of the sentence.
3. E. The underlined words are part of a series, so adjust your error antennae to feel out a
parallelism problem. Check the grammatical construction of each element. The underlined
portion contains the gerund form coming, but the other two PTA purposes are expressed in
the innitive form. All three reasons should be in the same form. Both Choices (A) and (C)
use the -ing form, so they can’t be right. Choice (D) is unnecessarily wordy, so now you
know the correct answer must be either Choice (B) or Choice (E). Both choices properly use
the innitive form, but Choice (B) unnecessarily repeats to and it adds information to the
original sentence.
4. D. The underlined portion is lengthy, so use your powers of concentration to home in on
the potential errors. You see a couple verbs and the pronoun they. Check the pronoun rst.
Whenever you see an underlined pronoun, check its reference to make sure it’s clear and
that it agrees in number with the noun.
CHAPTER 4 Applying What You Learned (We Hope) in Grammar Class: Sentence Correction 57
The pronoun they is plural, but the only plural noun in the sentence is tourists. It doesn’t
make sense that tourists would be experiencing an upsurge in the occurrence of border
violence. It’s more likely that they refers to the beach area, which is experiencing increased
violence. Only one area is mentioned, so the pronoun should be singular, it. That narrows
your choices considerably. The only two answers that change they to it are Choices (D) and
(E). The dierence between the two is that Choice (E) changes the verb tense to the simple
present. The upsurge is ongoing, so the original progressive tense in Choice (D) is better.
5. A. The rst thing you likely notice about the underlined part is that it contains a series of
causes of Grand Canyon deaths. An underlined series means check for parallel structure.
Each cause is presented as a noun, so there isn’t a blatant problem with parallelism. Some
of the answer choices change plane crashes to planes crashing to match drowning, but they
introduce new errors. Choices (B), (C), and (E) create sentence fragments, which don’t work
with the semicolon. The semicolon has to be followed by an independent clause. Choice (D)
unnecessarily repeats deaths. It doesn’t make sense to say the deaths result from drowning
deaths. The best answer is to leave this one exactly as it is.
6. E. To say that something seems as if to is improper, so Choice (A) is out. You can eliminate
Choices (B) and (C) as well, because their use of of doesn’t t with the rest of the sentence.
You use like to compare simple nouns, and Choice (D) improperly uses like to compare which
to the clause it is indicative. The best answer has to be Choice (E). It gets rid of as if without
creating another error.
7. B. The original sentence contains both a conjunction error and a subject-verb agreement
error.
Whenever you see neither, you must also see nor. Neither Choice (A) nor Choice (C) pairs nor
with neither. Eliminate them.
You’re left with Choices (B), (D), and (E). The verbs in these three choices are dierent.
Choice (B) contains a singular verb, and the other two have plural verbs. The subject of the
clause is neither, and neither is singular. Therefore, Choice (B) has to be correct because it
contains the singular verb.
8. D. This sentence-correction question involves a commonly tested pronoun reference
problem. Although the sentence initially refers to two separate companies, it then states
that they merged into one rm, so the correct pronoun to use when referring to only one
company is it. Therefore, you can eliminate Choices (A) and (C). Choice (E) contains the
proper pronoun, it, but refers to the new company in the plural, rms, so you can cross that
one out as well. You’re left with Choices (B) and (D), but Choice (B) creates a comma splice
because it’s an independent clause.
9. A. To maintain parallel structure in the sentence’s list, you need to begin the rst element
with an –ing word, so performing is a better choice than “the performance of.” You can
eliminate Choices (B), (C), and (E). Choice (D) contains performing, but it also adds the
redundant accomplishing. Performing the terms of an agreement is the same as accomplish-
ing them. So, the best answer is Choice (A). The dierent options for the initial preposition
in the answer choices are included to distract you from the real error. Each of them works
in the context of the sentence.
58 PART 2 Vanquishing the Verbal Section
10. B. The answer choices provide you with either the pronoun its or their. Search the sentence
to nd the noun the pronoun references. The policies belong to the plural universities, so
you need the plural pronoun their. Eliminate Choices (A), (D), and (E).
When you examine the dierence between the remaining answers, you see that Choice (B)
includes awarding and inserts “those of” in the comparison between the policies of the
universities in the second part of the sentence and Cambridge or Oxford in the rst part.
Because you can’t compare policies to Cambridge (as in Choice [C]) but must compare policies
to policies, you need to add “those of” as provided by Choice (B). Choice (C) is also wrong
because it’s idiomatically incorrect to say that something is “dissimilar from” another
thing and because the singular verb was is improperly paired with the plural subject policies.
CHAPTER5 Not as Enticing as a Bestseller: Reading Comprehension 59
IN THIS CHAPTER
» Getting familiar with the format of
reading-comprehension questions
» Reading through passages
eciently
» Taking a look at the kinds of
passages that appear on the GMAT
» Checking out the types of reading
questions
Not as Enticing as a
Bestseller: Reading
Comprehension
I
f you nd yourself reading approximately 350 words about white dwarfs in space, you’re not
encountering a sci- fable about the seven companions of an astronomical Snow White. You’re
more likely tackling a reading-comprehension problem on the GMAT.The GMAT test-makers
present yet another way to poke and prod your intellect with several paragraphs of fascinating
reading material and a few questions to test your comprehension of it. The questions may be
specic and focus on highlighted portions of the passage, or they may concern general themes,
like the author’s main idea.
Reading-comprehension questions are designed to test how well you understand unfamiliar
reading material. But you’re probably less concerned with the reason these passages are included
on the GMAT than you are with getting through all that reading and question-answering with
enough time left over to confront those pesky sentence-correction and critical-reasoning prob-
lems. What you need is a proven strategy. And in this chapter, we deliver by introducing you to
the types of passages and questions you’ll encounter and telling you how to deal with them.
Judging by Appearances: What Reading-
Comprehension Questions Look Like
The verbal section of the GMAT mixes reading-comprehension questions with critical-reasoning
questions and sentence-correction questions. So you may correct grammatical errors in a few
sentences and then come across a set of reading-comprehension questions. About one-third of
the 41 questions in the verbal section are reading questions. You’ll see a split screen with an
article passage on the left and a question with ve answer choices on the right.
Chapter5
60 PART 2 Vanquishing the Verbal Section
Although every passage has more than one question (usually, passages have about ve to eight
questions), only one question pops up at a time. You read the passage (which contains about
350words), click on the choice that best answers the question, and conrm your answer. As soon
as you conrm your answer, another question pops up on the right side of the screen. The passage
remains on the left. Sometimes a question refers to a particular part of the passage. For these
questions, the GMAT highlights the portion of the passage you need to focus on to answer the
question.
Approaching Reading Passages
Reading-comprehension questions don’t ask you to do anything particularly unfamiliar. You’ve
probably been reading passages and answering multiple-choice questions about them since you
were in elementary school. If you’re having diculty answering reading-comprehension ques-
tions correctly, don’t worry: Your reading skills are likely ne. You’re probably just not familiar
with the specic way you have to read for the GMAT.
You have less than two minutes to answer each reading-comprehension question, and that
includes reading the passage. Generally, you shouldn’t spend more than ve minutes reading a
passage before you answer its questions, so you have to read as eciently as you can. You need a
plan for getting through the passage in a way that allows you to answer questions correctly and
quickly. When you read a passage, focus on the following elements:
»
The passage’s general theme
»
The author’s tone
»
The way the author organizes the passage
Unless you have a photographic memory, you won’t be able to remember all a passage’s details
long enough to answer the questions. Don’t try to gure out the passage’s minutiae while you’re
reading it. If you encounter a question about a little detail, you can go back and reread the relevant
section. Instead of sweating the small stu, make sure you understand the author’s main point,
the author’s tone, and the overall way the author presents the information.
Mastering the message: The main point
Generally, people write passages to inform or persuade. Most of the passages on the GMAT are
informative rather than argumentative, and even the argumentative ones are pretty tame.
The main point of GMAT passages is often to discuss a topic, to inform the reader about a phenomenon,
or to compare one idea to another. Rarely does a GMAT passage seek to condemn, criticize, or enthu-
siastically advocate a particular idea or position.
Because most authors present the main theme in the rst paragraph or two, you’ll probably
gure it out in the rst few seconds of your reading. If it’s not clear in the rst paragraphs, it
probably appears in the last paragraph, where the author sums up the ideas. After you’ve gured
out the author’s overall theme, quickly jot down on your noteboard a word or two to help you
remember the theme. For a passage that describes the dierences between the ight patterns of
houseies and horseies, you can write compare ight — house/horse. Your notation gives you
something to refer to when you’re asked the inevitable main theme synthesis question (which we
discuss in greater detail in the later section “Getting to the point: Main-theme questions”).
CHAPTER 5 Not as Enticing as a Bestseller: Reading Comprehension 61
Absorbing the ambiance: Author’s tone
In addition to understanding the author’s main point, you need to know how the author feels
about the issue. You get clues to the author’s tone or mood by the words he uses. GMAT passages
either inform the reader about something or try to persuade the reader to adopt the author’s
viewpoint. Informative passages are often more objective than persuasive ones, so the author’s
tone is usually neutral. Authors of persuasive passages may exhibit more emotion. You may sense
that an author is critical, sarcastic, pessimistic, optimistic, or supportive. When you gure out
how the author feels about the topic, write a short description on your noteboard, like objective,
hopeful, or mildly critical. Knowing the tone of a passage helps you choose answers that exhibit the
same tone or level of bias.
Regardless of the author’s mood, don’t let your personal opinions about a passage’s subject mat-
ter inuence your answer. Getting emotionally involved with the content of the passage can cloud
your judgment. You may subconsciously rely on your opinions as you answer questions. To avoid
doing so, you may nd it helpful to remind yourself that correct answers are true according to the
passage or according to the author.
Finding the framework: The passage’s outline
Knowing the structure of a passage is much more important than understanding its details.
Instead of trying to comprehend everything the author says, focus on how the author lays out the
information.
Standard essay format includes an introduction with a thesis, two or three supporting para-
graphs, and a conclusion. Many GMAT passages are excerpts from larger works, so they may not
exhibit exact standard essay form, but they’ll contain evidence of all three elements. As you read,
determine the passage’s overall point and the main points of each paragraph.
You may nd it helpful to construct a mini-outline of the passage as you read it. Underneath the
main theme, jot down a word or two on your noteboard that describes the type of information
contained in each paragraph. So under compare ight— house/horse, you may list a synopsis of
each supporting paragraph: dierence in wingspan, size dierence— horse 3x bigger, ways ight helps
house. This outline tells you that in the rst supporting paragraph, you nd info about how the
two ies dier in wingspan. The second supporting paragraph is where you nd out how the
greater size of horseies aects their ight. And from the third supporting paragraph, you nd
out how the housey’s ight helps it in everyday life. Although you may not understand all the
fascinating details of the author’s account, you know where to go in the passage if you have to
answer a detail question.
Building an outline in your head or on your noteboard helps you know where in the passage you
can nd answers to questions about particular details. Doing so also helps you answer any ques-
tions that ask you how an author develops his point.
Even though you don’t need to read and understand every detail of a passage before you answer
its questions, we highly recommend that you scan the entire passage before you attempt the
questions. You need an idea of what a passage is about and how it’s organized before you look at
the questions. Any minutes you save by not reading the passage rst will be wasted when you
have to read and reread paragraphs because you don’t know where information is located or what
the passage is about.
62 PART 2 Vanquishing the Verbal Section
Sticking to the Subject: Types of Passages
You may think that because the GMAT measures your aptitude for MBA programs, its reading
passages deal with subjects like marketing and economics. You’re wrong. Although some of the
passages do concern business matters, you’ll also read about topics from the natural and social
sciences. The GMAT wants to see how well you analyze a variety of topics, unfamiliar and famil-
iar, so it presents you with articles about everything from the steel-making process to the quality
of artifacts from the Bronze Age.
In the following sections, we explore the types of reading passages found on the GMAT.
Experimenting with natural science passages
Physical and biological sciences mean big business. Some of the areas of commerce that depend
on science include pharmaceuticals, computers, agriculture, the defense industry, household
products, and materials manufacturing (such as plastics and polymers). These industries, taken
together, exert a huge inuence on American quality of life and the nation’s bottom line. Just
think of this country without computers and pharmaceuticals, not to mention modern
agriculture!
Although you may concede that the natural sciences are important, you may not be eager to
confront a chemistry passage halfway through the GMAT verbal section. The good news is that
the reading-comprehension questions don’t assume that you have any previous knowledge in
thesubject. If you do come across a reading passage on chemistry and it’s been 20 years since
you’ve studied the periodic table, relax. The answer to every question is located somewhere in the
passage.
You really don’t need to know a lot about a passage topic to answer the questions correctly.
Although it’s true that a chemistry major may read a passage about polymers more quickly than
someone who never took a college chemistry course, that doesn’t necessarily mean the chemistry
expert will answer more questions correctly. The chemistry major may actually be at a disadvan-
tage because he may try to answer questions based on outside knowledge instead of using only
the information stated in the passage.
Reading-comprehension questions test your reading skills, not the plethora of details you keep
tucked away in your long-term memory. When you come across a passage on a subject that you’re
familiar with, don’t rely on your outside knowledge to answer the question! Make sure the
answers you choose can be justied by information contained in the passage.
Natural science passages tend to be more objective and neutral than persuasive in tone. So usually
the main theme of a natural science topic is to explain, describe, or inform about a scientic event.
Gathering in social circles:
Social science passages
In addition to natural science passages, the GMAT presents passages about a dierent kind of
science: social science, which includes topics like law, philosophy, history, political science,
archeology, sociology, and psychology. The good news about social science passages is that their
topics tend to crop up more in the news and in daily conversation than does, for example, physics!
So you’re more likely to be comfortable, if not necessarily familiar, with them.
CHAPTER 5 Not as Enticing as a Bestseller: Reading Comprehension 63
Although passages about the social sciences are still mostly descriptive and informative, they’re
more likely to be persuasive than natural science passages, so you may see more variety in the
kinds of tones these passages display.
Getting down to business passages
Business passages may be objective or persuasive and are generated from elds like economics,
marketing, resource management, and accounting, among others. Finally, topics you’re familiar
with! You can forgo the archeology of New Zealand or an anatomy lesson on the long-horned
beetle. This is business, your chosen eld of study. At least it’s a topic you’re clearly interested in.
You’ll probably breeze right through most of these passages. But don’t let familiarity with the topic
serve as an excuse to slack o. You need your powers of concentration for every passage topic.
If the passage is on a familiar subject, don’t fall into the trap of using your own information to
answer questions. Being familiar with a passage topic is an advantage, but only if you approach
each question reminding yourself that the correct answer is based on information in the passage
and not on what you studied last semester in your marketing courses or discussed last week in
your sales meeting.
Approaching Reading-Comprehension
Questions
The GMAT verbal section has 41 questions, and you’re allotted 75 minutes to answer them. That
comes out to less than two minutes per question. If you spend too much time answering reading-
comprehension questions, you’ll have less time to consider the sentence-correction and critical-
reasoning questions that also comprise the verbal section. So having a system for tackling
reading-comprehension questions is just as important as knowing how to read through the pas-
sages. Your approach should include
»
Recognizing the type of question
»
Quickly eliminating incorrect answer choices
»
Managing questions that ask for the answer that isn’t supported by the passage
We show you how to do all three of these things in the following sections and provide a few
examples of what to look for so you know how to answer the questions correctly.
Identifying the question type
The rst step in answering a reading-comprehension question correctly is identifying the type of
question. Most reading-comprehension questions fall into one of these four categories:
»
Summarizing the main theme
»
Finding specic information
»
Making inferences
»
Assessing the author’s tone
64 PART 2 Vanquishing the Verbal Section
Each of the four question types requires a slightly dierent approach. Main theme and tone ques-
tions ask you to make determinations about the passage as a whole, and specic-information and
inference questions usually ask you to home in on particular parts of the passage. For example,
when you know that a question is about specic details in the passage, you can focus your atten-
tion on the portion of the passage that’s relevant to the information in the question.
We share all the details about each of the four categories of reading-comprehension questions in
the following sections.
Getting to the point: Main-theme questions
Main-theme questions ask you to identify the primary purpose of the whole passage. Almost
every passage has at least one question that asks you to identify the thesis of the passage, and
often it’s the rst question you answer for a particular reading passage.
You can identify main-theme questions by the language they contain. Here are some examples of
the ways main-theme questions may be worded:
»
The author of the passage is primarily concerned with which of the following?
»
The author’s primary goal (or purpose) in the passage is to do which of the following?
»
An appropriate title that best summarizes this passage is
While you read the passage, look for its main theme because you know you’ll probably be asked
about it. You may even want to write a sentence that briey states the passage’s primary purpose.
Then, if you’re asked a question about the passage’s main theme, you’ll look for an answer that
conveys an idea similar to your statement of the author’s purpose.
The best answer to a main-theme question is general rather than specic. If an answer choice
concerns information that’s discussed in only one part of the passage, it probably isn’t the correct
answer to a main-theme question. Here are some other ways to narrow in on the correct answer
for main-theme questions:
»
Eliminate answer choices that contain information that comes only from only the middle
paragraphs of the passage. These paragraphs probably deal with specic points rather than
the main theme.
»
Eliminate any answer choices that contain information that you can’t nd in the passage.
These choices are irrelevant.
»
Look at the rst words of the answer choices to see whether you can eliminate any answer
choices based on the rst words only. For example, if you’re trying to nd the best answer to
the author’s purpose in an objectively written natural science passage, you can eliminate
answers that begin with less objective terms, such as to argue that ..., to criticize ..., and to
refute the opposition’s position that....
Finding the details: Specic-information questions
Some GMAT reading-comprehension questions ask you about specic statements in the passage.
These questions are potentially the easiest type of reading-comprehension question because the
information you need to answer them is stated in the passage. You just need to nd it. This infor-
mation may be quantitative, such as years, gures, or numbers, or it may be qualitative, like
ideas, emotions, or thoughts.
CHAPTER 5 Not as Enticing as a Bestseller: Reading Comprehension 65
Specic-information questions are worded in many dierent ways, but they almost always con-
tain some reference to the passage. For example:
»
The passage states that ...
»
According to the passage, ...
»
In the passage, the author indicates that ...
To succeed on specic-information questions, read the question carefully and refer to the outline
of the passage you’ve written on your noteboard to remind you where the passage addresses cer-
tain types of information. And keep in mind that the correct answer may paraphrase the passage
rather than provide a word-for-word repeat.
Reading between the lines: Inference questions
Inference questions ask you about information that’s implied by the passage rather than directly
stated. These questions test your ability to draw conclusions, using evidence that appears in the
passage. For inference questions, you’re normally required to do one of these three things:
»
Identify a dierent interpretation of an author’s statement.
»
Infer the intended meaning of a word that’s used guratively in the passage.
»
Interpret the author’s statements one step beyond what is actually written.
For example, suppose you read a passage that compares the rapidity of wing beats between
houseies and horseies. Information in the second paragraph may state that the wings of horse-
ies beat at 96 bps (beats per second). Information in the fourth paragraph may say that a Purple
Winger is a type of horsey. From this information, you can infer that the wings of the Purple
Winger beat at a rate of 96 bps. This is an example of the third bullet: taking the author’s state-
ments one step beyond what is actually written. Note that the horsey conclusion doesn’t require
that you make great leaps of logic.
When you’re answering an inference question, look for the choice that slightly extends the mean-
ing of the passage. Choices that go beyond the scope of the passage are usually incorrect. Don’t
choose an answer that requires you to come up with information that isn’t somehow addressed
by the passage.
Sometimes knowing a great deal about a passage’s topic can be a detriment, because you may be
tempted to answer questions based on your own knowledge rather than the passage itself. Simply
answer the questions as they’re asked, and make inferences that can be justied by information
in the passage.
The GMAT loves inference questions, so expect to see a lot of them. They’re easily recognizable
because they usually contain either infer or imply in the question, like these examples:
»
It can be inferred from the passage that ...
»
The passage implies (or suggests) that ...
»
The author brings up...to imply which of the following?
Sometimes, the GMAT highlights in yellow the portion of the passage that discusses the material
in question. If the test highlights information for you, it’s likely an inference question rather than
a specic information type.
66 PART 2 Vanquishing the Verbal Section
Feeling moody: Questions about the author’s tone and style
As you read the passage, be sure to look for clues to the author’s tone as well as her purpose.
You’re bound to see questions that ask you to gauge how the author feels about the topic. Tone
and style questions commonly ask you to gure out the author’s attitude or complete the logical
ow of the author’s ideas. The author may be neutral, negative, or positive and may have dier-
ent attitudes about dierent types of information within the same passage. It’s up to you to
determine the nature and degree of the author’s feeling from the language used in the passage.
With practice, you’ll gure out how to distinguish between an enthusiastic author and one who’s
faking enthusiasm to mock the subject of the passage.
You can recognize questions about tone and style by the way they’re worded. Here are some
examples of how tone and style questions may appear on the GMAT:
»
The author’s attitude appears to be one of ...
»
With which of the following statements would the author most likely agree?
»
The tone of the passage suggests that the author is most skeptical about which of the
following?
When making determinations about the author’s style and tone, consider the passage as a whole.
You may nd one or two examples of negative comments in an article that is otherwise over-
whelmingly positive about a subject. Don’t make the mistake of quickly categorizing the passage
from a few words that happen to catch your attention. Instead, determine the main idea of the
passage and the author’s purpose (you need to do this to answer other questions, anyway) and
use that information to help you discern the author’s style and tone. For example, if an author’s
purpose is to argue against a particular point of view, critical words regarding the proponents of
that viewpoint reveal an overall critical attitude. However, you wouldn’t say the same about an
author of a passage that supports a viewpoint overall but includes one or two criticisms about
some supporters of the viewpoint.
Style and tone questions may point you to a specic portion of a passage, or they may be about
the entire passage. Even if a question does reference a specic part of the text, it’ll do so in rela-
tion to the passage as a whole. For example, you can usually answer a question that asks you why
an author chose to use certain words in a particular sentence only within the context of the entire
passage. So if you know the main idea, author’s purpose, and tone of the entire passage, you
should be able to eectively deal with questions about the use of a particular word or phrase in
one part of the passage.
Eliminating answer choices
One of the most eective ways of moving through reading-comprehension questions is to elimi-
nate incorrect answer choices. That’s because you’re looking for the best answer choice, not
necessarily the perfect answer choice. Sometimes, you’ll have to choose the best choice out of ve
pretty great choices, and other times you’ll choose from ve really crummy ones. Because the
denitive answer usually won’t pop right out at you, you have to know how to eliminate obviously
wrong choices. Chapter2 gives you general tips for eliminating answer choices. In this section,
we show you how to apply those techniques specically to reading-comprehension questions.
Much of the time, you can eliminate wrong choices without having to refer back to the passage.
As long as you carefully read the passage and have a good idea of the main theme, the author’s
purpose in writing the selection, and the author’s style or tone, you should be able to recognize
some wrong answers immediately.
CHAPTER 5 Not as Enticing as a Bestseller: Reading Comprehension 67
Some common wrong answers include the following:
»
Choices that concern information that isn’t found in the passage: Some answer choices
contain information that’s beyond the scope of the passage. Even if the information in these
choices is true, you can’t choose them. You have to choose answers based on what’s stated or
implied in the passage. Eliminate these choices, no matter how tempting they may be.
»
Choices that contradict the main theme, author’s tone, or specic information in the
passage: After you’ve read through the passage, you should be able to quickly eliminate most
of the choices that contradict what you know about the passage.
»
Choices that counter the wording of the question: You can also eliminate some answer
choices by paying careful attention to the wording of the question. For example, a question
may ask about a disadvantage of something discussed in the passage. If one of the answer
choices lists an advantage instead of a disadvantage, you can eliminate that choice without
thinking too much about it. Or a question may ask you to choose which answer the author is
most optimistic about. If one of the things listed is something the author is negative about, you
can eliminate that choice.
The GMAT may try to entice you with answer choices that deal with information directly stated
in the passage but don’t relate to the actual question at hand. Don’t choose an answer just
because it looks familiar. Make sure it actually answers the question.
»
Choices that contain debatable words: Question any answer choice that uses absolutes.
Examples are all, always, only, complete, rst, never, every, and none. An answer choice that
contains a word that leaves no room for exception is probably wrong. The GMAT makers don’t
want you calling them up complaining that you know of a circumstance where, say, not all re
engines are red. Beware: Usually the rest of an answer choice that includes a debatable word
sounds pretty good, so you may be tempted to choose it.
Don’t automatically eliminate an answer choice that contains a debatable word. If information
in the passage justies the presence of all or none in an answer choice, it may be right. For
example, if a passage tells you that all horseies beat their wings at a rate of 96 bps, the choice
with all in it may be accurate.
Dealing with exception questions
Most questions ask you to choose the one correct answer, but some questions are cleverly dis-
guised to ask for the one false answer. We call these gems exception questions. You’ll recognize
these questions by the presence of a negative word, usually except or not. When you see these
words capitalized in a question, you know you’re looking for the one answer choice that doesn’t
satisfy the requirements of the question.
You won’t see many exception questions on the GMAT, but when you do see that negative word,
take a moment to make sure you know exactly what the question is asking. Don’t get confused or
rush and automatically choose the rst choice that looks good. Remember: The question is asking
for the one answer out of ve that’s false or not part of the information stated or implied in the
passage.
Exception questions aren’t that dicult if you approach them systematically. Determining that
an answer denitely isn’t discussed in the passage takes time. You have to carefully look through
the passage for the choice and not nd it— then check again just to be sure. But a better way does
exist: Instead of determining that an answer isn’t discussed, eliminate the four true answers,
which leaves you with the one false (and, therefore, correct) answer.
68 PART 2 Vanquishing the Verbal Section
Identifying those choices that do appear in the passage is much easier than determining the one
choice that isn’t in the passage. After you’ve identied the four correct answers (remember to use
your erasable noteboard to keep track), you can click on the one false answer as the choice for that
question.
Take a look at two exception questions based on a fairly dicult natural science passage.
This passage is excerpted from The Earth Through Time, 7th Edition, by Harold L.Levin (Wiley):
Geologists have proposed the term eon for the largest divisions of the geologic time scale.
In chronologic succession, the eons of geologic time are the Hadean, Archean, Proterozoic, and
Phanerozoic. The beginning of the Archean corresponds approximately to the ages of the oldest
known rocks on Earth. Although not universally used, the term Hadean refers to that period of
time for which we have no rock record, which began with the origin of the planet 4.6 billion
years ago. The Proterozoic Eon refers to the time interval from 2,500 to 544 million years ago.
The rocks of the Archean and Proterozoic are informally referred to as Precambrian. The
antiquity of Precambrian rocks was recognized in the mid-1700s by Johann G.Lehman, a pro-
fessor of mineralogy in Berlin, who referred to them as the “Primary Series.” One frequently
nds this term in the writing of French and Italian geologists who were contemporaries of
Lehman. In 1833, the term appeared again when Lyell used it in his formation of a surpris-
ingly modern geologic time scale. Lyell and his predecessors recognized these “primary” rocks
by their crystalline character and took their uppermost boundary to be an unconformity that
separated them from the overlying— and therefore younger— fossiliferous strata.
The remainder of geologic time is included in the Phanerozoic Eon. As a result of careful
study of the superposition of rock bodies accompanied by correlations based on the abundant
fossil record of the Phanerozoic, geologists have divided it into three major subdivisions, termed
eras. The oldest is the Paleozoic Era, which we now know lasted about 300 million years. Follow-
ing the Paleozoic is the Mesozoic Era, which continued for about 179 million years. The Cenozoic
Era, in which we are now living, began about 65 million years ago.
The passage uses all the following terms to describe eons or eras, except
(A) Archean
(B) Paleozoic
(C) Holocene
(D) Phanerozoic
(E) Cenozoic
The terms in this passage may be unfamiliar to you, but if you read the passage carefully, you
should be able to get a general sense of what it’s talking about. For this exception question, which
tests you on unfamiliar terms, the best way to approach the question is to consult the text and
eliminate the four terms that it uses to describe eons or eras.
First, scan the answer choices so you have an idea of the words you’re looking for. Then begin at
the top of the passage and look for words that resemble the answer choices. You should be espe-
cially aware of any lists that occur in the text, because exception questions often focus on lists.
It’s very dicult for test-makers to come up with a good exception question without a list.
The passage contains three lists. The rst one appears in the rst paragraph. It names eons of
geologic time. The question refers to eons, and uses four terms that certainly resemble the answer
CHAPTER 5 Not as Enticing as a Bestseller: Reading Comprehension 69
choices. Consult this rst list and eliminate any choices that appear on it. The terms Archean and
Phanerozoic appear, so you can eliminate Choices (A) and (D). In the second paragraph, you see
the term Precambrian (which isn’t an answer choice) and a list of geologists who have mentioned
Precambrian rocks. The second paragraph doesn’t help with this question, so move quickly to the
third paragraph.
The third paragraph also provides a list of eras that are part of the Phanerozoic eon. In this list,
you see the terms Paleozoic, Mesozoic, and Cenozoic. Paleozoic is Choice (B), and Cenozoic is Choice
(E), so you can eliminate both of these terms. Therefore, the correct answer to this exception
question is Choice (C), Holocene, which isn’t mentioned in the passage and, in fact, is neither an
eon nor an era but the epoch in which you’re living!
Here’s another exception question based on the same passage.
Which of the following terms is not used in the passage to describe rocks that are more than
544 million years old?
(A) Precambrian
(B) Cenozoic
(C) Primary Series
(D) Archean
(E) Proterozoic
This question is more dicult because all the terms appear in the passage, but one of them
doesn’t apply to rocks that are more than 544 million years old. Begin in the same way you did
for the previous question, by scanning the answer choices so you know the kinds of words you’re
looking for.
When you nd a term, don’t automatically eliminate it. In this example, you must conrm that it
refers to rocks more than 544 million years old before you can cross it o.
The list in the second sentence of the rst paragraph doesn’t help because it has no corresponding
dates for the eons. The next sentence, however, says that Archean rocks are the “oldest known rocks
on Earth.” You can probably eliminate Choice (D), but keep reading to be sure. The last sentence of
the paragraph says that Proterozoic rocks are 544 million to 2,500 million (2.5 billion) years old.
And because Archean rocks are older than that, you can eliminate both Choices (D) and (E).
At the beginning of the second paragraph, you discover that both Archean and Proterozoic rocks
are referred to as Precambrian. Because both types of rock are older than 544 million years, you
can also eliminate Choice (A). Finally, in the very next sentence, you nd out that Precambrian
rocks are also called Primary Series rocks, so you can eliminate Choice (C). Choice (B) is the correct
answer.
You’d also know that Choice (B) is the correct answer if you happened to look at the last sentence
of the passage. That sentence tells you that the Cenozoic era started just 65 million years ago. The
question asks for the rocks that are not older than 544 million years. Clearly, Cenozoic rocks are,
at most, 65 million years old. So Choice (B) must be the one.
You can denitely skip the elimination process if you happen to stumble onto the right informa-
tion, but that haphazard method won’t work for all exception questions. You’re better o
approaching the question by eliminating the four answers that you nd in the passage or that
satisfy the criteria and locating the exception by process of elimination.
70 PART 2 Vanquishing the Verbal Section
Exception questions can take some time, but they’re among the easier reading-comprehension
questions because often the answers are right there in the text! So don’t get in a hurry and make
a mistake. Relax and use the proper approach, and you’ll do exceptionally well.
Reading-Comprehension Practice Questions
with Answer Explanations
To practice the approach to answering reading-comprehension questions, try your hand at these
practice questions. Read the passages and answer the questions, using the techniques we’ve dis-
cussed in this chapter. When you’re nished, read through the answer explanations that follow.
Reading-comprehension practice questions
In this practice section, we provide you with three passages, one of each of the subject types you’ll
see in the GMAT verbal-reasoning section. Try to answer the following ten questions within the
18-minute minimum average pace needed to nish all 41 verbal section questions before the
75minutes are up. For each question, choose the best answer from the ve options.
The GMAT won’t label answer choices with letters as we have here to make our explanations
easier to follow. To choose an answer on the computerized test, you’ll simply click on the oval
next to the choice.
Answer Questions 1–3 based on the following passage.
For most Americans and Europeans, this should be the best time in all of human history to
live. Survival— the very purpose of all life— is nearly guaranteed for large parts of the world,
especially in the “West.” This should allow people a sense of security and contentment. If life is
no longer as Thomas Hobbes famously wrote, “nasty, brutish, and short,” then should it not be
pleasant, dignied, and long? To know that tomorrow is nearly guaranteed, along with thousands
of additional tomorrows, should be enough to render hundreds of millions of people awe-struck
with happiness. And modern humans, especially in the West, have every opportunity to be free,
even as they enjoy ever-longer lives. Why is it, then, that so many people feel unhappy and
trapped? The answer lies in the constant pressure of trying to meet needs that don’t actually exist.
The term “need” has been used with less and less precision in modern life. Today, many
things are described as needs, including fashion items, SUVs, vacations, and other luxuries. People
say, “I need a new car,” when their current vehicle continues to function. People with many pairs
of shoes may still say they “need” a new pair. Clearly, this careless usage is inaccurate; neither
the new car nor the additional shoes are truly “needed.”
What is a need then? The Oxford English Dictionary denes the condition of “need” as
“lack of means of subsistence.” This denition points the way toward an understanding of
what a need truly is: A need is something required for survival. Therefore, the true needs of life
are air, food, water, and, in cold climates, shelter. Taken together, this is the stu of survival.
Because the purpose of life is to survive— or more broadly, to live— then these few modest
requirements are all that a modern human truly needs. Other things make life exciting or enjoy-
able, and these are often referred to as “the purpose of life”— but this is surely an exaggera-
tion. These additional trappings are mere wants and not true needs.
CHAPTER 5 Not as Enticing as a Bestseller: Reading Comprehension 71
1.
Which of the following most accurately states the main idea of the passage?
(A) Modern Americans and Europeans feel unhappy and trapped because they don’t distin-
guish true needs from mere wants.
(B) There are no human needs, and all so-called needs are merely wants.
(C) Human needs can never be satised in this life and, therefore, people will always be
unhappy.
(D) The satisfaction of human needs has resulted in nearly universal happiness for people in
the United States and Europe.
(E) There is no dierence between needs and wants; the desire for wealth and power is just as
real as the need for food and shelter.
2. According to the author, which of the following is an example of a fulllment of a need?
(A) Adding a roof to block moonlight from shining on a rudimentary sleeping structure built
on a tropical island
(B) Creating a pair of slippers from deer hide to protect one’s bare feet from being cut by
sharp rocks and stones
(C) Traveling several miles through dense foliage to obtain a particular berry, known for its
sweetness and antioxidant properties, to accompany one’s regular bland diet of rice and
beans
(D) Climbing a steep rock face for the exhilaration and sense of accomplishment
(E) Digging a hole to locate a new water supply after one’s prior single source of refreshment
has run out
3. Which of the following best denes the way the rst paragraph of the passage is organized?
(A) The author poses a question and provides context and then suggests an answer to the
question.
(B) The author presents an argument and develops that argument by referencing a famous
quote that reiterates the point that precedes it.
(C) The author presents an argument and then supports that argument by dening an essen-
tial term.
(D) The author compares life in one area of the world to life in another area of the world and
shows how one way of thinking about life is better than the other.
(E) The author poses a rhetorical question and explains why modern humans are incapable of
answering that question.
Answer Questions 4–6 based on the following passage.
A logarithmic unit known as the decibel (dB) is used to represent the intensity of sound.
The decibel scale is similar to the Richter scale used to measure earthquakes. On the Richter
scale, a 7.0 earthquake is ten times stronger than a 6.0 earthquake. On the decibel scale, an
increase of 10 dB is equivalent to a 10-fold increase in intensity or power. Thus, a sound regis-
tering 80 dB is ten times louder than a 70 dB sound. In the range of sounds audible to humans,
a whisper has an intensity of 20 dB; 140 dB (a jet aircraft taking o nearby) is the threshold of
immediate pain.
The perceived intensity of sound is not simply a function of volume; certain frequencies
of sound appear louder to the human ear than do other frequencies, even at the same volume.
Decibel measurements of noise are, therefore, often “A-weighted” to take into account the fact
that some sound wavelengths are perceived as being particularly loud. A soft whisper is 20 dB,
but on the A-weighted scale, the whisper is 30 dBA.This is because human ears are particularly
attuned to human speech. Quiet conversation has a sound level of about 60 dBA.
72 PART 2 Vanquishing the Verbal Section
Continuous exposure to sounds over 80 dBA can eventually result in mild hearing loss,
while exposure to louder sounds can cause much greater damage in a very short period of time.
Emergency sirens, motorcycles, chainsaws, construction activities, and other mechanical or
amplied noises are often in the 80 to 120 dBA range. Sound levels above 120 dBA begin to be
felt inside the human ear as discomfort and eventually as pain.
Unfortunately, the greatest damage to hearing is done voluntarily. Music, especially when
played through headphones, can grow to be deceptively loud. The ear becomes numbed by the
loud noise, and the listener often turns up the volume until the music approaches 120dBA. This
level of noise can cause permanent hearing loss in a short period of time, and in fact, many young
Americans now have a degree of hearing loss once seen only in much older persons.
4. The primary purpose of the passage is to
(A) argue for government mandates that decibel levels produced by headphones be reduced
(B) compare the scale used to measure intensity of sound to the scale used to measure the
strength of earthquakes
(C) describe the way that sound intensity is measured and explain its eect on human hearing
(D) dene which volume levels and sound exposure times are safe for humans and which are
harmful
(E) warn readers about the harmful eects of continuous exposure to sounds over 80 dBA
5. The author mentions that “emergency sirens, motorcycles, chainsaws, construction activities,
and other mechanical or amplied noises” fall in the 80 to 120 dBA range. It can be inferred
from this statement that these noises
(A) are unwanted, outside intrusions common in urban life
(B) can cause hearing loss with constant exposure
(C) are more dangerous to hearing than sounds of the same dBA level from headphones
(D) are loud enough to cause immediate pain
(E) have no negative impacts
6. The second paragraph of the passage states “Decibel measurements of noise are therefore often
‘A-weighted’ to take into account the fact that some sound wavelengths are perceived as being
particularly loud. A soft whisper is 20 dB, but on the A-weighted scale the whisper is 30 dBA.”
Therefore, for any particular sound, the A-weighted decibel level diers from the unweighted
decibel level in that
(A) the A-weighted number is 10 points higher than the unweighted number
(B) the A-weighted number is based on the way the noise is perceived in the human ear
(C) the unweighted number is always higher than the A-weighted number
(D) the A-weighted number is measured by more accurate instruments
(E) only on the unweighted scale does a 10 dB increase in sound equal a ten-fold increase in
intensity
Answer Questions 7–10 based on the following passage.
This passage is an excerpt from Microeconomics Theory and Applications, 9th Edition, by Edgar
K.Browning and Mark A.Zupan (Wiley):
In 1980, Washington, D.C., city ocials, hard-pressed for tax revenues, levied a 6 percent
tax on the sale of gasoline. As a rst approximation (and a reasonable one, it turns out), this tax
could be expected to increase the price of gasoline by 6 percent. The elasticity of demand is a
key factor in the consequences of this action, because the more sharply the sales of gasoline fall,
CHAPTER 5 Not as Enticing as a Bestseller: Reading Comprehension 73
the less tax revenue the city will raise. Presumably, city ocials hoped that gasoline sales would
be largely unaected by the higher price. Within a few months, however, the amount of gaso-
line sold had fallen by 33 percent.
1
A 6 percent price increase producing a 33percent quantity
reduction means the price elasticity was about 5.5.
The sharp sales drop meant that tax revenue was not increased. Further indications were
that when consumers had fully adjusted to the tax, tax revenues would actually decrease. (There
had been a 10 cent per gallon tax before the 6 percent tax was added, so although the 6 percent
levy was raising revenue, the gain was largely oset by the loss in revenue from the initial 10
cent tax following the reduction in sales.) This was not a general increase in gasoline prices but
a rise only within the D.C. city limits. Gasoline sold in the District of Columbia is a narrowly
dened product that has good substitutes— gasoline sold in nearby Virginia and Maryland.
Higher gasoline prices in the District of Columbia, when the prices charged in Virginia and
Maryland are unchanged, indicate high elasticity in the market.
No economist would be surprised at the results of this tax, but apparently city ocials
were. Observed one city councilman: “We think of ourselves here in the District as an island
to ourselves. But we’ve got to realize that we’re not. We’ve got to realize that Maryland and
Virginia are right out there, and there’s nothing to stop people from crossing over the line.”
The6percent gasoline tax was repealed ve months after it was levied.
7. The author is primarily concerned with doing which of the following?
(A) Arguing for increased gas taxes
(B) Arguing against increased gas taxes
(C) Ridiculing all local government ocials
(D) Advancing a particular ideology
(E) Explaining certain principles of supply and demand
8. It can be inferred from the passage that elasticity in the last sentence of the second paragraph
refers to
(A) uctuations in the price of gasoline in Washington, D.C.
(B) uctuations in the price of gasoline in Virginia and Maryland
(C) changes in the amount of tax collected at 6 percent
(D) changes in the number of vehicles in the region
(E) uctuations in the demand for gasoline sold in Washington, D.C.
9. For which of the following reasons does the second paragraph of the passage mention the origi-
nal gas tax of 10 cents per gallon?
(A) To show that Washington, D.C., residents were already overtaxed
(B) To distinguish between a straight 10 cent per gallon tax and a percent tax
(C) To explain why residents should not be subjected to dierent kinds of taxes
(D) To contrast the 10 cent tax that was included in the pump price and the 6 percent sales
tax that was added after the sale
(E) To show that with a sucient decrease in gasoline sales, the city would actually lose
money despite the higher tax
1
“Barry Asks Gasoline Tax Repeal,” Washington Post, November 2, 1980, p. A1.
74 PART 2 Vanquishing the Verbal Section
10. The passage suggests that a reason the tax increase failed to raise tax revenues in the District of
Columbia is that
(A) District of Columbia consumers decreased the amount of fuel they purchased and limited
their overall vehicle usage
(B) the amount of gas consumed by District of Columbia residents in their commute to nearby
states was suciently negligible to justify purchasing fuel outside the city limits
(C) consumers in the District of Columbia were upset that city council members would
decrease fuel taxes to increase tax revenues
(D) as a result of the tax increase, residents of Virginia and Maryland discontinued making
gas purchases in the District of Columbia
(E) District of Columbia city council members failed to convince legislators in nearby states to
increase their fuel taxes
Answer explanations
1. A. First, identify the question type. This one’s pretty easy because it contains the phrase
main idea right in the question. You’re dealing with a main-theme question, so the answer
concerns the general idea and purpose of the passage and is probably found in the rst or
last paragraphs of the passage.
Eliminate any choices that go beyond the scope of the information discussed in the passage.
You recall that the passage distinguished true needs from mere wants. Choice (C) says,
“Human needs can never be satised in this life....” The reading passage never mentions
anything about needs not being satised in this life. You may or may not agree with the
statement in Choice (C), but you can eliminate it because it discusses ideas that aren’t cov-
ered in the passage.
Next, look for choices that contradict what you remember from reading through the pas-
sage. Choice (B) states that “there are no human needs.” The passage specically lists
human needs of food, water, shelter, and so on. So Choice (B) has to be wrong. You may
also recall that this list of needs is included in a section in which the author distinguishes
between needs and wants. Choice (E) says that there’s “no dierence between needs and
wants”; you know that the passage says otherwise, so you can eliminate that option.
You’re left with Choices (A) and (D). If you have trouble choosing between them, consult
the passage. Concentrate on the rst paragraph, which says that although Americans and
Europeans should be happy, many are “unhappy and trapped.” You can, therefore, elimi-
nate Choice (D).
Choice (A) should be the correct answer. But take a moment to reread Choice (A) to make
sure it makes sense as the main idea of the passage. Choice (A) says, “Modern Americans
and Europeans feel unhappy and trapped because they don’t distinguish true needs from
mere wants.” This statement agrees with the author’s questioning of the reasons behind
modern unhappiness found in the rst paragraph and the author’s distinguishing of needs
from wants in the last paragraph.
2. E. The author describes a need as “something required for survival” and lists the true needs
as “air, food, water, and, in cold climates, shelter.” Eliminate answer choices that don’t
have something to do with air, food, water, and shelter. Climbing a rock face for the fun of
it likely falls within the author’s denition of a want because it makes life “exciting or
enjoyable.” So you can eliminate Choice (D). As nice as it would be to maintain your
pedicure with a nice pair of soft deer-hide slippers, foot apparel doesn’t fall within the
author’s criteria for survival. (Apparently, in the author’s world, clothing is optional!) Cross
o Choice (B).
CHAPTER 5 Not as Enticing as a Bestseller: Reading Comprehension 75
You’re left with Choice (A), which concerns shelter; Choice (C), which deals with food; and
Choice (E), which regards water. Each of the remaining answer choices addresses one of the
author’s categories of needs, so it’s up to you to determine which is required for survival.
Although it would be nice to sleep peacefully without the interruption of pesky moonlight,
the roof in Choice (A) is more likely a want than a need. The author claries that shelter is a
need in cold climates, not tropical islands. Because Choice (C) tells you that the berry seek-
ers already have a regular diet of rice and beans, you know they’re not searching for the
berry for survival purposes. The berry isn’t necessary for survival, so it’s unlikely that it ts
the author’s idea of a need.
By process of elimination, you settle on Choice (E) as the best answer. The purpose of the
hole excavation is to nd one of the author’s required elements for survival: water. And you
know that the exercise is urgent because the hole-digger has no other source for water.
Don’t be fooled by the reference to refreshment in Choice (E). You may think that refresh-
ment pertains to a want rather than a need, but the author tells you that water is necessary.
Therefore, you can conclude that refreshment that refers to water is also necessary.
3. A. Examine the way the author introduces the point in the rst paragraph of the passage.
The rst several sentences explain that modern humans should be happy because their
daily survival is virtually guaranteed. The author inserts the Hobbes quote about how rough
life used to be to show that modern life has improved considerably. The author then
wonders, given how good we have it, why modern humans are unhappy. The paragraph’s
ending statement is the author’s answer to this question. Find the answer that best
describes this organization.
Choice (D) and Choice (E) are pretty easy to eliminate. The author provides an answer to the
question, so modern humans aren’t incapable of answering it, and Choice (E) can’t be right.
The author references the “West” but doesn’t compare western thinking to the way people
think about life in other parts of the world. Choice (D) is wrong.
You may be tempted by Choice (B). The rst paragraph has a famous quote, but that quote
about the nastiness of life doesn’t restate the prior point that people should feel secure and
content. Choice (C) may also sound good at rst, but it describes the organization of the
entire passage rather than just the rst paragraph. The author doesn’t dene a need until
the last paragraph.
When you’re asked to evaluate the organization of reading content, make sure you know
the parameters of the portion you’re supposed to consider.
The best answer has to be Choice (A). The rst several sentences provide background for
the author’s question about why modern humans aren’t happy. Then the author answers
the question by stating that humans aren’t happy because they don’t know what a need is.
4. C. This passage is almost exactly 350 words, so it’s as long as any passage on the GMAT is
going to get. Don’t let the unfamiliar scientic concepts worry you. You’re probably
familiar with the term decibel, but you may have never encountered the A-weighted decibel
or dBA, as it’s abbreviated. Focus on the main point of the passage, which is to describe
dBAs and how human ears perceive them, and what type of information appears in each
paragraph so that you can approach this main-theme question systematically:
•
First, check out the rst word of each answer choice to nd obvious incorrect answers. The
tone of the passage is primarily objective and descriptive, so an answer that begins with
argue is likely wrong. If you read Choice (A) further, you know you can eliminate it. The
author doesn’t mention anything about government mandates.
Natural science passages are usually objective and informative. Their primary purpose is
rarely to argue in favor of or against a particular position.
76 PART 2 Vanquishing the Verbal Section
•
Next, eliminate answer choices that deal with information found in only one area of the
passage. The scales mentioned in Choice (B) appear only in the rst paragraph, so a com-
parison of them can’t be the purpose of the passage. The author discusses the harmful
eects of exposure to sound only in the last two paragraphs, so Choice (E) isn’t the pri-
mary purpose. For the same reason, you can likely eliminate Choice (D). While the author
does indeed dene the sound exposure levels and times that are safe for humans and does
warn readers about the harmful eects of sound exposure, neither Choice (E) nor Choice
(D) provides the overall reason for the passage.
•
Finally, choose the answer that incorporates information from the passage as a whole.
Choice (C) brings together the information in the rst two paragraphs (how sound
intensity is measured) and the information in the last two (how sound intensity aects
humans). Therefore, it’s the best answer.
5. B. The word infer in the question gives you a fairly obvious clue to the type of question
you’re dealing with. Again, you can rely on the process of elimination to answer it.
Begin by eliminating those choices that rely on outside information. This passage focuses on
noise levels and health eects. The passage doesn’t mention societal concerns, such as the
intrusive impacts of a plethora of noise in urban life. Therefore, you can cross out Choice (A).
All the other choices have something to do with noise levels and health, so don’t eliminate
them yet.
Next, look for choices that contradict what you know about the passage. One of the author’s
purposes in writing the passage is to warn young people of the hearing loss associated with
headphone use (or abuse). To say that the noises mentioned in the question are more dan-
gerous than noises at the same decibel level from headphones would be contradictory.
Because Choice (C) is inconsistent with what you nd out from the passage, you can elimi-
nate it.
You can use the information in the question to narrow down your choices. The question
indicates that the noises mentioned are in the 80 to 120 dBA range. Even if you don’t
remember all the specics of the passage, you probably remember that noises over 100 dBA
are very loud. You may even remember that 120 dBA is the threshold for feeling discomfort
in the ear. It’s, therefore, not logical to say, as Choice (E) does, that noises in this range
would have no health eects. Noises that loud have some impact on the ear!
You can also eliminate Choice (E) because it contains an implicit debatable word. No impacts
in this answer choice suggests none, and answer choices that contain the word none are
almost always wrong because none doesn’t allow for any exceptions. If the answer were
worded a little dierently to say “may have no negative impacts,” it could be correct. Short
exposure to noise may, in fact, have no impact.
You’re left with just two answer choices. If you happen to remember that 140 dB is the threshold
for immediate pain, you can answer the question without having to refer back to the text.
However, if you have any doubt, take a few seconds to be sure. Remember, with the computer-
ized test, you can’t go back to check your answers. After you conrm an answer, it can’t be
changed.
The last sentence of the rst paragraph indicates that 140 dB is the threshold of immediate
pain, and in the third paragraph, you read that 120 dBA can “eventually lead to pain.”
Therefore, you can eliminate Choice (D), so Choice (B) is probably the answer. Glancing at
the passage conrms that it indicates that constant exposure to sounds over 80 dBA can
result in hearing loss.
6. B. On the computerized test, the question would refer to a highlighted part of the passage
on the screen instead of quoting it, but for our purposes, we use the quotation. This
problem is probably a specic-information question because it refers to details of the
passage without using infer or imply.
CHAPTER 5 Not as Enticing as a Bestseller: Reading Comprehension 77
You can eliminate Choice (E) because the passage doesn’t mention a dierence between a
10dB increase and a 10 dBA increase. Choice (D) also refers to information not covered in
the passage. Nowhere does the reading suggest that instruments used to measure
A-weighted decibels are more accurate; it just indicates that sounds are measured dier-
ently with the A-weighted scale. Cross out Choice (D). Likewise, Choice (C) is incorrect
because it directly contradicts prominent information from the reading. A whisper registers
a higher number on the A-weighted scale, so Choice (C) can’t be correct.
The two choices that are left, Choices (A) and (B), both provide correct information, but
only one answers the question. A whisper does register 30 dBA on the A-weighted scale, as
opposed to 20 dB on the normal decibel scale, so Choice (A) provides good information. But
if you refer back to the passage, you nd that some wavelengths are heard more clearly
than others. The passage specically states that the reason for the A-weighted scale is to
take into account those noises that are perceived better by the human ear, which is how the
A-weighted scale diers from the unweighted scale. Because sounds other than a whisper
may have more or less than 10 points dierence between their A-weighted and unweighted
numbers, Choice (B) is a better answer than Choice (A).
7. E. When you’re answering a question about an author’s purpose, looking at the beginning
words of each answer choice can be helpful. The author doesn’t appear to be particularly
argumentative or condescending in this piece, so you can probably eliminate Choices (A),
(B), and (C) right o the bat. Additionally, Choice (C) contains the debatable word all. The
author doesn’t talk about all local ocials in D.C., much less all local ocials in general.
This leaves Choices (D) and (E). You can eliminate Choice (D) because the author doesn’t
advance “a particular ideology.” Instead, the author is stunned that the city council didn’t
know the basic theory of supply and demand. Choice (E) is the best answer of the ve.
To double-check your answer, read through the answers you eliminated based solely on rst
words. Choice (A) is clearly wrong because the author shows that increased taxes actually
resulted in decreased revenues. Choice (B) seems more logical because the author is showing the
problems with the gas tax increase in Washington, D.C.But if you check the passage, you’ll notice
that the author never advocates for lower taxes in the passage. The author explains why the gas
tax failed in the unique case of Washington, D.C., but that isn’t enough to make Choice (B) the
primary purpose for writing the passage. The author is primarily concerned with explaining the
principles of supply and demand, using the Washington, D.C., gas tax as a case study.
8. E. That this question is an inference question is pretty obvious. Be careful not to make an
inference that goes beyond the scope of what’s stated in the passage.
Eliminate incorrect answer choices. Because this is an inference question, it may be hard to
recognize answer choices that use outside knowledge. The point of inferring is, after all, to
extend the reasoning beyond what’s actually written. But one of the choices strays too far
from the information in the passage. Choice (D) mentions changes in the number of vehi-
cles in the region, but the passage says nothing about people getting rid of their cars or not
driving through D.C. in reaction to the increase in the price of gas. Eliminate Choice (D).
Choice (B) is inconsistent with the passage as a whole, so you can also cross it o. The pas-
sage is about price increases in Washington, D.C., and specically not about price increases
in Maryland and Virginia. This leaves you with three possible answers, each of which could
t with the term elasticity in this passage. You need to go back and reread the sentence
that’s referenced in the question and also reread the surrounding sentences to understand
the sentence’s context.
The sentence clearly doesn’t apply to “the amount of tax collected at 6 percent,” so you can
cross out Choice (C). The sentence does mention changes in price in D.C., yet if you read the
entire second paragraph carefully, especially the last two sentences, you’ll see that the
author discusses lower demand in D.C. because of good substitutes: gas in Maryland and
78 PART 2 Vanquishing the Verbal Section
Virginia. The paragraph states outright that prices have gone up in D.C.— but this is an
inference question, which means you’re looking for an implication. It’s not the prices that
are elastic, which means Choice (A) is wrong. Elasticity must refer to the demand for gas,
because low price and demand are positively related. So Choice (E) is the best answer to this
dicult question.
Don’t forget to consider the context of the passage beyond the specic sentence and para-
graph mentioned in the question. A valuable clue to this question can be found in the third
sentence of the rst paragraph, which states that “The elasticity of demand is a key factor”.
This indicates that elasticity as used in the passage will probably be associated with demand.
9. E. This question is also an inference one, even though it doesn’t contain words that suggest
inference. You know it’s an inference question because you’re asked about the reason the
author mentions something, and the passage doesn’t directly state the reason.
As usual, start by eliminating obviously incorrect answer choices that don’t deal with the
subject matter of the passage. The author doesn’t mention residents being overtaxed or
undertaxed; the article just mentions gas prices and shifting demand. So you can eliminate
Choice (A). Choice (D) is incorrect because the passage doesn’t mention collecting the taxes
dierently or at dierent times. The article makes no eort to distinguish between the
straight 10 cent tax and the percentage tax, so you can also cross out Choice (B).
This leaves you with just two possible answers, Choices (C) and (E). Quickly referring to the
second paragraph of the passage reveals that before the authors mention the 10-cent tax,
they indicate that lower demand may actually result in lower tax revenue. To show how this
could be true, the authors mention that the city was previously collecting 10 cents on each
gallon. When less gasoline was sold, the city lost this revenue. Choice (E) is a better answer
than Choice (C) because it pinpoints the authors’ reasons for mentioning the earlier tax.
10. B. To answer this inference question, note that the tax increase was implemented with the
intent to increase tax revenue. The passage states that tax revenues didn’t increase essen-
tially because city ocials didn’t account for the elasticity in the market. Consumers found
equal, less-expensive substitutes in nearby gas stations outside the D.C. city limits.
Eliminate answer choices that are blatantly wrong. Choice (C) presents information that’s
contrary to the details of the passage. City ocials didn’t decrease fuel taxes; they increased
them. You can easily narrow your choices to four.
Choice (A) provides an explanation for the decreased revenues. If consumers limited their
overall gas consumption, tax revenues would fall. This isn’t the reason the author suggests,
however. The passage doesn’t say that D.C. residents stopped buying fuel altogether. It sug-
gests that they stopped buying fuel in D.C. and started buying it in Virginia and Maryland.
Furthermore, D.C. residents may actually have been consuming more gas than usual rather
than less because they were driving longer distances to fuel up. Eliminate Choice (A).
Just because an answer choice makes logical sense doesn’t mean it’s correct. The answer
has to make sense given the information in the passage.
You can also cross o Choices (D) and (E) from the list. Both answers require you to infer
information that’s beyond the scope of the passage. You don’t know anything about the
fuel-buying habits of Virginia and Maryland residents, nor can you imagine that D.C. o-
cials tried to work with ocials in neighboring states. In fact, the passage states that D.C.
ocials were surprised that their constituents bought gas elsewhere, so it’s unlikely that
they had the forethought to negotiate with other governments.
The remaining answer is Choice (B). If D.C. residents went outside of the city limits to pur-
chase fuel, the overall cost of the trip must have been more cost eective than buying gas
within the city. Otherwise, they would have continued to purchase fuel in D.C.
CHAPTER6 Let’s Think This Through Logically: Critical Reasoning 79
IN THIS CHAPTER
» Getting the lowdown on the
makeup of GMAT critical-
reasoning questions
» Deducing the nitty-gritty of
informal logic
» Distinguishing among the
dierent question types
» Practicing your approach for each
type of critical-reasoning question
Let’s Think This Through
Logically: Critical Reasoning
Y
ou’re taking the GMAT to go to business school, not to get a PhD in philosophy, so you’re
probably wondering why you need to be tested in logic and critical reasoning. Don’t
worry — answering the critical-reasoning questions on the GMAT doesn’t require any
knowledge of formal logic. You won’t be constructing syllogisms or using fancy Latin words,
like ad hominem, for logical fallacies. The GMAT verbal section contains questions that test you
on informal logic, which is a lot like the kind of reasoning you use to decide between a chocolate
frosted doughnut and a bran mun when the oce pastry cart passes by. We ll you in on this
logic (for the GMAT, not the pastry cart) in this chapter. The people who run the admissions
oces at business schools want to make sure their future students can think through situations
clearly and carefully. That’s where the critical-reasoning question comes in.
About a third of the questions in the GMAT verbal section are critical-reasoning questions. This
question type tests your ability to analyze an argument. The good news is that you analyze argu-
ments all the time, even though you may not know you’re doing so. When you see a commercial
advertising a new product that claims it’ll make your life better, you probably question that claim.
If a weight-loss drug helped someone lose 50 pounds, you ask, “Is that a typical result?” If four
out of ve dentists recommend a chewing gum, you say, “Did they ask only ve dentists?” When
a mutual fund boasts of its performance, you ask, “Is that better than the market average?” You’ll
use this same kind of thinking to ace the critical-reasoning questions on the GMAT.
Focusing on “Critical” Concepts: An Overview
Critical-reasoning questions consist of an argument, a question, and ve answer choices. You’ll
encounter short passages from a variety of sources, such as speeches, advertisements, newspa-
pers, and scholarly articles. You may see an argument like this: “The local sales tax must be
raised to fund city services. Admittedly, this increased sales tax will impose a greater hardship on
Chapter6
80 PART 2 Vanquishing the Verbal Section
the poorest citizens. But if the sales tax is not increased, all city services for the poor will have to
be cut.” The paragraph reects the type of arguments you encounter in the news every day.
In the following sections, we clue you in on what to expect when you approach a critical-
reasoning question on the GMAT— from the length and format of the argument, to the type of
questions you’ll be asked, to how to gure out the correct answer.
Understanding the structure of the questions
Each critical-reasoning question has essentially the same structure. The question usually begins
with a two- to ve-sentence paragraph that contains the argument. The question contains all the
information you need to answer the question. Don’t rely on any outside information! Even if you
happen to be an expert in the area a question covers, don’t rely on your expertise to answer the
question.
The short argument paragraph is followed by a question (or possibly two questions, although the
computer displays only one at a time). The questions usually fall conveniently into one of a few
types. The question may ask that you weaken or strengthen an argument, draw a conclusion,
analyze the structure of an argument, or identify an unstated assumption the author makes. We
examine each of these question types in the section “Getting from Point A to Point B: Types of
reasoning,” later in this chapter.
Each question has ve possible answer choices, which are often long, sometimes even longer
than the argument or question. For this reason, you’ll spend most of your time for each question
examining the answer choices.
As with most GMAT questions, you can quickly eliminate one or two of the answers that are obvi-
ously wrong. The remaining answers will be more dicult to eliminate, so spend your time ana-
lyzing these better answer choices.
Figuring out how to answer the questions
To break down a critical-reasoning question, follow these three steps:
1. Read the question.
2. Read the argument paragraph, focusing on the specic information you need to know to
answer the question.
3. As you read the argument, look for inconsistencies and/or assumptions in the logic.
The best way to tackle a critical-reasoning question is to read the question rst to determine its
type. The later section “Thinking Inside the Box: Question Types” shows you how to distinguish
critical-reasoning question types. When you rst read the question, don’t read all the answer
choices; doing so takes way too much time and clutters your thinking. You need to concentrate on
only the information you need to nd to answer the question.
After you gure out what kind of question you’re dealing with, you can read the paragraph very
carefully. Be sure to locate the conclusion of the argument. The conclusion may come at the
beginning, middle, or end of the paragraph. When you’ve identied the conclusion, you can better
understand the rest of the paragraph. As you read the paragraph, look for inconsistencies or gaps
in the argument that may help you answer the question. Isolating the argument’s premises,
assumptions, and conclusion helps you determine the method of reasoning.
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 81
The argument paragraph usually isn’t too complicated, and therefore you may be tempted to read
it too quickly. Force yourself to read slowly and carefully so you don’t skim over the word or
words that provide the keys to the argument. If you read thoroughly enough, you’ll be able to
eliminate some— or even most— of the answer choices. When you’re down to two possible
answers, you can then easily refer back to the text to make sure you choose the correct answer.
Making a Case: Essentials of Informal Logic
You can score well on the GMAT critical-reasoning questions without knowing the elements of
informal logic, but if you understand a few terms and concepts, you can score even higher. You
really just need to know the two basic components of a logical argument and a few methods of
coming up with a conclusion, which we outline in the following sections.
Fighting fair: The elements of an argument
A logical argument consists of premises and a conclusion, and when you’re analyzing arguments,
identifying what parts are premises and what makes up the conclusion can help. The premises give
the supporting evidence that you can draw a conclusion from. You can usually nd the conclusion
in the argument because it’s the statement that you can preface with therefore. The conclusion is
often but not always the last sentence of the argument. For example, take a look at this simple
argument:
All runners are fast. John is a runner. Therefore, John is fast.
The premises in the argument are “All runners are fast” and “John is a runner.” They provide the
supporting evidence for the conclusion that John is fast, which is the sentence that begins with
therefore. Not all conclusions in the GMAT critical-reasoning arguments will begin with therefore
or other words like it (such as thus and so), but you can try adding therefore to any statement you
believe is the conclusion to see whether the argument makes sense. We give you plenty of sample
arguments in this chapter so you can use them to practice identifying premises and conclusions.
Getting from Point A to Point B:
Types of reasoning
Each logical argument has premises and a conclusion, but not every argument comes to a conclu-
sion in the same way. For the purposes of the GMAT, you should be familiar with two basic types
of logical reasoning: deductive and inductive (which we explain further in the next sections). You
use both types of reasoning all the time, but now you can apply denitions to your logical genius.
Elementary, my dear Watson: Deductive reasoning
In deductive reasoning, you come up with a specic conclusion from more general premises. The
great thing about deductive reasoning is that if the premises are true, the conclusion must be
true! The following is an example of a deductive reasoning argument:
All horses have hooves. (General premise)
Bella is a horse. (More specic premise)
Therefore, Bella has hooves. (Very specic conclusion)
82 PART 2 Vanquishing the Verbal Section
If the premise that all horses have hooves is true, and if Bella is, in fact, a horse, then it must be
true that Bella has hooves. The same holds true for all examples of deductive reasoning. Here’s
another example:
All who take the GMAT must complete an analytical essay. (General premise)
You’re taking the GMAT. (More specic premise)
Therefore, you have to complete an analytical essay. (Very specic conclusion)
This example shows the relationship between the truth of the premises and that of the conclu-
sion. The rst premise is categorically true: The GMAT requires you to write an essay. The second
premise, however, may not be true. Certainly, you’re thinking of taking the GMAT or you wouldn’t
be reading this book, but you may still decide not to take the test. This possibility doesn’t aect
the logic of the argument. Remember, in deductive reasoning, the conclusion must be true if the
premises are true. If you take the test, you have to write an essay, so this argument is valid.
When you analyze deductive reasoning arguments for the GMAT, the only way you can prove that
a conclusion is true is by showing that all premises are true. The only way to prove that a deduc-
tive reasoning conclusion is false is to show that at least one of the premises is false.
Perhaps I’m just generalizing: Inductive reasoning
In deductive reasoning, you draw a specic conclusion from general premises. With inductive
reasoning, you do just the opposite; you develop a general conclusion from specic premises.
Inductive reasoning diers from deductive reasoning in that the conclusion in an inductive rea-
soning argument could be false even if all the premises are true. With inductive reasoning, the
conclusion is essentially your best guess. That’s because an inductive reasoning argument relies
on less complete information than deductive reasoning does. Consider this example of an induc-
tive argument:
Bella is a horse and has hooves. (Specic premise)
Smoky is a horse and has hooves. (Specic premise)
Nutmeg is a horse and has hooves. (Specic premise)
Shadow is a horse and has hooves. (Specic premise)
Therefore, it is likely that all horses have hooves. (General conclusion)
SURE SOUNDS GREEK TO ME: ORIGINS OF
LOGICAL THOUGHT
Legend has it that a Greek philosopher named Parmenides in the 5th century BC had plenty of time
on his hands while living in a Greek colony off the west coast of Italy. So he whiled away the hours con-
templating logical thought and became one of the first Westerners to record his findings. He penned a
philosophical poem in which an unnamed goddess instructs him in the ways of determining truth about
the universe. His poem explored the contrast between truth and appearance and portrayed truth to be
firm and steadfast, whereas appearance (the way mortal men usually think) was unstable and wavering.
Parmenides’s work influenced other great Greek thinkers, like Plato, Aristotle, and Plotinus.
Unfortunately, you won’t have a goddess to guide you through the critical-reasoning questions of the
GMAT, but you can rely on Aristotle’s method of developing syllogisms to examine GMAT arguments.
He’s the one who came up with this famous syllogism: “All humans are mortal; Socrates is human;
therefore, Socrates is mortal.”
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 83
Because inductive reasoning derives general conclusions from specic examples, you can’t come
up with a statement that “must be true.” The best you can say, even if all the premises are true,
is that the conclusion can be or is likely to be true.
Inductive reasoning arguments come in all sorts of avors, but the folks who create the GMAT
tend to favor three types: analogy, cause and eect, and statistical. To excel on the GMAT, you
want to get very familiar with these three methods of inductive reasoning:
»
Analogy arguments: An analogy argument tries to show that two or more concepts are
similar so that what holds true for one is true for the other. The strength of the argument
depends on the degree of similarity between the persons, objects, or ideas being compared.
For example, in drawing a conclusion about Beth’s likes, you may compare her to Alex: “Alex is
a student, and he likes rap music. Beth is also a student, so she probably likes rap music, too.”
Your argument would be stronger if you could show that Alex and Beth have other similar
interests that apply to rap music, like hip-hop dancing or wearing bling. If, on the other hand,
you show that Alex likes to go to dance clubs while Beth prefers practicing her violin at home,
your original conclusion may be less likely.
»
Cause-and-eect arguments: A cause-and-eect argument concludes that one event is the
result of another. These types of arguments are strongest when the premises prove that the
alleged cause of an event is the most likely one and that no other probable causes exist. For
example, after years of football watching, you may conclude the following: “Every time I wear
my lucky shirt, my favorite team wins; therefore, wearing my lucky shirt causes the team to
win.” The above example is weak because it doesn’t take into consideration other, more-
probable reasons (like the team’s talent) for the wins.
»
Statistical arguments: Arguments based on statistical evidence rely on numbers to reach a
conclusion. These types of arguments claim that what’s true for the statistical majority is also
true for the individual. But because these are inductive-reasoning arguments, you can’t prove
that the conclusions are absolutely true. When you analyze statistical arguments on the GMAT,
focus on how well the given statistics apply to the circumstances of the conclusion. For
example, if you wanted people to buy clothing through your website, you might make this
argument: “In a recent study of the preferences of consumers, 80 percent of shoppers
surveyed spent more than six hours a day on the Internet; therefore, you’ll probably prefer to
buy clothes online.” You’d support your conclusion if you could show that a positive correlation
occurs between the amount of time people spend on the Internet and a preference for buying
clothing online. If you can’t demonstrate that correlation, the statistics regarding time spent on
the Internet have little to do with predicting one’s preference for online shopping.
To do well on the critical-reasoning questions, you need to recognize premises and conclusions
in arguments, determine whether the argument applies deductive or inductive reasoning (most
will be inductive), and, if the argument is inductive, gure out the method the author uses to
reach the conclusion. As you can induce, knowing a little about logical reasoning is essential to
scoring well on the GMAT!
Thinking Inside the Box: Question Types
When you were growing up, you probably experienced clichés. You had your jocks, your stoners, the
smart kids (that was you!), and various other categories. Labels were important because they gave
you clues on how to deal with someone who was a member of a particular group. You knew better
than to pick a ght with a jock, and it was a good bet that you could get a match from a stoner. Well,
we categorize GMAT questions for the same reason. After you gure out a critical-reasoning
84 PART 2 Vanquishing the Verbal Section
question’s type, you know just how to deal with it. Most of the critical-reasoning questions you’ll
encounter on the GMAT t into one of the following ve categories:
»
Strengthening or weakening arguments: The argument presents premises and a conclusion
and asks you to evaluate the answer choices to determine which one would best strengthen or
weaken the author’s conclusion.
»
Drawing conclusions from premises: The argument paragraph consists of a bunch of
premises but doesn’t provide a conclusion. Your job is to choose the best conclusion for the
argument.
»
Seeking assumptions: This more-subtle type of question requires you to discover an essential
premise of the argument that the author doesn’t state directly.
»
Making inferences: For these less-common question types, you have to surmise information
that isn’t directly stated, usually about one of the premises rather than the conclusion.
»
Finding the method of reasoning: In these questions, you’ll be asked to nd an argument in
the answer choices that uses the same method of reasoning as the original given argument.
Because each question type has a best way to handle it, recognizing what type of question you’re
dealing with before you try to answer it is important. That’s why you read the question before you
tackle the argument. You’ll immediately know what you need to look for when you read the argu-
ment from the wording of the question.
Stalking Your Prey: How to Approach
Each Question Type
Knowing the types of questions you’ll face is valuable only if you know the specialized strategies
for dealing with each one. The following sections give you the tips you need to make approaching
each of the question types second nature. You get some practice questions, too, so you’ll know
just what to expect when you take the actual GMAT.
Strengthening or weakening arguments
Critical-reasoning questions that ask you how to best support or damage an argument are some
of the easiest to answer, which is a good thing because they appear the most frequently. You
probably analyze ideas every day and think of evidence to attack or defend those ideas. Because
you already have the skill to evaluate arguments, it doesn’t take much work for you to modify that
skill to t this specic GMAT question format. This question category has two subtypes: One asks
you to strengthen an argument, and the other asks you to weaken it. You’ll recognize these ques-
tions because they include words that mean to strengthen or weaken (like support, bolster, or
impair), and they almost always contain an “if true” qualier.
Here are a couple samples of the ways the questions could be worded:
»
Which of the following statements, if true, would most seriously weaken the conclusion
reached by the business owners?
»
Which of the following, if true, provides the most support for the conclusion?
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 85
Nearly all these questions contain the words if true, but not all questions that have if true in them
are strengthening- or weakening-the-argument types. To make sure an “if true” question is
really a strengthening or weakening question, look for the identifying language that asks you to
either strengthen or weaken the argument.
Here are three simple steps to follow when approaching strengthening- or weakening-the-
argument questions:
1. Read the question carefully so you know exactly what you’ll be strengthening or
weakening.
In most cases, you’ll be asked to strengthen or weaken the conclusion of the main argument.
But in less-frequent cases, you may be asked to support or impair a dierent conclusion, like
the view of the author’s opponent.
2. Examine the argument to nd the premises and conclusion and to determine what
method of reasoning the author uses to reach the conclusion.
Usually the author uses inductive reasoning, so you’ll need to gure out whether the argument
relies on analogy, statistics, or cause and eect to arrive at the conclusion. In the following
sections, we tell you what to look for in each type of reasoning.
3. Evaluate the answer choices to determine which choice best ts with the author’s
conclusion and method of reasoning.
Assume all the answer choices are true and then determine which one best either supports or
undermines the specic conclusion addressed in the question.
Always assume that all the answers to strengthening- or weakening-the-argument questions are
true. Almost all these questions include the words if true in them to remind you that you’re sup-
posed to assume that each answer choice presents a true statement. Don’t fall into the trap of
trying to evaluate whether answer choices are true or false! Your only job is to determine whether
the choices help or hurt the argument. This means that a statement like “humans do not breathe
air” could be a correct answer choice even though you know it’s not true. Perhaps you’re sup-
posed to weaken the conclusion that a company must pump air into an underwater habitat for
humans. If humans don’t breathe air, pumping in air may not be necessary. Make sure you don’t
dismiss any answer choices simply because you know they aren’t usually true.
Analyzing analogy arguments
Analogy arguments rely on the similarity of the two persons, things, or ideas being compared.
Therefore, if the author uses an analogy to reach a conclusion, answer choices that show similari-
ties between the compared elements will support the conclusion, and choices that emphasize the
dierences between the elements will weaken the conclusion. Take a look at this example of an
analogy argument.
Hundo is a Japanese car company, and Hundos run for many miles on a gallon of gas. Toyo is
also a Japanese car company; therefore, Toyos should get good gas mileage, too.
The author’s conclusion would be best supported by which of the following?
(A) All Japanese car manufacturers use the same types of engines in their cars.
(B) British cars run for as many miles on a tank of gas as Hundos do.
(C) The Toyo manufacturer focuses on producing large utility vehicles.
(D) Toyo has been manufacturing cars for more than 20 years.
(E) All Japanese cars have excellent service records.
86 PART 2 Vanquishing the Verbal Section
Recognizing the premises and conclusion in this argument is simple. The author states directly
that Hundo cars are Japanese and get good gas mileage and that Toyo cars are Japanese; therefore,
Toyos also get good gas mileage. Your job is to nd the answer that perpetuates the similarity
between Hundos and Toyos.
You can generally eliminate answer choices that introduce irrelevant information, such as Choices
(B), (D), and (E). The author compares Japanese cars, so what British cars do has nothing to do
with the argument. The length of time that Toyo has been in business tells you nothing about how
similar its cars are to Hundo’s. And the question is talking about gas mileage, not service records,
so don’t spend too much time considering Choice (E).
Choice (C) tells you the focus of Toyo producers, but it doesn’t give you any information about
how that compares to Hundo, so the best answer is Choice (A). If all Japanese manufacturers sup-
ply their cars with the same engines and Hundo and Toyo are both Japanese manufacturers, it’s
more likely that Toyos will achieve a gas mileage similar to that experienced by Hundos.
Considering cause-and-eect arguments
Questions that ask you to evaluate arguments often apply cause-and-eect reasoning. If the
argument uses cause and eect to make its point, focus on the causes. Almost always, the correct
answer to a question that asks you to strengthen the conclusion is an answer choice that shows
the cause mentioned is the most likely source of the eect. The best answer for a question for
which you have to weaken the argument points to another probable cause of the eect. Here’s
how you’d apply this reasoning to a sample question.
Average hours of television viewing per American have rapidly increased for more than three
decades. To ght the rise in obesity, Americans must limit their hours of television viewing.
Which of the following, if true, would most weaken the author’s conclusion?
(A) A person burns more calories while watching television than while sleeping.
(B) Over the last 30 years, the number of fast-food restaurants in America has increased.
(C) Americans spend most of their television time watching sporting events rather than
cooking shows.
(D) Television viewing in Japan has also increased over the past three decades.
(E) Studies show that the number of television commercials that promote junk food has risen
over the past ten years.
To tackle this question, rst identify the conclusion you’re supposed to weaken and the premises
the author states or implies to reach that conclusion. The conclusion is pretty easy to spot. The
last thought of the argument is that Americans must limit their hours of television viewing to
curb the rise in obesity. The author makes this judgment using the following evidence:
»
The author directly states that the number of television viewing hours has increased over the
last 30 years.
»
According to the author, the number of obese Americans has also increased.
»
The author implies that television viewing causes obesity.
To weaken the argument that Americans have to reduce their television watching, you have to
nd the answer choice that shows that there’s another cause for the rise in obesity.
You may have been tempted to select Choice (A) because it shows that television watching may be
less fat-producing than another activity, sleeping. But it doesn’t give you another reason for the
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 87
rise in obesity. Choice (A) could be correct only if it showed that Americans were sleeping more
than they were 30 years ago. It doesn’t, so move on.
On the other hand, stating that during the same time period, the number of fast-food restaurants
also increased introduces another possible cause of obesity and weakens the conclusion that
Americans have to stop watching so much TV to get slimmer. Maybe it’s the popularity of fast
food that’s the culprit! Choice (B) is a better answer than Choice (A), but read through all the pos-
sibilities before you commit. Choice (C) is wrong because there’s nothing in the argument that
suggests that the type of television Americans watch aects their obesity; nor does Choice (C)
show that viewing patterns have changed over the last three decades. Choice (D) is also out
because it doesn’t correlate what’s happening in Japan with what’s happening in America. You
don’t know whether Japanese citizens weigh more now than they did 30 years ago, so the infor-
mation in Choice (D) is useless.
If the question had asked you to strengthen the conclusion, Choice (E) would be a good option. It
shows a reason that increased television watching could cause obesity. But the question asks you
to weaken the conclusion, so Choice (B) is the best answer. It’s the only one that shows that
another cause could be to blame for the rise in obesity.
Taking a stab at statistical arguments
If you see statistics used to promote an argument, you’re looking for an answer that shows
whether the statistics actually relate to the topic of the conclusion. If they do, you’ll strengthen
the conclusion. On the other hand, an answer choice that shows the statistics are unrelated to the
conclusion signicantly weakens that conclusion. The following is an example of a statistical
argument critical-reasoning question you could nd on the GMAT.
In a survey of 100 pet owners, 80 percent said that they would buy a more expensive pet food if
it contained vitamin supplements. Consequently, CatCo’s new premium cat food should be a
top-seller.
Which of the following best demonstrates a weakness in the author’s conclusion?
(A) Some brands of cat food contain more vitamin supplements than CatCo’s does.
(B) CatCo sells more cat food than any of its competitors.
(C) Some of the cat owners surveyed stated that they never buy expensive brands of cat food.
(D) Ninety-ve of those pet owners surveyed did not own cats.
(E) Many veterinarians have stated that vitamin supplements in cat food do not greatly
increase health benets.
Because the argument hinges on statistics, eliminate answers that don’t directly address the sta-
tistical evidence. Those surveyed stated that they’d pay more for pet food with vitamin supple-
ments, but they didn’t provide information on whether the amount of vitamin supplements was
important. So even though Choice (A) may entice you, it isn’t the best answer because it doesn’t
address the statistics used in the argument. Choice (B) doesn’t regard the survey results, either,
and it supports the conclusion rather than weakens it. The argument has nothing at all to do with
veterinarians, so Choice (E) can’t be right. Only Choices (C) and (D) deal with the survey the
author uses to reach the conclusion that CatCo’s premium cat food will be a big seller.
You can eliminate answer choices that show an exception to the statistical evidence. Exceptions
don’t signicantly weaken a statistical argument.
Therefore, Choice (C) is wrong and Choice (D) is the best answer because it demonstrates a weak-
ness in the statistics the author uses to support the conclusion. The preferences of dog or bird
owners isn’t a good indicator of the habits of cat owners.
88 PART 2 Vanquishing the Verbal Section
Dabbling in deductive-reasoning arguments
Rarely will you see a strengthen- or weaken-the-argument question that uses deductive reason-
ing to reach a conclusion. It’s just too hard to come up with challenging answer choices for weak-
ening deductive arguments, because the only way to weaken them is to question the accuracy of
the evidence, and correct answers are pretty easy to spot. The only way to strengthen a deductive
argument is to reinforce the validity of the premises, which seems sort of silly. Even though
GMAT creators don’t want to make things too easy for you, one or two deductive arguments may
crop up. To weaken an argument with a conclusion that must be true, look for an answer choice
that shows that one of the premises is untrue. For example, you may see a question with the fol-
lowing argument:
All horses have tails. Nutmeg is a horse. Therefore, Nutmeg must have a tail.
The only way to weaken this argument is to question one of the two premises. Answer choices like
“Scientists have recently developed a breed of horses that has no tail” or “Although Nutmeg looks
like a horse, she’s really a donkey” would weaken the conclusion.
Delving into drawing conclusions
Another common critical-reasoning question type tests your ability to draw logical conclusions
(or hypotheses). The GMAT gives you a series of premises (the evidence), and you choose an
answer that best concludes the information. Questions that ask you to draw conclusions from
premises may be worded like this:
»
Which of the following conclusions is best supported by the preceding information?
»
Assuming the preceding statements are true, which of the following must also be true?
»
The experimental results support which of the following hypotheses?
As you read through the premises, think of a logical conclusion of your own. Then look through
the answer choices to see whether one listed comes close to what you’ve thought up.
The key to correctly answering drawing-conclusions questions is to look for an answer choice
that addresses all the information contained in the premises. Eliminate any choices that are o
topic or incomplete. A conclusion that addresses only part of the information may be plausible,
but it probably isn’t the best answer. For example, consider the following premises:
Five hundred healthy adults were allowed to sleep no more than ve hours a night for one month.
Half of the group members were allowed 90-minute naps in the afternoon each day; the remaining
subjects were allowed no naps. Throughout the month, the subjects of the experiment were tested
to determine the impact of sleep deprivation on their performance of standard tasks. By the end of
the month, the group that was not allowed to nap suered signicant declines in their perfor-
mance, while the napping group suered more moderate declines.
The best conclusion for these premises would have to address all the following:
»
The nightly sleep deprivation of healthy adults
»
The allowance for naps for half of the study group
»
The smaller decline in performance of standard tasks for the group who took naps
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 89
Any conclusion that fails to address all three points isn’t the best conclusion. For example, the
statement “Sleep deprivation causes accumulating declines in performance among healthy
adults” wouldn’t be the best conclusion because it fails to address the eect of naps. A better
conclusion would be “Napping helps reduce the declines in performance caused by nightly sleep
deprivation among healthy adults.”
You’ll often see more than one plausible conclusion among the answer choices. Your task is to
identify the best choice. Don’t fall for the trap of choosing an answer that just restates one of the
premises. Answer choices that restate a premise may entice you because they echo part of the
information in the argument, but the best choice must contain an element of each of the pieces
of information presented in the question.
The process is pretty simple, really. Try this sample question to see for yourself.
Over the last eight years, the Federal Reserve Bank has raised the prime interest rate by a
quarter-point more than ten times. The Bank raises rates when its Board of Governors fears
ination and lowers rates when the economy is slowing down.
Which of the following is the most logical conclusion for the preceding paragraph?
(A) The Federal Reserve should be replaced with regional banks that can respond more
quickly to changing economic conditions.
(B) The Federal Reserve has raised the prime rate in recent years to try to control ination.
(C) The economy has entered a prolonged recession caused by Federal Reserve policies.
(D) The monetary policy of the United States is no longer controlled by the Federal Reserve.
(E) The Federal Reserve has consistently raised the prime rate over the last several years.
You know from the language that this is a drawing-conclusions question, so you don’t have to
look for a conclusion in the argument. Just read through the premises and formulate a quick con-
clusion, something like “Because the Federal Reserve has raised interest rates many times over
the last eight years, it must fear ination.”
Eliminate answer choices that aren’t relevant or that contain information not presented by the
premises. The argument says nothing about regional banks or the termination of the Federal
Reserve’s control over U.S. monetary policy, so you can disregard Choices (A) and (D). Then get
rid of any choices that don’t take all premises into consideration. Choice (E) just reiterates the
rst premise, so it’s wrong. You’re left with Choices (B) and (C), but Choice (C) contradicts the
information in the premises. The problem says the Federal Reserve responds to the economy, not
the other way around, so it’d be wrong to say the Federal Reserve causes a recession. Choice (B)
is clearly the best answer. It takes into consideration the information that the Federal Reserve has
raised rates and that raising rates is its response to ination.
Be careful to avoid relying on outside knowledge or opinions when answering drawing-
conclusions questions. You may have studied the Federal Reserve Bank and have opinions about
monetary policy. Choices (A), (C), and (D) reect some possible opinions about the Federal
Reserve. Don’t get trapped into choosing an answer because it supports your opinion.
Spotting those sneaky assumptions
Some GMAT critical-reasoning questions ask you to identify a premise that isn’t there. For these
types of questions, the author directly states a series of premises and provides a clear conclusion,
90 PART 2 Vanquishing the Verbal Section
but in getting to that conclusion, the author assumes information. Your job is to gure out what
the author assumes to be true but doesn’t state directly in drawing the conclusion to the argu-
ment. Seeking-assumptions questions may look like these:
»
The argument in the preceding passage depends on which of the following assumptions?
»
The conclusion reached by the author of the preceding passage is a questionable one. On
which of the following assumptions did the author rely?
»
The preceding paragraph presupposes which of the following?
Words like assume, rely, presuppose, depend on, and their derivatives usually indicate seeking-
assumptions questions. Remember, these questions ask you to look for the ideas the author relies
on but doesn’t state.
As you read seeking-assumptions questions, look for information that’s necessary to the argu-
ment but isn’t stated by the author. In these questions, the author always takes for granted
something on which the entire argument depends. You just need to identify what that is. To do so
eectively, choose an answer that links the existing premises to the conclusion. The assumption
you’re seeking always bears directly on the conclusion and ties in with one or more premises,
often with the last premise. Therefore, the best answer often contains information from both the
last premise and the conclusion.
Women receive fewer speeding tickets than men do. Women also have lower car insurance rates.
It is clear that women are better drivers than men.
The preceding conclusion is based on which of the following assumptions?
I. Men and women drive cars equal distances and with equal frequency.
II. Having lower car insurance rates indicates that one is a better driver than those who have
higher rates.
III. Speeding tickets are equally awarded for violations without any gender bias on the part of
police ocers.
(A) I only
(B) III only
(C) I and III only
(D) II and III only
(E) I, II, and III
As always, read the question rst. Because it references assumptions, we bet you gured out
pretty quickly that it’s a seeking-assumptions question.
Next, read through the argument and try to gure out the assumption or assumptions the author
makes in reaching the conclusion that women are better drivers. The author moves from the
premises to the conclusion pretty quickly and assumes that fewer speeding tickets and lower car
insurance rates indicate better driving skills. The author also assumes that men and women have
equal driving experiences. Use this information to examine each of your options.
Look at Statement I rst. It ts with your second observation that men and women experience
equal driving situations, so eliminate any answer choices that don’t include Statement I. This
means that you can get rid of Choices (B) and (D), which leaves you with Choices (A), (C), and (E).
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 91
Before you continue reading through your options, examine the remaining answer choices. You’ll
see that it’s best to examine Statement II next, because if it’s true, you won’t even have to read
Statement III; you’ll know the answer is Choice (E). You have to read Statement III only if you
determine that Statement II isn’t an assumption. (For more about strategies for answering Roman
numeral questions, see Chapter2.)
The information in Statement II links the author’s last premise, that women have lower insur-
ance rates, to the conclusion that women are better drivers. Thus, Statement II is also correct. You
can eliminate Choices (A) and (C), and by process of elimination, the answer must be Choice (E).
If you read through Statement III, you’ll conrm that it, too, is an assumption the author makes
about men and women having an equal playing eld in the driving game.
If you nd seeking-assumption questions to be tricky, try arguing the opposite position. For
example, in the sample question, you could’ve taken the opposing view, that men are better driv-
ers. This means you’ll be looking for ways to undermine the conclusion. If you assume the prem-
ises to be true, the best way to attack the conclusion is to show that the author assumes things
that aren’t true. For example, you may argue that men have more accidents because they drive
more, they get more tickets because police are less forgiving with male speeders, and they have
higher car insurance rates because they drive more-expensive cars. Those counterarguments
expose the author’s assumptions!
Using your noggin to make inferences
Critical-reasoning inference questions ask you to make an inference (using inductive reasoning)
based on the argument in the passage. Making-inferences questions are pretty easy to recognize
because they usually include the word infer, such as the following examples:
»
Which of the following statements can be correctly inferred from the preceding passage?
»
Which of the following can be inferred from the preceding statements?
The key to answering these questions correctly is to know that they usually ask you to make an
inference about one of the premises in the argument rather than about the entire argument or the
conclusion. Because these questions usually deal with the premises and not the conclusion, you
should choose an answer that makes a plausible inference about one or more of the premises. Like
the correct answer choices for the drawing-conclusions questions, the best answers to this type
of question don’t go beyond the scope of the information provided in the paragraph. Here’s what
one looks like.
The highest-rated television shows do not always command the most advertising dollars. Ads
that run during shows with lower overall ratings are often more expensive because the audience
for those shows includes a high proportion of males between the ages of 19 and 34. Therefore,
ads that run during sporting events are often more expensive than ads running during other
types of programs.
Which of the following can properly be inferred from the preceding passage?
(A) Advertisers have done little research into the typical consumer and are not using their
advertising dollars wisely.
(B) Sports programs have higher overall ratings than prime-time network programs.
(C) Advertisers believe males between the ages of 19 and 34 are more likely to be inuenced
by advertisers than are other categories of viewers.
(D) Advertising executives prefer sports programs and assume that other Americans do
as well.
(E) Ads that run during the biggest sporting events are the most expensive of all ads.
92 PART 2 Vanquishing the Verbal Section
You know you’re dealing with an inference question before you read through the argument
because you’ve read the question rst and it contains the word inferred. Focus on the premises of
the argument as you read it. Then look through the answer choices and eliminate any that don’t
address one of the premises or that present inferences that require additional information.
The argument says nothing about advertising research or whether the particular advertising
practice is wise, so you can eliminate Choice (A) immediately. You’re stretching beyond the scope
of the information if you infer that advertisers are unwise. Likewise, Choice (D) mentions the
preferences and assumptions of advertisers, but none of the premises discuss advertisers, so you
can get rid of Choice (D). The inference in Choice (E) relates to the conclusion rather than any of
the premises, so you can probably eliminate it right away. Furthermore, just because sporting
events ads are “often more expensive” than other ads doesn’t necessarily mean that they’re
always the most expensive. This leaves you with Choices (B) and (C).
Choice (B) contradicts information in the argument. The author implies that some sporting events
have lower overall ratings even though they have higher advertising rates. You’re left with Choice
(C). You need an explanation for the information in the second sentence that states that advertis-
ing is often more expensive for lower-rated shows viewed by males who are between 19 and
34 years old. This practice would be logical only if males of these ages were more susceptible to
advertising than other groups. It makes sense that Choice (C) is the correct answer.
Remember to check your outside knowledge about the critical-reasoning subjects at the door! You
may know that Super Bowl ads are the most-expensive ads, which may tempt you to pick Choice
(E). Using your own knowledge rather than what’s expressly stated in the test questions will
cause you to miss questions that someone with less knowledge may answer correctly.
Making your way through method-
of-reasoning questions
Method-of-reasoning questions are the rarest form of GMAT critical-reasoning question types.
This type of question either directly asks you what type of reasoning the author uses to make an
argument or, more often, asks you to choose an answer that uses the same method of reasoning
as the argument. You may see method-of-reasoning questions phrased like these:
»
Which of the following employs the same method of reasoning as the preceding argument?
»
The author’s point is made by which method of reasoning?
»
David’s argument is similar to Katy’s in which of the following ways?
The two types of method-of-reasoning questions may seem dierent, but each of them asks you
to do the same thing: to recognize the type of reasoning used in the argument.
For the purposes of the GMAT, the methods of reasoning are as follows:
»
Deductive, which is reaching a specic conclusion from general premises
»
Inductive, which is drawing a general conclusion from specic premises and includes the
following methods:
•
Analogy, which shows that one thing is suciently similar to another thing such that what
holds true for one is true for the other
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 93
•
Cause and eect, which shows that one event resulted from another
•
Statistics, which uses population samples (surveys) to reach conclusions about the population
as a whole
Questions that ask you to specically choose what kind of reasoning the author uses are straight-
forward, so we focus on the other type of question, which asks you to choose an answer that
mimics the reasoning method of the given argument. When you know you’re dealing with this
type of question, you just need to focus on the way the author makes the argument to make sure
you choose an answer that follows the logic most exactly.
Don’t choose an answer just because it deals with the same subject matter as the given argument.
These choices are often traps to lure you away from the answer that more exactly duplicates the
author’s logic but addresses another topic.
It doesn’t matter whether the argument makes sense. If the given argument isn’t logical, pick an
answer choice that isn’t logical in the same way.
You may focus on the method of reasoning better if you substitute letters for ideas in the argument.
For example, say you’re presented with this argument: “Balloons that contain helium oat. Jerry’s
balloon doesn’t oat, so it contains oxygen rather than helium.” You could state this logic with
letters like this: “All A (helium balloons) are B (oaters). C (Jerry’s balloon) isn’t B (a oater), so
C isn’t A.” Then you can apply that formula to your answer choices to see which one matches best.
Some of the reasoning methods may be as obscure as the one in this sample question.
A teacher told the students in her class, “The information that you read in your history book is
correct because I chose the history book and I will be creating the test and assigning your
grades.”
The reasoning in which of the following statements most closely resembles that of the preced-
ing argument?
(A) The decisions made by the Supreme Court are just because the Court has the authority to
administer justice.
(B) The people who have fame are famous because they deserve to be famous.
(C) Those who play sports get better grades because of the link between the health of the
body and the health of the mind.
(D) Because my favorite teacher chooses to drive this kind of car, I should as well.
(E) Of 100 professors surveyed, 99 agree with the conclusions reached by the scientist in his
paper on global warming.
Reading the question rst tells you that you’ll have to analyze the way the author reaches the
conclusion in the argument. As you read, you nd that this illogical cause-and-eect argument
states that information is correct because someone in a position of authority (the teacher) says
so, so you need to nd an equally illogical argument based on power and authority.
Because this is a cause-and-eect argument, you can eliminate any choices that don’t use cause and
eect to reach a conclusion. All choices contain an element of cause and eect except Choice (D),
which presumes an analogy between a favorite teacher and the writer, and Choice (E), which uses
statistical evidence. (Note that just because Choice [D] also concerns a teacher doesn’t automati-
cally make it the correct answer.) Disregard Choices (D) and (E) and examine the other three
choices.
94 PART 2 Vanquishing the Verbal Section
Among Choices (A), (B), and (C), the only choice that uses power to justify a cause-and-eect
relationship is Choice (A). Choice (B) is faulty because it uses circular reasoning, which means it
uses its conclusion as a premise, instead of using power to advance its position. Choice (C) doesn’t
work because its logic isn’t necessarily faulty. Instead, it relies on a logical correlation between
physical health and intellectual prowess. Therefore, Choice (A) is the answer that most nearly
matches the kind of reasoning in the original argument.
Critical-Reasoning Practice Questions
and Answer Explanations
With practice, you’ll probably nd that critical-reasoning questions become some of the easiest
question types to master in the GMAT verbal section. To master your approach, work through
these practice questions and read through the answer explanations.
Critical-reasoning practice questions
This set of 11 critical-reasoning practice questions gives you a taste of what to expect from this
verbal question, which tests your ability to analyze arguments. To mimic the approximate amount
of time you’ll have to answer critical-reasoning questions on the actual exam, try to answer these
11 questions in about 18 minutes. Answer each question based on the passage that precedes it, and
choose the best answer from the ve answer choices provided.
Don’t expect to see letters before the answer choices on the computerized GMAT.Each answer
will have an oval next to it that you select by clicking on it. We’ve put letters next to the answers
in this practice section to make it easier to discuss the answer in the explanations that follow the
questions.
1. It seems that Americans are smarter than they were 50 years ago. Many more Americans are
attending college now than in the past, and the typical entry-level job in business now requires
a college degree.
Which of the following statements, if true, would most seriously weaken the argument in the
preceding paragraph?
(A) High-school courses are more rigorous now than they were in the past.
(B) Tuition at colleges and universities has more than tripled in the past 25 years.
(C) High-school class sizes have gotten smaller, and computers have introduced a more indi-
vidualized curriculum.
(D) Businesses are not requiring as high a level of writing or math skills as they did in past
decades.
(E) Many of the skills and concepts taught in high school 50 years ago are now taught in
college.
Questions 2 and 3 are based on the following argument.
Rachel: The legal drinking age in America should remain at 21, because teens have not yet
reached an age where they are able to consume alcohol responsibly. Additionally, the actions of
18-year-olds are more likely to be imitated by teens aged 15 to 17 than are the actions of those
who are signicantly older, so lowering the drinking age to 18 would also result in increased
alcohol consumption by younger teens trying to emulate the actions of their older peers.
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 95
Mackenzie: The drinking age in America should be lowered to 18, because keeping it at 21 has
not only failed to curb teen drinking but has encouraged those teens who do drink to do so in
private, uncontrolled environments where they are more prone to life-endangering behavior.
Many youths in European countries drink from an early age, and those countries have substan-
tially fewer alcohol-related problems than we do in America.
2. Which of the following, if true, would most signicantly weaken Mackenzie’s argument?
(A) The idea that Europeans and other nations with low or no minimum drinking ages do not
have alcohol-related problems is a myth.
(B) If Americans are allowed to give their lives for this country at age 18, then they should be
considered old enough to make the proper decision as to what to put in their bodies.
(C) More American high-school students drink now than they did decades ago, when the
drinking age was lower.
(D) In European culture, youths are taught at an early age that it is acceptable to either
abstain from alcohol entirely or drink in moderation and that it is never acceptable for
them to abuse alcohol, regardless of their age.
(E) European youths are just as likely as American youths to drink in private, uncontrolled
environments.
3. Rachel’s argument is based on which of the following assumptions?
(A) Those who have reached the age of 21 are able to consume alcohol more responsibly than
those who are 18.
(B) When European teenagers consume alcohol, they do so in public, controlled
environments.
(C) Teens who are 15 to 17 years old are more impressionable than those who are aged 18 or
older.
(D) The impressionability of one’s actions on others should not be a consideration when
deciding the legal age to consume alcohol.
(E) Consuming alcohol in private, uncontrolled environments is not more dangerous than
consuming alcohol in more public environments, such as bars or restaurants.
4. A recent census of all American females revealed that the current average age that females in
America marry is 27. The average age that females have their rst child is also 27. According
to a census taken 20 years ago, the average ages that females married and had their rst child
were 23 and 25 years, respectively.
If the information recorded in the two censuses is true, which of the following must also be
true about American females?
(A) Currently, more females are having their rst child before they marry than they did 20
years ago.
(B) On average, females are currently waiting longer to have their rst child than they did 20
years ago.
(C) Females today are more likely to complete their education before getting married and
having children than they were 20 years ago.
(D) On average, females had larger families 20 years ago than they have today.
(E) Twenty years ago, most females waited at least two years after they were married to have
their rst child.
96 PART 2 Vanquishing the Verbal Section
5. Continuous technological advances are critical to many types of business, because they allow
machines to do the work previously done by humans— and they don’t have to be compensated.
Banking executives are always looking for ways to cut costs, so they support a heavy emphasis
on automated technology in the workplace. Yet what customers look for most in their banks is
to be recognized by their teller and feel a sense of familiarity and friendliness upon entering, so
the reliance of banks on machines should be minimized, rather than exacerbated.
Which of the following best outlines the main idea of the argument?
(A) Banks should reduce their dependence on technology.
(B) Bank patrons desire personal attention.
(C) Machines can work faster than humans.
(D) Bank executives are a greedy bunch.
(E) Bank automation is inevitable.
6. A school board candidate has indicated that cheating through the use of cellphones in the class-
room is on the rise this year and has proposed a ban on cellphones in schools altogether. School
ocials cite only a marginal increase in the number of students who cheat this year in com-
parison to the last two years, so this is just a ploy to make voters think a quality education is his
top priority.
Which of the following, if true, best strengthens the conclusion of the preceding argument?
(A) The school board candidate has continuously voted down proposals to increase the budget
for area schools.
(B) The school board candidate has continuously voted in favor of budget increases for area
schools.
(C) This year, schools in the district have smaller class sizes and better student/teacher ratios
than they have had in past years.
(D) The ratio of teachers to number of students has decreased signicantly over the past sev-
eral years because of a growth in number of students district-wide without a concomitant
rise in the number of teachers to accommodate the increase.
(E) The school board candidate has a daughter who attends a school in the district, and he
does not want her to own a cellphone.
7. Springeld is the rst city to ban fast-food advertisements marketed specically toward chil-
dren. Although eating fast food has been linked to weight gain, banning these advertisements
will do little to curb childhood obesity, and it should be the job of the parent, not the govern-
ment, to tell children what to eat.
The argument would be most weakened if which of the following were true?
(A) Families are increasingly relying on the fast-food industry for nancial reasons and will
continue to frequent these establishments on their own terms, regardless of their chil-
dren’s preferences.
(B) Studies indicate that, generally speaking, adults tend to be more inuenced by advertising
than children.
(C) If children learn that adults are trying to limit their fast-food intake, they will want to
consume fast food even more.
(D) Those opposed to fast-food marketing geared toward children are welcome to buy airtime
for their cause, too.
(E) Watching an advertisement has been shown to increase one’s desires for a product, par-
ticularly when the product is a food item.
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 97
8.
Patients who feel they have a good relationship with their doctors generally show more
improvement in their health than those who lack a connection with their doctors. Patients who
like their doctors show improved emotional well-being, are less anxious about their symptoms,
and are more likely to follow doctors’ advice.
Which one of the following, if true, would provide the most support for the argument?
(A) Patients are more likely to take legal action against a doctor for malpractice if they believe
that the doctor failed to establish a connection with them during their oce visits.
(B) Recently, medical schools and health insurers have taken measures to improve doctor-
patient communication.
(C) Doctors who work in stressful environments are much less likely to take the time to con-
nect with patients than doctors in more relaxed settings.
(D) The average physician spends about 15 minutes with each patient during routine oce
visits.
(E) A large number of studies have conrmed that the more anxious a patient is, the more
protracted his or her recovery from a medical condition is.
9. The legislature is considering a law banning the use of cellphones by people who are driving a
moving car. Drivers texting and talking while driving are distracted by their phone conversa-
tions and can’t give their full attention to driving their vehicles. Banning the use of cellphones
by drivers will make the roads safer.
The argument depends on assuming which one of the following?
(A) A study by a sociologist has shown that the use of cellphones is occasionally a contribut-
ing factor in trac accidents.
(B) The proper role of the legislature is to enact laws that protect the safety of drivers and
passengers in automobiles.
(C) Drivers who hold their cellphones in their hands are more distracted than drivers who use
a hands-free headset or speakerphone while driving.
(D) Because drivers talking and texting on cellphones are distracted, they are more prone to
getting into accidents.
(E) Many drivers engage in behavior that distracts them from their driving, such as eating,
adjusting the radio, reading maps, and talking on cellphones.
10. Many Americans do not take all the vacation time to which they are entitled. There are several
reasons for this: They feel that they are indispensable at work, they fear the resentment of co-
workers, or they dread discovering that their workplaces can actually function perfectly well
without them. This is a mistake; vacation time gives workers a chance to rest, recover, and gain
perspective that in turn can lead to more creativity and better performance at work.
The claim that many Americans don’t take all the vacation time to which they are entitled
plays which one of the following roles in the argument?
(A) It is a recommendation of a policy that the American workplace should implement.
(B) It is evidence of the author’s claim that vacation time gives workers a chance to rest.
(C) It is the conclusion of the argument.
(D) It is a statement of a principle that the author wishes all people would observe.
(E) It is a statement of fact about which the author expresses an opinion.
98 PART 2 Vanquishing the Verbal Section
11. A large Southern state university has changed its teaching practices. Formerly, instructors
without PhDs taught most introductory courses; now professors with PhDs will teach all intro-
ductory classes. That means the average class size will increase from 44 students per class to
600 per class, but overall the students’ learning experience should improve.
Which one of the following is an assumption required by this argument?
(A) Requiring professors with PhDs to teach all introductory classes will mean that the uni-
versity must hire more faculty with doctorates.
(B) Students tend to participate in smaller classes more than they do in large lectures, even
when the lectures are supplemented by weekly discussion sections.
(C) Major private universities already have implemented a format in which professors with
PhDs teach all introductory classes as large lectures.
(D) A class taught by a PhD, even in a lecture format with hundreds of students, is a better
learning environment than a smaller class taught by an instructor without a PhD.
(E) Services that rank colleges and universities usually consider the percentage of classes
taught by PhDs when computing rank.
Answer explanations
1. E. Read the question rst so you know what to focus on in the passage. Because this
question asks you to weaken the argument, you know you need to gure out what the
conclusion is and what kind of reasoning the author uses in moving from the premises to
the conclusion.
When you examine the argument, you may notice that the conclusion actually comes rst.
The author concludes that Americans are smarter than they were 50 years ago and does so
by contrasting current college participation and entry-level job requirements with those of
the past. The method of reasoning is similar to analogy, except instead of showing similari-
ties between Americans now and 50 years ago, the author shows the dierences. To weaken
the conclusion that Americans are smarter today, you need to nd the answer choice that
shows that things really aren’t all that dierent today than they were 50 years ago.
First, eliminate answer choices with irrelevant information. Neither college tuition rates nor
class size and curriculum have anything to do with levels of intelligence, so Choices (B) and
(C) are wrong. Plus, you’re looking for an answer that shows that things aren’t much dier-
ent between now and yesterday, and Choices (B) and (C) accentuate the dierence.
Then, get rid of any answer that tends to strengthen rather than weaken the conclusion that
Americans are smarter. More-dicult high-school courses seem to indicate that Americans
may indeed be smarter, so disregard Choice (A). This leaves you with Choices (D) and (E),
and your job is to choose the one that shows that now and then aren’t all that dierent. Not
only does Choice (D) demonstrate a dierence between the eras, but it also refutes the
premise that businesses are looking for the higher skill levels of a college education.
The correct answer must be Choice (E). If skills that were part of the high-school curriculum
50 years ago are now oered in college, actual education hasn’t changed all that much from
then to now. Americans must now attend college to acquire the high-school skills of earlier
times, and businesses need to require college degrees to make sure their employees have the
same skills that high-school students had in the past. If the skill levels are the same,
Americans aren’t really any smarter than they were 50 years ago.
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 99
You must know precisely what point a paragraph is arguing before you can strengthen or
weaken that argument. Take the time to understand the premises, conclusion, and method
of reasoning so you can quickly eliminate answer choices and accurately select the best
answer. When you really understand the argument, attacking or defending it is fairly easy.
2. E. First, a quick review of Mackenzie’s argument indicates that she is in favor of lowering
the drinking age, not opposed, so you can quickly eliminate any answer choices that include
support for doing so, such as Choices (B) and (C), because those choices actually strengthen
Mackenzie’s argument.
Now, determine which of the remaining options best weakens Mackenzie’s argument that
the legal drinking age should be lowered. The remaining answers focus on Mackenzie’s
premise that because European countries have lower drinking ages and fewer problems with
alcohol, lowering the drinking age in America would likewise lead to fewer alcohol-related
problems. She makes her argument based on an analogy between Europe and America, so
weaken her contention by showing that Europe and America are substantially similar in
their approach to teenage drinking. It may sound surprising to weaken an analogy with a
similarity, but in this case Mackenzie’s analogy seeks to liken the alleged present state of
aairs in Europe to the supposed future state of aairs in America if the American drinking
age is lowered. Showing a similarity between present-day Europe and present-day America
can therefore weaken the argument that a change in the drinking age will reduce alcohol-
related problems in America.
Mackenzie doesn’t say that European countries have no alcohol-related problems, just that
there are fewer, so Choice (A) is irrelevant to her argument. Choice (D) provides a concrete
dierence between European and American culture that reveals why European teens tend to
be more responsible than American teens when it comes to alcohol consumption, so this is
an answer choice that seems to lend support to Mackenzie’s argument that a lower drinking
age won’t result in less-responsible drinking among American teens. On the other hand,
Choice (E) reveals a similarity between European and American youth, which best serves to
weaken Mackenzie’s analogy between the lower drinking age in Europe and the proposed
lower drinking age in America. If both European and American youths drink in private,
uncontrolled environments despite the dierence in the drinking ages of the two cultures,
it’s unlikely that changing the drinking age in America will aect the behavior that
Mackenzie claims is dangerous (drinking in private).
3. A. Rachel argues for retaining the current legal drinking age of 21. She bases her conclusion
on the premises that younger drinkers are more likely to inuence the behavior of 15- to
17-year-olds and that teens haven’t reached an age where they can drink alcohol
responsibly.
To nd the correct answer to questions that ask for an assumption, look for the answer
choice that links one or more of the premises to the conclusion. Eliminate answer choices
that don’t relate to at least one of the premises of the argument.
Choices (B) and (E) relate to one of Mackenzie’s premises, so it’s unlikely that they would
reveal one of Rachel’s assumptions. Cross out those two answers on your noteboard.
You can also check o Choice (D) because it contradicts Rachel’s premise that the eect an
18-year-old’s alcohol consumption can have on younger peers is an important consideration
in determining the legal drinking age. It’s also unlikely that Choice (C) is correct because
Rachel doesn’t make comparisons regarding the impressionability of teens based on their
ages. Her premise is that younger teens are more likely to be inuenced by 18-year-olds
than 21-year-olds. Furthermore, Choice (C) doesn’t link one of Rachel’s premises to her
conclusion in the way that Choice (A) does.
100 PART 2 Vanquishing the Verbal Section
If Rachel concludes that the legal drinking age must remain at 21 because younger drinkers
don’t consume alcohol responsibly, she must think that 21-year-olds have achieved some
level of responsibility that’s greater than those who are younger. Choice (A) links the rele-
vance of one of Rachel’s premises (a lower level of responsible drinking) to her conclusion
that people who are younger than 21 shouldn’t be able to legally consume alcohol. So the
correct answer is Choice (A).
4. B. This question asks you to come up with a conclusion based on the information in the
paragraph.
Notice that the question asks you for what must be true rather than what could be true. So
you can cross out any answers that aren’t absolutely true given the data in the paragraph.
All you know from the paragraph is the average marrying age for females today and 20 years
ago and the average age that females have their rst child today compared to 20 years ago.
The paragraph says nothing about the number of children females have or had, so you can
easily wipe Choice (D) out of contention. Furthermore, the paragraph provides no explana-
tion for why the data has changed over the years, so you can’t know the reason that the
average age has increased. So Choice (C) can’t be right.
Don’t choose an answer based on an assumption or your own experience. The paragraph
merely reports data instead of commenting on it, and it treats the age of marrying and
having one’s rst child as two separate statistics. You can’t make assumptions about how
the two sets of data are related.
That means that Choice (A) doesn’t have to be true. Just because the average age for marry-
ing and having a rst child are currently the same doesn’t mean that more American
females are having their rst child before they marry. For example, the increased marrying
age could be the result of females who marry when they’re older and have no children.
Eliminate Choice (E) for the same reason. You can’t assume from these limited statistics
that the females who are 23 when they marry are the ones who are having their rst child
at 25. There are too many other variables in the population.
The only thing you know for sure is that, because the average age for having a rst child has
risen over the last 20 years, on average, females are having their rst child at a later age
than they did 20 years ago. Choice (B) is the only answer that must be true.
5. A. Asking for the main point of an argument is another sneaky way of getting you to pick
out the conclusion. This paragraph makes it easy for you because the conclusion follows the
so in the last sentence: Banks should rely less on machines. The rst sentence of the
argument equates machines with technological advances, which means that you can say
that the main point is that banks should rely less on technology, Choice (A).
Choices (C), (D), and (E) require you to make assumptions that aren’t supported by the
argument. Because you read newspaper headlines, you may think that Choice (D)’s assertion
about the avarice of bank executives is a foregone conclusion, but, alas, it isn’t mentioned in
the argument. (You should also have been alerted by the debatable word inevitable in Choice
[E]). The paragraph does suggest that bank patrons want personal attention (Choice [B]), but
this statement is a premise rather than the conclusion. So the correct answer is Choice (A).
6. D. The rst step to answering any question that asks you to strengthen a conclusion is to
gure out exactly what that conclusion is. In this case, the paragraph argues that the
candidate’s proposal to ban cellphones in schools is a campaign strategy to make voters
think he cares about the quality of education. The argument is based on the statistic that
the increase in the number of students who cheat has been insignicant. To support the
author’s argument, nd the answer that best supports the contention that cheating really
hasn’t increased all that much.
CHAPTER 6 Let’s Think This Through Logically: Critical Reasoning 101
Eliminate choices that don’t pertain to the author’s argument. You can disregard Choices (A)
and (B). The argument is concerned with the implications surrounding a cellphone ban, not
the candidate’s position on a budget increase. You’re assuming too much (or relying on your
own opinion) to make a determination of whether the candidate’s vote for or against a
budget increase has anything to do with education quality.
Choice (E) indicates that a reason other than cheating may be the reason the candidate
wishes to impose the cellphone ban, but that absurd personal reason doesn’t support the
author’s argument that the candidate is proposing the ban for political reasons.
The answer must be either Choice (C) or Choice (D). Both deal with the number of actual
students in the district, so they may reect on the validity of the candidate’s claim that
cheating has increased and the author’s claim that it hasn’t. Having smaller class sizes tells
you nothing about the overall number of students. The district could have hired more teach-
ers to accommodate the same number of students. The only answer that relates to the
cheating statistic is Choice (D). The marginal increase in cheating could be due to an
increase in number of students rather than an increase in cellphone cheating, which sup-
ports the author’s argument that the candidate’s reason for banning cellphone use is
unfounded.
7. E. The implication is that the advertising ban is designed to curb childhood obesity. The
author states that this ban won’t work, which suggests that the author thinks that the
fast-food advertisements don’t cause childhood obesity. To weaken this argument, show
that the advertisements do indeed lead to obesity. If it’s been proven that watching an ad
increases one’s desire for something, then banning the ads would reduce the desire for fast
food that produces weight gain in children. Choice (E) weakens the author’s argument by
showing that the advertisement ban will indeed curb childhood obesity. Choice (A) seems to
strengthen the author’s argument, and Choices (B), (C), and (D) deal with tangents that
don’t relate to whether the advertisement would be eective in curbing childhood obesity.
The correct answer is Choice (E).
8. E. The argument claims that patients do better when they feel a connection to their doctors;
the premises are three factors that result from liking one’s doctor. To support this argu-
ment, you need to nd statements that link those factors with health improvements. Choice
(A) doesn’t help. It illustrates the danger of people not liking their doctors but doesn’t
prove the point that patients who like their doctors are healthier. Choice (B) may suggest
that improving doctor-patient communication is desirable, but it doesn’t specically link
improved communication to improved patient health. Choice (C) presents a reason for poor
doctor-patient communication but doesn’t show how that aects patient health. Choice (D)
provides evidence of how the average doctor doesn’t have a good relationship with patients,
but it doesn’t show the results of good doctor-patient rapport. Choice (E) does support the
conclusion by linking one eect of liking a doctor (less anxiety) to a greater improvement
in health. Choice (E) is correct.
9. D. You’re looking for an assumption. Assumptions connect the premises to the conclusion.
The conclusion that if drivers can’t use cellphones, the roads will be safer is based on the
evidence that drivers on phones are distracted; the author assumes that distracted drivers
are unsafe drivers. (Yes, that’s obvious, but the author doesn’t explicitly say what the
connection is, so it’s an assumption.) Choice (A) is tricky and could be a possible answer if
you were asked to support the legislator’s argument, but information about the results of a
specic cellphone use study is way too specic to be the legislator’s assumption. Assump-
tions are rarely based on particular statistical data. See whether you can nd a better
answer. Choice (B) is wrong; the author probably does assume that this is the legislature’s
job, but this assumption isn’t necessary to the specic argument connecting distraction
102 PART 2 Vanquishing the Verbal Section
and road safety. Choice (C) doesn’t work; the author isn’t concerned with distinctions
among types of cellphones users. Choice (D) is something the author assumes— it explains
the connection between cellphones and distracted drivers and dangerous roads. Choice (E)
contains mostly irrelevant details about other behaviors, and to the extent it addresses
drivers on cellphones, it just repeats evidence the argument already explicitly states. Choice
(D) is the best answer.
10. E. The claim in the question is a statement of fact in the rst sentence that the speaker
explores more thoroughly, concluding with the statement that it’s a mistake. She’s not
suggesting that it’s a good thing, so Choices (A) and (D) are wrong. It’s not evidence, so
Choice (B) is wrong. Her actual conclusion is that refraining from taking vacation is a
mistake, so Choice (C) is wrong. The claim is a statement of fact that provides the back-
ground information for the author’s opinion about what Americans should do with their
vacation time, so Choice (E) is correct.
11. D. The author concludes that having classes taught by PhDs instead of instructors improves
students’ learning experience, so he must assume that PhDs, even in very large classes, are
somehow better at teaching than instructors in smaller ones. Choice (A) isn’t his assump-
tion. In fact, the reference to increased class sizes suggests that the university won’t be
hiring more faculty. Choice (B) contradicts the author’s conclusion by suggesting that
student participation is a good thing. Choice (C) is interesting information but isn’t essen-
tial to the conclusion about the practices of the particular Southern state university in the
argument, especially because it doesn’t mention students’ learning experiences. Choice (D)
looks like the right answer. The author does seem to think that a class taught by a PhD is
somehow superior, which explains why he thinks the change would benet students. Choice
(E) explains why the university may want to increase classes taught by PhDs, but it doesn’t
explain how that would benet students. Choice (D) is correct.
CHAPTER7 Bringing It Together: A Mini Practice Verbal Section 103
IN THIS CHAPTER
» Practicing sentence correction,
reading comprehension, and
critical reasoning questions
» Finding out why right answers
are right and wrong answers are
wrong
Bringing It Together: A Mini
Practice Verbal Section
L
ike the real GMAT verbal section, the mini practice test in this chapter has an approximately
equal distribution of each of the three types of verbal questions. It contains nine reading-
comprehension questions, ten sentence-correction questions, and nine critical-reasoning
questions. The total of 28 questions makes this mini verbal test a little over half the size of
the 41-question GMAT verbal section. To get more practice, take the full-length practice exams
included with this book.
Although we can’t simulate a computer in this book, don’t let that deter you. Just mark the answers
right in the book, and try not to look at the answer key until after you’ve answered the questions.
We designate each answer choice with a letter to make it easier to reference it in the answer expla-
nations, but on the actual computerized exam, you’ll simply click the oval that precedes each
answer choice to mark your answer.
To best mimic the computer experience during this mini practice test, answer each question in
sequence and don’t go back and change any of your answers after you’ve moved on to the next
question. At the actual exam, you won’t have a test booklet to write in, so try not to write any-
thing except your answers on the pages of this book. To keep your notes and record eliminated
answers, use scratch paper to simulate the noteboard you’ll use on test day.
Take the time to read through the answer explanations at the end of the chapter, even for the
questions you get right. The explanations apply the techniques covered in the other chapters of
this book and show you why a certain answer is a better choice than the others.
Chapter7
104 PART 2 Vanquishing the Verbal Section
Working Through Verbal Reasoning
Practice Questions
If you’re the competitive type and want to subject yourself to a timed test, give yourself just a
little less than 52 minutes to complete the 28 questions in this section.
Here’s a quick review of the directions for the three types of verbal questions that appear in this
mini practice test (and on the real GMAT):
»
Sentence-correction questions: Choose the answer choice that best phrases the underlined
portion of the given sentence according to the rules of standard English. The rst answer
choice duplicates the phrasing of the underlined portion; the other four choices provide
alternative phrasings. Choose the one that rephrases the sentence in the clearest, most
grammatically correct manner.
»
Reading-comprehension questions: Choose the best answer to every question based on
what the passage states directly or indirectly.
»
Critical-reasoning questions: Pick the answer choice that best answers the question about
the argument provided.
1. A study of energy consumption revealed that homeowners living within 100 miles of the Gulf of
Mexico used less energy from November 1 to April 30 than did homeowners in any other region
of the United States. The same study found that from May 1 to October 31, those same home-
owners used more energy than any other homeowners.
Which of the following, if true, would most contribute to an explanation of the facts above?
(A) People who own homes near the Gulf of Mexico often own second homes in cooler loca-
tions, where they spend the summers.
(B) Air conditioning a home is a more energy-ecient process than heating a similarly sized
home.
(C) Homes near the Gulf of Mexico require very little heating during the warm winters, but
air conditioners must run longer in the summer to cool the warm, humid air.
(D) The average daily temperature is lower year-round near the Gulf of Mexico than in other
areas of the United States.
(E) Because of the large number of reneries located in the Gulf region, the price of energy
there is less than in any other area of the country.
2. A conservation group is trying to convince Americans that the return of gray wolves to the
northern United States is a positive development. Introduction of the wolf faces signicant
opposition because of the wolf’s reputation as a killer of people and livestock. So that the wolf
will be more acceptable to average Americans, the conservation group wants to dispel the myth
that the wolf is a vicious killer.
Which of the following, if true, would most weaken the opposition’s claim?
(A) Wolves are necessary for a healthy population of white-tailed deer because wolves kill the
weaker animals and limit the population to sustainable numbers.
(B) In a confrontation, black bears are much more dangerous to humans than wolves are.
(C) Wolves are superb hunters, operating in packs to track down their prey and kill it.
(D) There has never been a documented case of a wolf killing a human in the 500-year
recorded history of North America.
(E) Wolves occasionally take livestock because domestic animals are not equipped to protect
themselves the way wild animals are.
CHAPTER 7 Bringing It Together: A Mini Practice Verbal Section 105
Questions 3–6 refer to the following passage.
This passage is excerpted from The Big Splat, or How Our Moon Came to Be, by Dana Mackenzie, PhD
(Wiley):
It is hard for us to imagine today how utterly dierent the world of night used to be from
the daylight world. Of course, we can still re-create something of that lost mystique. When we
sit around a campre and tell ghost stories, our goose bumps (and our children’s) remind us of
the terrors that night used to hold. But it is all too easy for us to pile in the car at the end of our
camping trip and return to the comfort of our incandescent, uorescent, oodlit modern word.
Two thousand, or even two hundred, years ago there was no such escape from the darkness. It
was a physical presence that gripped the world from sunset until the cock’s crow.
“As dierent as night and day,” we say today. But in centuries past, night and day really
were dierent. In a time when every scrap of light after sunset was desperately appreciated,
when travelers would mark the road by piling up light stones or by stripping the bark o of trees
to expose the lighter wood underneath, the Moon was the traveler’s greatest friend. It was known
in folklore as “the parish lantern.” It was steady, portable, and— unlike a torch— entailed no
risk of re. It would never blow out, although it could, of course, hide behind a cloud.
Nowadays we don’t need the moon to divide the light from the darkness because electric
lights do it for us. Many of us have never even seen a truly dark sky. According to a recent sur-
vey on light pollution, 97 percent of the U.S. population lives under a night sky at least as bright
as it was on a half-moon night in ancient times. Many city-dwellers live their entire lives under
the equivalent of a full moon.
3. The primary purpose of this passage is to
(A) compare and contrast nighttime in the modern world with the dark nights of centuries
past
(B) explain why the invention of the electric light was essential to increasing worker
productivity
(C) lament the loss of the dark nights and the danger and excitement that moonless nights
would bring
(D) describe the diminishing brightness of the moon and the subsequent need for more elec-
tric lights
(E) argue for an end to the excessive light pollution that plagues 97 percent of the U.S.
population
4. When the author says “Many city-dwellers live their entire lives under the equivalent of a full
moon,” he is essentially saying that
(A) city-dwellers will never be able to truly appreciate the mystique and beauty of a truly dark
night
(B) there is no longer a need for moonlight because articial light is sucient
(C) city-dwellers are missing out on much of the beauty of the natural world
(D) the amount of articial light that shines in cities is enough to produce the same amount
of light as a full moon
(E) it is easier to view the moon from cities than from rural areas
106 PART 2 Vanquishing the Verbal Section
5. The passage mentions all the following as possible ways for travelers to nd the path at night
except
(A) piles of light-colored stones
(B) the moon
(C) a torch
(D) railings made of light wood
(E) trees with the bark stripped o
6. The author includes the statistic “97 percent of the U.S. population lives under a night sky at
least as bright as it was on a half-moon night in ancient times” to primarily emphasize which
of the following points?
(A) Modern humans have the luxury of being able to see well at night despite cloud cover or a
moonless night.
(B) Most modern people cannot really understand how important the moon was to people in
centuries past.
(C) Americans are unique among the people of the world in having so much articial light at
night.
(D) A full moon in ancient times was brighter than modern electric lights, which are only as
bright as a half-moon.
(E) Light pollution is one of the most important problems facing the United States in the 21st
century.
7. The sugar maples give us syrup in March, a display of beautiful owers in spring, and their
foliage is spectacular in October.
(A) their foliage is spectacular in October
(B) spectacularly, their foliage changes color in October
(C) has spectacular foliage in October
(D) spectacular foliage in October
(E) October foliage that is spectacular in orange and red
8. The Industrial Revolution required levels of nancing which were previously unknown; for
instance, Florence had 80 banking houses that took deposits, made loans, and performed many
of the other functions of a modern bank.
(A) which were previously unknown
(B) that were previously unknown
(C) unknown before that time
(D) which had been unknown in earlier times
(E) that was previously unknown
9. His eorts to learn scuba diving, a major goal Bob had set for himself for the coming year,
has not successfully begun, seeing as how his fear of claustrophobia is triggered anytime he is
underwater.
(A) has not successfully begun, seeing as how
(B) have not successfully begun, seeing as how
(C) have not been successful because
(D) has not been successful because
(E) have not yet met with success, on account of
CHAPTER 7 Bringing It Together: A Mini Practice Verbal Section 107
10. The intern’s day-to-day duties varied considerably, but typically they included tasks like pick-
ing up coee, clean up the oce and arranging meetings for executives.
(A) tasks like picking up coee, clean up the oce, and arranging meetings for executives
(B) tasks like picking up coee, cleaning up the oce, and arranging meetings for executives
(C) tasks such as picking up coee, cleaning up the oce, and arranging meetings for
executives
(D) tasks such as pick up coee, clean up the oce, and arrange meetings for executives
(E) tasks like pick up coee, clean up the oce, and arrange meetings for executives
11. You never want to think that your spouse may be the person trying to hide assets from you, but
they very well might be trying too.
(A) but they very well might be trying too
(B) but they very well might be trying to
(C) but he or she very well might be trying to
(D) but he or she very well might be doing so
(E) but they very well might be doing so
12. After the move, Amanda started shopping at a grocery store that was closer to her new home,
but she found it had fewer produce, less varieties of fresh juice, and less options for healthy
eating then her previous store of choice.
(A) fewer produce, less varieties of fresh juice, and less options for healthy eating then her
previous store of choice
(B) less produce, fewer varieties of fresh juice, and fewer options for healthy eating than her
previous store of choice
(C) less produce, fewer varieties of fresh juice, and fewer options for healthy eating then her
previous store of choice
(D) fewer produce, fewer varieties of fresh juice, and less options for healthy eating than her
previous store of choice
(E) fewer produce, fewer varieties of fresh juice, and fewer options for healthy eating than
her previous store of choice
Questions 13 and 14 are based on the following information.
Tom: The unemployment rate has dropped below 5 percent, and that is good news for America.
A lower unemployment rate is better for almost everyone.
Shelly: Actually, a low unemployment rate is good for most workers but not for everyone.
Workers are certainly happy to have jobs, but many businesses are negatively aected by a low
unemployment rate because they have fewer applicants for jobs, and to expand their workforce,
they have to hire workers they would not usually hire. The wealthiest Americans also privately
complain about the inability to get good gardeners, housecleaners, and nannies when most
Americans are already employed. So a low unemployment rate is not, in fact, good for America.
108 PART 2 Vanquishing the Verbal Section
13. Which of the following, if true, would most weaken the argument that a low unemployment rate
is bad for business?
(A) Businesses must pay skilled or experienced workers higher salaries when the unemploy-
ment rate is low.
(B) The states don’t have to pay unemployment compensation to as many workers when
unemployment is low.
(C) Higher unemployment generally means higher enrollment levels in college and graduate
school.
(D) Ination can increase with low unemployment, making capital more expensive for any
business seeking to expand.
(E) Low unemployment rates generally mean that Americans have more money to spend on
the goods and services created by American businesses.
14. Shelly’s conclusion that “a low unemployment rate is not, in fact, good for America” relies on
the assumption that
(A) What is bad for businesses owners and the wealthy is bad for America.
(B) Fluctuations in the unemployment rate aect the number of applicants for job openings.
(C) Wealthy Americans rarely employ other Americans as housecleaners or nannies.
(D) Business owners always want what is best for their workers even when it negatively
impacts the bottom line.
(E) Low unemployment hurts some workers because they would prefer to stay at home and
collect unemployment checks.
15. A particular company makes a system that is installed in the engine block of a car and, if that
car is stolen, relays the car’s location to police via satellite. The recovery rate of stolen cars with
this device is 90 percent. This system helps everyone because it is impossible for a thief to tell
which cars it is installed on. For these reasons, insurance companies try to encourage custom-
ers to get this system by oering lower rates to those who have the system. Competing systems
include brightly colored steel bars that attach to the steering wheel and loud alarms that go o
when the car is tampered with. These systems simply encourage thieves to steal dierent cars,
and when cars with these devices are stolen, the police rarely recover them.
Which of the following is the most logical conclusion to the author’s premises?
(A) Insurance companies should give the same discount to car owners who have any protec-
tive system because their cars are less likely to be stolen.
(B) The police shouldn’t allow car owners to install the loud sirens on their cars because
everyone simply ignores the sirens anyway.
(C) Car owners with the system that relays location to the police should prominently adver-
tise the fact on the side window of their cars.
(D) Thieves should simply steal the cars with loud alarms or bright steel bars because those
cars probably wouldn’t also have the more eective system installed.
(E) Insurance companies should give less of a discount, or no discount at all, to the siren and
steering-wheel systems because they aren’t as eective as the relay system.
CHAPTER 7 Bringing It Together: A Mini Practice Verbal Section 109
16. The managers were asked to rate their depth of knowledge having been increased as a result of
the emergency simulation, and in each area, they reported large gains.
(A) their depth of knowledge having been increased
(B) how much their depth of knowledge had increased
(C) if they had more knowledge
(D) how deep their knowledge is
(E) their knowledge depth
17. Keeping the nose of her kayak directly into the wind, she paddled ercely toward the safety of
the harbor through the seeming endless waves, each of those larger than the last.
(A) through the seeming endless waves, each of those larger than the last
(B) through the seeming endless waves, each larger than the last
(C) through the seemingly endless waves, each of those larger than the last
(D) through the seemingly endless waves, each larger than the last
(E) through waves that seemingly have no end, each larger than the last
18. Companies X and Y have the same number of employees working the same number of hours per
week. According to the records kept by the human resources department of each company, the
employees of company X took nearly twice as many sick days as the employees of company Y.
Therefore, the employees of company Y are healthier than the employees of company X.
Which of the following, if true, most seriously weakens the conclusion?
(A) Company X allows employees to use sick days to take care of sick family members.
(B) Company Y oers its employees dental insurance and company X doesn’t.
(C) Company X oers its employees a free membership to the local gym.
(D) Company Y uses a newer system for keeping records of sick days.
(E) Both companies oer two weeks of sick days per year.
Questions 19–23 refer to the following passage.
This passage is excerpted from Brand Name Bullies: The Quest to Own and Control Culture, by David
Bollier (Wiley):
For millennia, the circulation of music in human societies has been as free as the circula-
tion of air and water; it just comes naturally. Indeed, one of the ways that a society constitutes
itself as a society is by freely sharing its words, music, and art. Only in the past century or so
has music been placed in a tight envelope of property rights and strictly monitored for unau-
thorized ows. In the past decade, the proliferation of personal computers, Internet access, and
digital technologies has fueled two conicting forces: the democratization of creativity and the
demand for stronger copyright protections.
While the public continues to have nominal fair use rights to copyrighted music, in practice
the legal and technological controls over music have grown tighter. At the same time, creators
at the fringes of mass culture, especially some hip-hop and remix artists, remain contemptu-
ous of such controls and routinely appropriate whatever sounds they want to create interesting
music.
110 PART 2 Vanquishing the Verbal Section
Copyright protection is a critically important tool for artists in earning a livelihood from
their creativity. But as many singers, composers, and musicians have discovered, the benets of
copyright law in the contemporary marketplace tend to accrue to the recording industry, not to
the struggling garage band. As alternative distribution and marketing outlets have arisen, the
recording industry has sought to ban, delay, or control as many of them as possible. After all,
technological innovations that provide faster, cheaper distribution of music are likely to disrupt
the industry’s xed investments and entrenched ways of doing business. New technologies al-
low newcomers to enter the market and compete, sometimes on superior terms. New technolo-
gies enable new types of audiences to emerge that may or may not be compatible with existing
marketing strategies.
No wonder the recording industry has scrambled to develop new technological locks and
broader copyright protections; they strengthen its control of music distribution. If metering de-
vices could turn barroom singalongs into a market, the music industry would likely declare this
form of unauthorized musical performance to be copyright infringement.
19. Which of the following most accurately states the main idea of the passage?
(A) Only with the development of technology in the past century has music begun to freely
circulate in society.
(B) The recording industry is trying to develop an ever-tighter hold on the distribution of
music, which used to circulate freely.
(C) Copyright protection is an important tool for composers and musicians who earn their
living from their music.
(D) Technology allows new distribution methods that threaten to undermine the marketing
strategies of music companies.
(E) If music is no longer allowed to ow freely through the society, then the identity of the
society itself will be lost.
20. Given the author’s overall opinion of increased copyright protections, what is his attitude
toward “hip-hop and remix artists” mentioned in Paragraph 2?
(A) wonder that they aren’t sued more for their theft of copyright-protected music
(B) disappointment that they don’t understand the damage they are doing to society
(C) envy of their extravagant lifestyle and increasing popularity
(D) approval of their continued borrowing of music despite tighter copyright controls
(E) shock at their blatant sampling of the music of other artists
21. According to the passage, new technology has resulted (or will result) in each of the following
except
(A) new locks on music distribution
(B) newcomers’ competing in the music market
(C) better music
(D) democratization of creativity
(E) faster, cheaper distribution of music
CHAPTER 7 Bringing It Together: A Mini Practice Verbal Section 111
22. The author of the passage would likely agree most with which of the following statements?
(A) Small-time musicians do not benet from strict copyright protections in the same man-
ner as record companies do.
(B) Copyright protections are designed to let music artists keep more of the money they earn
through their talent.
(C) Recording companies are largely undeserving of their greedy reputations.
(D) Recording companies embrace new technologies because they help encourage the spread
of music.
(E) Copyright protections encourage creativity among musicians because the artists must nd
new ways to share their music with the masses.
23. The nal sentence of the passage seems to imply what about the executives of the record industry?
(A) They have found ways to make money from any performance of any music at any time.
(B) They are boldly leading the music industry into a new technological era of vastly
increased prots.
(C) They want their music to be performed as often as possible by the maximum number of
people to create greater exposure for artists.
(D) They don’t actually like music or know anything about music and are attempting to limit
the society’s exposure to music.
(E) No performance of music anywhere is safe from their attempts to control the distribution
of all music.
24. Five new loon pairs successfully raised chicks this year, bringing to 24 the number of pairs
actively breeding in the lakes of Massachusetts.
(A) bringing
(B) and brings
(C) and it brings
(D) and it brought
(E) and brought
25. New laws make it easier to patent just about anything, from parts of the human genome to a
peanut butter and jelly sandwich. Commentators are concerned about the implications of allow-
ing patents for things that can hardly be described as “inventions.” However, the U.S.Patent
and Trademark Oce believes that allowing for strong copyright and patent protections fosters
the kind of investment in research and development needed to spur innovation.
Which of the following can be properly inferred from the preceding statements?
(A) It was not possible in the past to patent something as common as a peanut butter and
jelly sandwich.
(B) The U.S.Patent and Trademark Oce is more interested in business prots than in true
innovation.
(C) Investment in research and development is often needed to spur innovation.
(D) The human genome is part of nature and shouldn’t be patented.
(E) Commentators who are concerned about too many patents aren’t very well informed.
112 PART 2 Vanquishing the Verbal Section
26. The process of “gerrymandering,” or manipulating voter-district boundaries so that one party
gains a considerable advantage in a district over another, is making the modern political climate
more divisive than ever. It ensures that people with likeminded ideals end up densely packed in
the same districts, and those people then elect ocials who also share those likeminded ideals.
These elected ocials are less prone to compromise, and this creates an unnecessary and
harmful divide between parties.
Assuming all the following statements are true, which would most signicantly weaken the
argument made above?
(A) Gerrymandering sets up an unfair advantage by creating some districts that are nearly
guaranteed to vote for a particular party, thereby freeing up more time and resources for
that party to campaign elsewhere.
(B) People with likeminded ideals have an innate desire to live alongside others who share
similar belief systems, regardless of their political aliation.
(C) All elected ocials are typically strong in their convictions.
(D) When people with likeminded ideals live in the same district, they tend to continuously
elect politicians with very similar beliefs.
(E) Gerrymandering can be executed by both political parties.
27. In a recent survey, one out of six Americans were shown to have vision problems, which is a
notable increase over the past two decades. The amount of time Americans spend in front of
computer and television screens has risen sharply, and to reduce the number of Americans suf-
fering from vision issues, the amount of screen exposure must also be reduced.
Which of the following, if true, would most substantially weaken the author’s conclusion?
(A) Increased screen time is directly correlated with vision problems.
(B) The connection between screen time and vision problems is not entirely clear.
(C) Screen time has increased globally and not just in America.
(D) Americans can reduce their risk of vision problems caused by too much screen time by
dimming the screen and using a larger font.
(E) The majority of Americans with vision problems are older people, and the percentage of
people over age 60 has steadily increased over the past twenty years.
28. Despite the fact that they were colonists, more Americans thought of themselves as British citi-
zens, and throughout the early years of the American Revolution, more than half of all Ameri-
cans were loyal to Britain.
(A) more Americans thought of themselves as British citizens
(B) fewer Americans felt that they were British citizens
(C) most Americans thought of themselves as British citizens
(D) many of them felt like British citizens
(E) most Americans believed we were British citizens
CHAPTER 7 Bringing It Together: A Mini Practice Verbal Section 113
Understanding What’s Right
with Answer Explanations
You can check your answers to the practice questions by reading through the following explana-
tions. To get the most benet, read through every explanation, even the ones for the questions
you answered correctly.
1. C. This critical-reasoning question asks you to strengthen the argument by providing a
piece to the cause-and-eect pattern. With cause-and-eect questions, you select the
answer choice that could logically cause the eects noted in the premises. So for this
problem, you have to decide which of the ve choices helps explain why Gulf Coast homes
use little energy in the winter and a great deal of energy in the summer. Without even
looking at the answer choices, you may conclude that the Gulf Coast climate is milder than
other parts of the nation in the winter and perhaps hotter in the summer. The correct
answer probably addresses that issue.
You can eliminate Choice (A) because if most Gulf Coast residents spend the summer else-
where, their vacant homes would use less energy during summer months rather than more.
This answer would produce the opposite eect of that explained in the argument. Choice (B)
would also produce the opposite eect of that found in the argument. Another important
reason for eliminating Choice (B) is that it doesn’t provide a way of comparing energy use
in the Gulf region to energy use in the rest of the country, which is the real issue in this
argument.
Choice (C) sounds like the answer we imagined before reading through the choices. It
explains why the Gulf region would have lower energy use in winter and higher use in
summer, which may explain why it’s dierent from the rest of the country as a whole.
Although Choice (C) is probably the correct answer, read through the remaining two choices
just to be sure.
Choice (D) doesn’t work because a region that’s cool year-round would have high energy
consumption in the winter for heat and low consumption in the summer. And you can elim-
inate Choice (E) because the argument is about energy consumption, not energy price. So
the correct answer is Choice (C).
2. D. This critical reasoning question asks you to weaken the opposition’s statement that the
wolf is vicious, so look for a statement that shows that the wolf isn’t a danger to people or
livestock. Begin by eliminating answers that don’t address the appropriate conclusion.
Choice (A) deals with the benecial impact of wolves on the ecosystem but doesn’t talk
about their propensity toward viciousness to humans or livestock, so eliminate it. You can
also eliminate Choice (C) because the hunting prowess of the wolf isn’t the issue, and this
choice may actually strengthen the contention that wolves are dangerous. Choice (E) also
doesn’t weaken the conclusion in question; it argues that wolves may threaten livestock.
This leaves you with Choices (B) and (D). Choice (B) compares the danger posed by wolves
with the danger posed by black bears. Even if a wolf is less dangerous than a bear, that
doesn’t mean a wolf isn’t dangerous. The best answer is Choice (D), because it provides a
statistic that weakens the opposition’s argument that wolves are dangerous to humans.
114 PART 2 Vanquishing the Verbal Section
3. A. For a primary-purpose reading-comprehension question, you’re looking for the reason
the author wrote the passage.
Focus on the passage as a whole and not on any particular portion. You usually can nd
clues to the main theme and the author’s purpose in the rst and last paragraphs.
The main idea of this passage is that night was very dierent in centuries past than it is in
current times, and the author’s purpose is to show how this is true. So look for an answer
that reects this purpose.
You can start by eliminating answers based on their rst words. The words compare and
contrast, explain, and describe reect the author’s purpose, but lament and argue imply more
emotion on the part of the author than is displayed in the passage, so eliminate Choices (C)
and (E). Worker productivity has nothing to do with showing how our ancestors perceived
night dierently, so you can eliminate Choice (B). Choice (D) is simply wrong; the author
doesn’t maintain that the moon is actually getting darker, just that it’s become overshad-
owed by electric lights. So that leaves Choice (A) as the correct answer.
4. D. Arguably the biggest clue to Choice (D) lies in the second-to-last sentence, when the
author references a “recent survey of light pollution” in cities. This implies that there is so
much visible light in cities that residents need no longer “mark the road by piling up light
stones or by stripping the bark o of trees to expose the lighter wood underneath” to light
their way to their destination. It’s always wise to consider all the other possible answer
choices, though, just to make sure. Choices (A) and (C) are somewhat similar, in that they
both intimate that city-dwellers are missing out on the beauty of nature and the world
around them. This doesn’t appear to be the focus of the passage, however; the passage is
more focused on how people used to make up for the lack of light and how they no longer
need to do so to function after dark. So, you can probably eliminate both options. Choice (E)
doesn’t make a lot of sense; it is probably easier to get a good look at the moon in a rural
area, where tall buildings, pollution, and so on are less likely to block your view. You’re
down to either Choice (B) or (D). The two choices seem similar, but of the two, Choice (D) is
the stronger option. The last sentence provides that articial light is “equivalent” to
moonlight, which is more synonymous to the “same amount” of illumination in Choice (D)
than “sucient” in Choice (B).
5. D. This specic-information exception question asks you to refer to the text to eliminate
answers that are ways in the passage that travelers can nd a path at night. The second
paragraph specically mentions Choice (A), light-colored stones; Choice (B), the moon;
Choice (C), torches; and Choice (E), trees with the bark stripped o. Railings, Choice (D),
aren’t mentioned anywhere in the passage so it’s the correct answer.
6. B. This question asks you about the use of a specic statistic. To answer this question
correctly, keep in mind the author’s purpose for writing the passage, which you’ve already
considered in the third question. Find the choice that links the statistic to the author’s
purpose of comparing nighttime now and nighttime in centuries past. Eliminate Choice (C)
because the author compares time periods, not modern countries. Because the passage
doesn’t indicate that the moon is brighter than electric lights, you can eliminate Choice (D).
Although the 97 percent statistic may lead you to conclude that light pollution is a big
problem, that’s not the author’s reason for using the statistic, so eliminate Choice (E).
Choice (A) is a little more plausible, but Choice (B) is better because the author is more
concerned with showing how night skies are dierent now than with showing that the
modern well-lit sky is a luxury.
CHAPTER 7 Bringing It Together: A Mini Practice Verbal Section 115
7.
D. This sentence-correction question has a parallelism problem. You know this because the
underlined portion is a part of a list of elements joined by a conjunction and not all the
elements in the list exhibit the same construction. The third element is expressed as a
clause, and the other elements are noun phrases. Because the sentence contains an error,
you know Choice (A) is wrong. Choices (B) and (C) don’t change the clause to a phrase.
Although Choice (E) is a noun phrase, its construction is unnecessarily wordy: foliage that is
spectacular versus spectacular foliage. Choice (E) also introduces new information (the colors
orange and red), which alters the original sentence. Choice (D) maintains parallel construc-
tion without adding unnecessary words, so it’s the correct answer.
8. B. This sentence-correction question has an improperly used pronoun. You use which to
introduce nonessential clauses. Because the information after the which is essential to the
meaning of the sentence, you have to use that instead. You can eliminate Choices (A) and
(D) because both keep the which construction. Choice (C) uses too many words to mean
previously unknown, and Choice (E) changes which to that but presents a new problem
because that refers to levels, which is plural, so it requires the plural verb have. So Choice (B)
is the only answer that corrects the problem without creating new ones.
9. C. The underlined portion of this sentence-correction question has problems with agree-
ment and rhetorical construction. The plural subject eorts doesn’t work with the singular
verb has. Because you nd an error, you automatically eliminate Choice (A). Choice (D)
doesn’t correct the agreement error. This leaves you with Choices (B), (C), and (E), all of
which correct the agreement problem, but because is a better, clearer construction than
seeing as how and on account of, so Choice (C) is the best answer.
10. C. There are two issues with the sentence about the intern’s task in the original version.
First, there is the issue of using like instead of such as to introduce a series of examples. Use
like to compare two nouns: “Like Dave, Joe performs many duties.”
The second problem with the sentence is that it lacks parallelism. In the list of the intern’s
tasks, two of the verbs (picking and arranging) take on the gerund form (meaning they end in
-ing) while the third verb, clean, doesn’t. All three tasks in the series have to have the same
grammatical construction, meaning clean must be changed to its gerund form, cleaning, for
the sentence to be correct. The only sentence that eectively corrects both issues is Choice (C).
11. D. The small underlined portion of this sentence contains three errors. The rst concerns
the pronoun they, which is a plural pronoun that renames the singular noun spouse.
Eliminate Choices (A), (B), and (E). And of course too in Choice (A) means also and thus is
wrong. The other error snuck in here is the good ol’ dangling preposition. Standard writing
English frowns upon ending a sentence with a preposition like to. Of the remaining two
answers, Choice (D) corrects the preposition error.
12. B. The sentence as written has two problems: it confuses the use of less and fewer and of
then and than. The author uses less and fewer improperly. Fewer refers to nouns you can
actually count, such as socks, lollipops, and red trucks, whereas less is used for items that
can’t be easily quantied, such as rain or sugar. Since produce can’t be easily counted, the
use of fewer in the original sentence is incorrect— so you can go ahead and knock out
Choices (A), (D), and (E) right o the bat. “Varieties of juice” can be counted. Therefore,
fewer is correct in this circumstance. You’ve narrowed your choices down to either Choice (B)
or Choice (C). Because Choice (C) uses then to make a comparison, it must be wrong. Then
references time and is never used in comparisons. Choice (B) xes the errors.
116 PART 2 Vanquishing the Verbal Section
13. E. This critical-reasoning question requires you to weaken Shelly’s argument that a low
unemployment rate is bad for business. Choices (A) and (D) give two examples of how low
unemployment hurts businesses, so they actually strengthen the argument instead of
weaken it. Eliminate them along with Choices (B) and (C), because these statements are
basically o topic; they deal with government and universities, not businesses. Choice (E) is
the correct answer, because employed American workers’ buying more American products
provides a signicant advantage for businesses.
14. A. This critical-reasoning question asks you to identify an assumption that Shelly relied on
in making her conclusion that a low unemployment rate isn’t “good for America.”
When you’re asked to nd an assumption, look for a statement that supports the conclusion
but isn’t actually stated in the argument.
Eliminate choices that don’t support the conclusion. Whether businesses favor workers over
the bottom line may aect the unemployment rate, but it doesn’t show how low unemploy-
ment isn’t good for America, so Choice (D) is incorrect. Choice (E) doesn’t support the con-
clusion, either. The conclusion is about what’s good for America in general, not a select few
disinclined workers.
A person’s assumption wouldn’t contradict a stated premise, so Choice (C) can’t be right.
Choice (B) may support the conclusion, but it’s actually stated in the given premises and,
therefore, can’t be an unstated assumption. Choice (A) is the correct answer because it links
Shelly’s premises about businesses and wealthy Americans to her conclusion about America
in general.
15. E. This critical-reasoning question requires you to draw a conclusion from the premises
included in the argument.
Look for an answer choice that addresses all the information in the premises. You can
eliminate conclusions that are o topic or incomplete.
Eliminate choices that don’t include all the elements of the argument. Choices (B), (C), and
(D) don’t mention the insurance companies that are the subject of one of the premises. This
leaves you with Choice (A) and Choice (E), which oer nearly opposite conclusions. The
premises indicate that one of the reasons insurance companies like the engine-block
system is that thieves don’t know which cars have it installed. Choice (A) concludes that
cars with any protective system, including alarms and steering-wheel bars, should get a
discount because those cars are less likely to be stolen. This conclusion doesn’t ow logi-
cally from the premises, however, because the reasons given for the insurance discounts are
a high recovery rate of stolen vehicles and the general deterrent to all car thefts. Neither of
these advantages comes from the alarms or steering-wheel bars. Choice (E) addresses all
the premises and logically concludes the argument, making it the correct answer.
16. B. The underlined portion in this sentence-correction question is passive, so you can
eliminate Choice (A). Choices (C), (D), and (E) don’t address both the knowledge increase
and the knowledge depth, so you can eliminate them, too. The best answer is Choice (B).
It makes the construction active and includes both the increase and depth of knowledge.
17. D. You probably rst noticed that the underlined portion of this sentence-correction
question contains a modication error. Adjectives like seeming modify nouns and pronouns.
They can’t modify other adjectives like endless. Adverbs must be used for that. Instead of
seeming, you can use the adverb seemingly. Therefore, you know you can disregard Choice
(A). You can also eliminate Choice (B) because it doesn’t make the change to seemingly.
Choices (C), (D), and (E) change seeming to seemingly.
CHAPTER 7 Bringing It Together: A Mini Practice Verbal Section 117
This underlined portion also has a problem with redundancy. Each refers suciently to
waves; of those isn’t necessary. Choice (C) doesn’t x this error, so it’s wrong. Choices (D)
and (E) both x each of the errors, but Choice (E) creates another. The sentence is past
tense, so the verb have should be in past tense like this: seemingly had no end. Choice (D)
corrects both original errors and doesn’t introduce more, so it’s the correct answer.
18. A. This critical-reasoning question asks you to weaken the conclusion that the employees
of company Y are healthier than the employees of company X.The author draws the
conclusion that Y’s employees are healthier than X’s employees based on the cause-and-
eect argument that more sick days mean sicker employees.
To weaken cause-and-eect arguments, look for an answer choice that shows another
cause is possible for the eect.
Choice (E) doesn’t distinguish between the two companies. It can’t show another cause for
the dierent number of sick days and, therefore, can’t be right. Choice (D) dierentiates
between the two companies’ record-keeping, but it doesn’t explain how company Y’s new
records system accounts for fewer sick days. Dental insurance shouldn’t aect the number
of sick days, so Choice (B) doesn’t work. Choice (C) doesn’t address the issue of company
X’s greater number of sick days, so free gym memberships don’t matter. The best answer is
Choice (A) because it provides a reason other than employee health for the greater number
of sick days that company X’s employees take.
19. B. This reading-comprehension question asks for the main idea of the passage.
Answers to main-theme questions are usually more general than specic in their wording.
Choices (C) and (D) each focus on sub-themes in the passage but not the main idea.
Copyright protection and technology are specic subjects covered in the passage, but they
don’t make up the main idea, which is that the music industry is trying to control distribu-
tion of music. You can eliminate Choice (A) because it’s not supported by any part of the
passage. The passage clearly states that music has circulated freely in society for millennia.
Choice (E) is wrong because it goes beyond what’s stated in the passage. The author may
well imply that without the free ow of music, society will lose its identity, but this isn’t
the passage’s main idea. So that leaves Choice (B) as the best answer.
20. D. This reading-comprehension question asks about the author’s attitude toward hip-hop
and remix artists as specically mentioned in the second paragraph. The real GMAT would
highlight this phrase in yellow. You’ve already answered a question about the main idea, so
you know the author is concerned about the tightening grip the recording industry has on
the distribution of music. Because the hip-hop and remix artists defy the music industry,
they’ll likely meet with the author’s approval. Although Choice (A) may express a valid
opinion, you can eliminate it because it isn’t supported by the passage. The author probably
approves of hip-hop and remix artists, so he or she doesn’t think they’re doing damage—
Choice (B) is completely o base. Envy and shock are usually too strong emotions for GMAT
passages, so rule out Choices (C) and (E). The correct answer is Choice (D).
21. C. Here’s another specic-information reading-comprehension question looking for an
exception. Examine the text and eliminate the answers you nd there. The one that remains
is your correct answer. In connection with technology, the passage mentions Choice (A),
new locks on music distribution, in the second paragraph; Choice (B), newcomers’ compet-
ing in the market, in the third paragraph; Choice (D), democratization of creativity, in the
rst paragraph; and Choice (E), faster, cheaper distribution of music, in the third para-
graph. The author certainly doesn’t mention better music. So Choice (C) is correct.
118 PART 2 Vanquishing the Verbal Section
22. A. If you picked Choice (B), you may not have read closely enough, or you may have stopped
reading right after the author refers to copyright protections as, “... a critically important
tool for artists in earning a livelihood from their creativity,” because the author then goes
on to lament how such protections tend to benet the recording companies more than the
artists. As for Choice (C), because a key point made by the author throughout the passage is
that recording companies are, in fact, greedy, and will do just about anything to make and
keep as much money as possible, you can easily eliminate that answer. Choice (D), too, can
be eliminated with relative ease, as the author makes several references to the fact that
record companies do just the opposite of embracing new technologies. They instead seek to
“ban, delay, or control” them for their own benet. Choice (E) can also be knocked out of
contention because the author doesn’t go into whether artists are nding “new ways to
share their music with the masses”; he instead discusses how copyright protections are
intended to help recording companies maintain control of music distribution to the fullest
extent possible. Choice (E) also refers to the artist’s creative ways to avoid technological
and legal controls rather than the creativity associated with producing the artwork itself.
Choice (A) is your best option, justied by the author’s statement that “the benets of
copyright law in the contemporary marketplace tend to accrue to the recording industry,
not to the struggling garage band.”
23. E. For this reading-comprehension inference question, you need to determine what the
nal sentence implies about recording-industry executives. The nal sentence mentions
that if it were possible, executives would try to stop unauthorized singalongs. This shows
that the author thinks that executives will go to any length to control the distribution of
music. Choices (B) and (C) paint the executives in a positive light, which is certainly not
warranted by the last sentence. You can also eliminate Choice (D) because the last sentence
has nothing to do with whether executives like or dislike music. Choice (A) is closer, but the
sentence doesn’t talk about making money from singalongs so much as stopping them
altogether. That makes Choice (E) the correct answer.
24. A. This sentence-correction question tests your knowledge of verb forms and grammatical
construction. You’re not dealing with word choice, because all the answer choices include a
form of the verb to bring. Choices (C) and (D) introduce the pronoun it, which has no clear
reference, so they’re not right. Choice (B) applies a singular verb to a plural subject. Choice
(E) includes and, which would make the comma in the non-underlined part of the sentence
improper. The sentence is best as is.
25. A. This critical-reasoning question asks you to draw an inference from the passage.
Inference questions generally focus on a premise rather than on a conclusion. The passage
implies that the patent oce wants to promote invention, so Choice (B) doesn’t work.
Choices (D) and (E) express opinions that aren’t presented in the passage. Although you
may agree that the genome shouldn’t be patented or that people who are concerned about
patents aren’t well informed, the question doesn’t ask you for your opinion.
Don’t choose answer choices to critical-reasoning questions just because you agree with
them. Base your answers on the opinions stated or implied by the paragraph.
Because Choice (C) is stated in the passage, it can’t be an inference. The answer must be
Choice (A), because it ows logically from the rst premise and isn’t stated in the passage.
CHAPTER 7 Bringing It Together: A Mini Practice Verbal Section 119
26.
B. Choice (A) sounds more like an additional argument in favor of gerrymandering creating
an “unnecessary and harmful divide between parties,” so that answer can’t be right since it
strengthens rather than weakens the original argument. The same can be said for Choice
(D); if folks are electing very similar politicians in their districts and those politicians share
the same ideals, this would likely contribute to the divide between parties and help elimi-
nate the political “middle.” Choice (E) is irrelevant; that both sides can take part in gerry-
mandering doesn’t mean they do or that they do at the same time. So, that argument also
falls at. You’ve narrowed the options down to either Choice (B) or (C). Of the two, Choice
(B) is the stronger option. It presents an alternative to gerrymandering as the reason that
certain districts tend to elect people from the same party over and over again, which
arguably contributes to a sharper divide between parties. Choice (B) is your best bet.
27. E. Choice (E) is best because it presents a logical, alternative explanation for the statistics
surrounding Americans with vision problems. It isn’t screen time that causes the spike in
problems but, instead, a large population of aging Americans. Choice (A) would strengthen
rather than weaken the initial argument, so you know that one can’t be right. Choice (B) is
a possibility, but you can assume the GMAT is probably looking for something a bit more
precise. Choice (C) is irrelevant; the argument is specic to American vision problems, so it
doesn’t matter how much time people in other parts of the world spend looking at screens.
Choice (D), too, is irrelevant. What people do to reduce vision issues doesn’t call into
question the role of screen time in vision problems.
28. C. The nal sentence-correction question contains an improper comparison. The term more
requires a comparison between two things (more Americans thought of themselves as
British citizens than what?). The sentence doesn’t oer a comparison. Because there’s an
error, eliminate Choice (A). Choice (B) uses the term fewer, which also requires a compari-
son, and this answer choice changes the meaning of the sentence. Choice (D) gets rid of
more but introduces the pronoun them, which doesn’t have a clear reference and, therefore,
can’t be right. Choice (E) also contains a pronoun error: its inclusion of the rst-person
pronoun we. We weren’t around during the American Revolution, so Choice (E) is incorrect.
Choice (C) changes more to most, so it eliminates the comparison problem and is the correct
answer.
3
Acing the
Analytical-
Writing Section
IN THIS PART ...
Gain an understanding of the AWA, including the topics
you’ll have to write about and what GMAT readers are
looking for when they score your essay.
Craft an exemplary GMAT essay by organizing your
thoughts, writing what the readers are looking for, and
avoiding common grammar and mechanics errors.
Take a look at some sample AWA essays to nd out
what works and what doesn’t.
Try your hand at some practice AWA writing prompts.
CHAPTER8 Analyze This: What to Expect from the Analy tical Writing Assessment 123
IN THIS CHAPTER
» Getting to know the AWA
» Figuring out the capability of the
essay software
» Considering how your essay is
scored
Analyze This: What to
Expect from the Analy tical
Writing Assessment
T
he analytical writing assessment (or AWA, as it’s aectionately known) can be intimidat-
ing. You’re required to write an analytical essay on a topic that the computer reveals to
you just as your time begins to tick away. To earn the top score, you’re expected to provide
an excellent analysis and insightful examples and demonstrate a mastery of standard written
English. Did we mention that you’re supposed to do this in only 30 minutes? If it seems a little
overwhelming, relax. You can do it; we show you how in this chapter.
First, you need to know what you’re up against, so we walk you through the AWA and let you
know what to expect. Then, we give you a sneak peak at the writing task required of you. Finally,
we get to the part that interests you most— how the AWA is scored.
Fitting in the AWA with the Rest of the GMAT
The AWA is a stand-alone section of the GMAT.The GMAT reports your analytical writing score
separately from your integrated reasoning score and your quantitative and verbal reasoning
scores. In other words, your combined total GMAT score (with a maximum of 800 points) reects
how well you do on only the multiple-choice verbal- and quantitative-reasoning sections of the
test. So you can write gibberish on the essay portion of the test and still earn an 800 for your
GMAT score (but we certainly don’t recommend that strategy!).
Each business program determines the importance of the analytical writing section dierently.
Some schools may give it the same weight as your combined quantitative and verbal score. Other
schools may assign it less weight. Check with the specic schools you’re interested in attending
to see how they use the AWA score. The bottom line is that regardless of how a business program
uses your essay score, it will be reported to them. So it’s to your advantage to do as well on the
AWA as you can.
Chapter8
124 PART 3 Acing the Analytical-Writing Section
Another reason to be well prepared for the AWA is that it’s typically the rst section of the
GMAT.If you feel that you did well on the essay, this condence may sustain you through the rest
of the test. However, if you’re unprepared for the AWA and have a dicult time completing the
essay, your bad start can have a negative impact on your entire test session.
Calling 411: Your AWA Writing Tools
The analytical writing assessment consists of one essay prompt, which the GMAT refers to as a
task. The task requires you to write an analytical essay within 30 minutes. You type your response,
using the computer software provided at the testing center. At the end of the 30 minutes, your
task is complete and only what you’ve actually typed into the computer contributes to your score,
meaning any handwritten notes or great ideas in your head don’t count!
You’ll be able to use typical word-processing functions like cut, paste, undo, and redo. You can
access these word-processing functions with the mouse or by using special keystrokes that the
GMAT species for you before you begin the test. You can also use your noteboard to take notes
as you plan your response.
Some of the following word-processing features you may be accustomed to won’t be available:
»
Automatic corrections: If you regularly use a program like Word or WordPerfect, you
probably don’t even notice the automatic corrections anymore. You type in comittment and
your computer displays commitment without you even realizing it. The GMAT won’t automati-
cally correct your mistakes.
»
Spelling and grammar check: You know that spelling-and-grammar-check function that has
saved you from turning in some truly hideous college papers? The function tells you, for
example, that you have just written a passive sentence with subject-verb agreement problems
and three misspelled words. You can’t count on that because spelling and grammar check
won’t be available, either!
»
Synonym nder: You won’t have access to that groovy built-in thesaurus that helped you nd
synonyms for six of your seven uses of the word cool (one of which is groovy).
Analyzing an Argument
The analytical writing assessment task requires you to analyze an argument. The GMAT doesn’t
want your opinion on a topic. Instead, you’re supposed to critique the way someone else reaches an
opinion. To score well on this task, you need to analyze the reasoning behind the argument and
write a critique of the argument. First, you need to briey explain what kind of reasoning the author
uses (for all about dierent kinds of reasoning, consult Chapter6). Next, you point out the strengths
and weaknesses of the argument. Finally, you consider the validity of the assumptions that the
author makes and what eect alternative explanations would have on the author’s conclusion.
Here’s a paraphrase of the directions for the analysis of an argument task on the GMAT:
»
Write a critique of the argument presented but don’t provide your own opinion.
»
Think for a few minutes about the argument and organize your response before you start
writing. Leave time for revisions when you’re nished.
CHAPTER 8 Analyze This: What to Expect from the Analy tical Writing Assessment 125
You’ll be scored based on your ability to accomplish these tasks:
»
Organize, develop, and express your thoughts about the given argument.
»
Provide pertinent supporting ideas with examples.
»
Apply the rules of standard written English.
Now that you have the directions down, check out this example essay prompt:
The following is an excerpt written by the head of a governmental department:
“Stronger environmental regulations are not necessary in order to provide clean air and water. We
already have lots of regulations on the books and these are not being adequately enforced. For
example, the Clean Air Act amendments, adopted in 1990, have never been fully enforced and, as a
result, hundreds of coal-burning power plants are systematically violating that law on a daily basis.
The Clean Water Act is also not being enforced. In the state of Ohio alone there were more than
2,500 violations in just one year. Instead of passing new regulations that will also be ignored, this
department should begin by vigorously enforcing the existing laws.”
Examine this argument and present your judgment on how well reasoned it is. In your discussion,
analyze the author’s position and how well the author uses evidence to support the argument. For
example, you may need to question the author’s underlying assumptions or consider alternative
explanations that may weaken the conclusion. You can also provide additional support for or
arguments against the author’s position, describe how stating the argument dierently may make it
more reasonable, and discuss what provisions may better equip you to evaluate its thesis.
Racking Up the Points: How the GMAT
Scores Your Essay
According to the folks who make the GMAT, the AWA is designed to measure your ability to think
and your ability to communicate your ideas. To assess how well you do in each of these areas, the
GMAT employs the services of two separate readers (one of which may be a computer program
called an automated essay-scoring engine). Based on their analysis of your written masterpiece,
these readers individually assign you a score between 0 and 6, with 6 being the highest.
In the following sections, we give you the lowdown on who evaluates your AWA, what the dier-
ent scores mean, and how to get a new score if the rst one you receive is way o.
Getting to know your readers
Two independent readers judge your analytical writing task, and each of the readers assigns your
essay a score from 0 to 6in half-point increments. If the two readers who are scoring your essay
dier by more than a single point, a third reader will adjudicate. This means that the third read-
er’s score will be used in conjunction with the other scores.
For example, if one reader assigns your essay a 3 and the other reader gives it a 5, a third reader
is brought in. If the third reader also gives your essay a 5, then the 3 would be discarded and your
two scores for that essay would be 5 and 5. If, however, the third reader splits the dierence and
assigns you a 4, you’d have two 4s (the score from the third reader and the average of the rst
two scores).
126 PART 3 Acing the Analytical-Writing Section
The benet of having more than one reader evaluate your essay is that if one reader happens to
assign you an unfairly low score, he won’t be able to sabotage your score.
College and university faculty members from a variety of academic disciplines score your essays.
Some are from business management programs, but you can’t expect that the particular readers
who score your tasks will have any special knowledge of business. So avoid using jargon or
assuming that your reader has had all the same business classes that you’ve had.
The automated scoring program that may grade your essay is designed to reect the judgment of
human readers, so it looks for the same elements that human readers do. Regardless of who (or
what) reads your essay, your goal is to present quality analysis and sound reasoning with a mini-
mum of grammatical errors. In Chapter9, we tell you how to avoid common writing errors.
Readers look for two things when they take on your essays: clear analysis and good writing. For
an essay to earn a score of 5 or 6, it must clearly analyze the argument, demonstrate good orga-
nization, and provide specic, relevant examples and insightful reasoning. The essay must dem-
onstrate clear control of language and apply a variety of sentence structures. It can have some
minor aws in the way you use standard written English but not too many.
Keeping all these things in mind as you write your essay is a tough order for 30 short minutes. To
help you through the process, consult Chapter9, where we discuss strategies for analyzing argu-
ments quickly and eectively and go over the most common errors test-takers make when they
write under pressure.
Interpreting the scores
The GMAT reports your AWA score as a number from 0 to 6in half-point increments. For one
administration, a score of 6, the highest possible score, lands you in the 90th percentile, meaning
that 90 people out of every 100 test-takers received a lower score. A score of 6 is obviously dicult
to earn, and only about 10 percent of test-takers achieve that score! For the same test, a score of
5.5 puts you in the 81st percentile; a score of 5, in the 57th percentile; 4.5, the 43rd percentile;
and4, the 20th percentile.
The mean nal score on the AWA is about 4.4. The typical essay, therefore, falls somewhere
between 4 (adequate) and 5 (strong). A number of papers fall into the 3 (limited) category or
lower, and the cream of the crop is recognized with a 6 (outstanding). To make sure your score
surfaces to the creamy top, practice using the techniques we provide in Chapter9.
Requesting your essay be rescored
After receiving your essay score, you may think it’s too low. If that’s the case and you truly think
you wrote a better essay than your score represents, you can take advantage of the GMAT’s AWA
rescoring service. Within six months of your exam, you can pay $45 to have an independent
reader score your essay. The new score stands, whether it increases or decreases, so requesting a
new score can be risky. But if you think a real discrepancy exists, you can take your chances by
sending in a rescoring request form. The new score result is sent to you and the schools that have
already received your original AWA score.
The rescoring service applies only to the AWA.The GMAT won’t rescore the other three sections,
which makes sense because you can’t do much to change a multiple-choice test score!
CHAPTER9 Present Per fect Paragraphs: How to WriteaGMAT Essay 127
IN THIS CHAPTER
» Writing the right way: Errors to
avoid
» Boosting your score with writing
strategies
Present Per fect
Paragraphs: How to
WriteaGMAT Essay
K
nowing what to expect from the analytical writing assessment (AWA) gives you an advan-
tage on the GMAT, but if you want to earn a high score, you need to know what you’re
expected to do and how to do it. To perform well on the analytical writing task, you have to
combine good analysis with a good writing style. If you lack either of these key components, your
score will suer. In this chapter, we start with common writing errors that you should avoid and
then discuss the steps to writing your analysis.
Avoiding Grammar, Punctuation,
and Mechanics Errors
One of the aspects of the analytical writing assessment that causes the most trouble for test-
takers is the requirement that they demonstrate a good control of standard written English. Stan-
dard written English isn’t so standard anymore, and it doesn’t mirror the way most Americans
speak (or text and email, for that matter!). Emailed messages are often sentence fragments, and
you don’t have to worry about things like spelling and punctuation when you text. Because you
can’t always rely on what sounds right to you, you have to know the writing rules.
In the following sections, we identify a few common mistakes that plague GMAT test-takers.
Writers everywhere seem to repeat these same writing errors. The essay readers will notice these
errors, and their presence in your essay will aect your score. If you identify the errors you make
most often, you can begin to eliminate them now. Don’t wait until test day to isolate your writing
issues! In addition to the information we give you in this chapter, you can nd more info on
applying the rules of grammar and punctuation and on correcting writing problems in Chapter4
and in English Grammar For Dummies by Geraldine Woods (Wiley).
Chapter9
128 PART 3 Acing the Analytical-Writing Section
Punctuation errors
The role of punctuation is to guide the reader through sentences and paragraphs. Without proper
punctuation, your reader won’t know where one thought ends and another begins. Punctuation
errors are among the most common mistakes test-takers make on the essay portion of the GMAT,
and we’re not talking about simply ending a sentence with a period.
Many people confuse colons and semicolons. Semicolons join independent clauses when the
thoughts they convey are related enough to keep them in the same sentence: It’s almost test day; I
need to write a practice essay this weekend. (Independent clauses can stand alone as complete sen-
tences. For more information on the dierence between independent and dependent clauses, see
Chapter4.) You can also separate two independent clauses with a colon when the second inde-
pendent clause expands on or species the idea conveyed in the rst. Jenny learned a very important
lesson: Never leave a chocolate bar on the front seat of the car on a hot day. Independent clauses don’t
have to follow a colon, however. A colon can be followed by a list of examples or a pertinent
phrase or clause as long as the colon is preceded by an independent clause. Before leaving for the
exam, Saul made sure he had all of his supplies: admissions voucher, photo ID, and a bottle of water to gulp
during the break. If the colon doesn’t follow an independent clause, you’ve used it improperly, as
in this incorrectly punctuated sentence. Before leaving for the exam, Saul made sure he had: his admis-
sions voucher, photo ID, and a bottle of water.
The most common punctuation errors involve commas. You use commas to separate items in a
series, to replace omitted words, and to set o nonessential phrases and clauses and parentheti-
cal expressions. You also use them to separate parts of the sentence:
»
Insert a comma before the coordinating conjunction (for, and, nor, but, or, yet, or so) that joins
two independent clauses: Bailey thought she had remembered her admissions voucher, but she
discovered she had left it on the printer. (But don’t place a comma before a conjunction if it joins
elements that aren’t independent clauses: Bailey remembered her admissions voucher but forgot
her photo ID.)
»
Include a comma between a beginning dependent clause and an independent clause: If Bailey
had printed the voucher the day before, she could have placed it in her car. (But you don’t need a
comma between the clauses if the independent clause comes rst: Bailey could have placed the
admissions voucher in her car if she had printed it the day before.)
Two comma errors GMAT essay-writers often make are comma splices and run-on sentences:
»
Comma splices occur when you join two independent clauses with just a comma and no
coordinating conjunction, like this: Harold made several errors in his GMAT essay, one was a
comma splice. To correct a comma splice, do one of the following:
•
Make the independent clauses two separate sentences. (Harold made several errors in his
GMAT essay. One was a comma splice.)
•
Substitute a semicolon for the comma. (Harold made several errors in his GMAT essay; one
was a comma splice.)
•
Add a coordinating conjunction after the comma. (Harold made several errors in his GMAT
essay, and one was a comma splice.)
»
Run-on sentences result when you join together two independent clauses with a coordinating
conjunction and no comma: Harold made several punctuation errors in his GMAT essay and one
was a run-on sentence that made his writing seem needlessly wordy.
To correct a run-on, you just add a comma before the conjunction: Harold made several punctu-
ation errors in his GMAT essay, and one was a run-on sentence that made his writing seem need-
lessly wordy.
CHAPTER 9 Present Per fect Paragraphs: How to WriteaGMAT Essay 129
Sentence-structure problems
GMAT essay-readers focus on more than how you punctuate your sentences. They also notice
how you form your words. To avoid a negative critique, steer clear of these two problems with
sentence structure:
»
Sentence fragments: You may be able to blame your propensity for sentence fragments on
technology, but you can’t translate your email and texting style to the GMAT essays. A sen-
tence must have a subject and a verb and convey a complete thought. Watch out for depen-
dent clauses masquerading as complete sentences. Even though they contain subjects and
verbs, they can’t stand alone as sentences without other information. Here are
some examples:
•
A sentence and a fragment: I will return to the workforce. After I earn my MBA.
•
A complete sentence: I will return to the workforce after I earn my MBA.
»
Modier errors: Modiers are words and phrases that describe other words. The rule of
thumb is to place modiers as close as possible to the words they modify:
•
Sloppy: The assistant found the minutes for the meeting held on Saturday on the desk.
•
Better: The assistant found Saturday’s meeting minutes on the desk.
Faulty forming of possessives
One writing element that you may overlook when you’re frantically composing a 30-minute essay
is forming possessives. Although your training in putting together proper possessives likely
began in elementary school, you may appreciate this refresher:
»
Standard-issue nouns: Use the possessive form of a noun when the noun is immediately
followed by another noun that it possesses. Most possessives are formed by adding an
apostrophe and an s to the end of a singular noun: Steve’s boss. This practice is usually true even
if the singular noun ends in s: Charles’s test score. If the possessive noun is plural and ends in s,
you just add an apostrophe to the end of the word: The brothers’ dogs; many clients’ nances.
»
Pronouns: The possessive forms of personal pronouns are my, his, her, your, its, our, and their
for pronouns that come before the noun and mine, his, hers, yours, its, ours, and theirs for
possessive pronouns that occur at the end of a clause or that function as a subject.
None of the possessive personal pronouns contains an apostrophe. It’s is a contraction of it is, not
the possessive form of it. As opposed to proper pronouns, possessive indenite pronouns do con-
tain apostrophes: Somebody’s dog has chewed my carpet. For information on indenite and personal
pronouns, see Chapter4.
Spelling issues
If you’re like most people in America, you’ve come to rely on your word-processing program to
correct your errors in spelling. The spell-check feature is one of the most popular and useful tools
because it allows you to take your mind o of spelling and concentrate on what you’re writing.
And if you use an autocorrect feature on your word-processing program, you may not even realize
how often your computer corrects your misspelled words.
The bad news is that you won’t have a spell-check function available when you write your essay on
the GMAT.This means that when you take the GMAT, you’ll be responsible for correcting your own
130 PART 3 Acing the Analytical-Writing Section
spelling, perhaps for the rst time in years! One or two spelling errors may not be enough to lower
your score, but in conjunction with any of the other errors we discuss in this chapter, a few spelling
mistakes can make the signicant dierence between one score and the next half-point higher.
A good way to avoid potential spelling errors is to steer clear of unfamiliar words. If you’ve never
used a word before and have any doubt about its meaning or how it’s spelled, avoid using it. If you
use unfamiliar words, you risk not only misspelling the word but also using it inappropriately.
Stick to what you know when you write your analytical essay. If you have enough time before the
test, you can always broaden your vocabulary. Developing an extensive vocabulary will pay o in
your career as well as on the GMAT.
More dos and don’ts
Here are a few more things to keep in mind when preparing for your essay:
»
Use simple, active sentences. To increase your score, keep your sentences simple and active.
The more complex your sentences, the greater your chances of making mistakes in grammar.
You may think that long sentences will impress your readers, but they won’t. Furthermore,
they may cause you to make writing errors more easily.
Another important characteristic of strong, persuasive sentences is the use of active voice.
Active voice is clearer and more powerful than passive voice.
»
Provide clear transitions. Use transitions to tell the reader where you’re going with your
argument. You need only a few seconds to provide your readers with words that signal
whether the next paragraph is a continuation of the previous idea, whether it refutes the last
paragraph, or whether you’re moving in a new direction. Transitions are key to good
organization.
»
Use precise descriptions. Use descriptive words to keep your readers interested and
informed. If you use specic, well-chosen words to clearly illustrate your points and examples,
your writing will have more impact and you’ll earn a higher score.
»
Avoid slang expressions. Stick to formal English, and avoid contractions and slang. Your
readers are professors and should be familiar with formal English, so they expect you to use it
in your essays. Using sentence fragments and slang is okay when emailing a friend, but on the
GMAT, employ a more professional style.
Practice makes perfect!
You can practice writing in GMAT style in creative ways. For example, if you write a lot of emails,
practice writing them more formally. When your friends send you unpunctuated emails full of
misspellings and grammatical errors, respond with proper punctuation, superior spelling, good
grammar, and perfect paragraphs.
You can’t prepare for the GMAT with emails alone, so here are some things to think about when
writing practice essays:
»
Write your essay under test conditions. Give yourself a 30-minute time limit and study in a
quiet environment.
»
Use only those items you’ll have available on the test. Type on your word processor but disable
your automatic spell correction, use an erasable board or a single sheet of paper for scratch,
and don’t use reference books.
»
Take your practice essays seriously (practice the way you want to perform).
CHAPTER 9 Present Per fect Paragraphs: How to WriteaGMAT Essay 131
Building a Better Essay: Ten Steps
to a Higher Score
If you’re going to write well, you need something to write about. Remember that your analytical
writing score is based on the quality of your argument as well as the quality of your writing. Even
though you’ve been writing for years in college or in the workplace, you probably haven’t had to
produce very many analytical essays in just 30 minutes. In this section, we take you through a
ten-step process to help you create better essays in less time.
With a plan in mind, you can use your essay time more eciently and earn a better score. Using
part of your 30 minutes to develop a plan means you’ll be more organized than someone who just
starts writing whatever comes to mind. In fact, you’ll likely type for only about 20 minutes during
the 30-minute task because you’ll spend 5 minutes outlining your argument and 5 minutes
proofreading what you’ve typed.
Work out your timing during your practice tests and note the amount of time you generally need
for each part of the task. Remember that you have only 30 minutes, so you’ll never have all the
time you want for any of the three stages, but with practice you’ll nd the formula that ts your
strengths. For example, you may be an excellent typist who can write very fast when you get
started. In that case, you can aord a little more time for pre-writing and will need additional time
for proofreading all that text you typed. If, on the other hand, you write or type fairly slowly, you’ll
need to spend at least 20 minutes to get your great ideas on the computer screen and saved for
posterity. Here are the ten steps you should follow during your 30-minute analytical writing task:
1. Read the analytical writing prompt carefully before you begin writing.
Although this step may seem obvious, you may hurry through reading the prompt in your rush
to start the essay and may miss important elements of your assignment. Take enough time to
truly understand the argument you’re to analyze. Read the prompt more than once; read it
quickly the rst time to get an idea of the subject matter and then read it more slowly to catch
all the details. Some of your best arguments and examples will come to you when you’re
reading the prompt carefully.
2. Don’t waste time reading the directions.
You can make up some of the time you spend carefully reading the prompt by skimming over
the directions that follow. We’ve paraphrased the instructions for the essay in Chapter8 and
onthe practice tests, so you know what you’re supposed to do. The most you need to do is skim
the directions to make sure nothing has changed and move on.
3. Plan your essay format ahead of time.
Knowing how to structure your essay can help you plan it. Make sure you have an introduction
that discusses and presents your position (or thesis), supporting paragraphs that use examples
and arguments to persuade others to see your way of reasoning, and a conclusion that briey
summarizes what you’ve said in the previous paragraphs. The length of your essay isn’t as
important as the quality of your analysis. Use as many paragraphs as you need to make your
point in the allotted time. Just be sure that you know what you’re going to write about before
you begin writing.
4. Use the erasable noteboard.
Brainstorm and write down your thoughts so you don’t forget them. Don’t rely on your
memory; that’s what the noteboard is for. Jotting down a word or two can preserve your idea
until you’re ready to write about it.
132 PART 3 Acing the Analytical-Writing Section
5. Write a brief thesis statement.
Write a brief thesis statement indicating the main points of your evaluation of the argument
and why you think that way. We recommend that you actually type this statement on the
computer because it’s the key sentence of your introductory paragraph.
For example, say you’re asked to evaluate the strength of this argument: “Corporations exist to
makea prot for shareholders; therefore, the primary duty of the corporation is not to employ
workers or to provide goods and services but to make as much money as possible.” Your thesis may
be that the argument errs in simplifying the role of corporations and failing to provide adequate
support for making the simplistic assertion that corporations exist primarily for shareholder prots.
6. Create a quick outline based on your thesis.
After you’ve created your thesis and have typed it into the computer, return to your notepad
and make a brief outline. Because your ideas are already on the noteboard, outlining is a very
simple process. Select the best arguments and examples to support your thesis. Decide in what
order you want to address these ideas and number them for use as the topic sentences for the
supporting paragraphs of your essay. Under each topic, list several examples and anecdotes
that you’ll use to support your topic.
For example, your main topics in the evaluation of the purpose of corporations argument may
be that (1) the conclusion is too simplistic, and (2) the argument fails to provide adequate
support for its position.
7. Write your introduction.
Move from a general statement to more specic ones and end with your thesis. In fact, your
introduction may consist of only two sentences: a general introduction to the topic and your
thesis statement. A complete introduction for the shareholder duty argument could consist of an
introductory sentence or two that restates the conclusion and premises of the original argument.
Then you’d lead into the thesis statement with a statement of the problems with the argument.
8. Write your supporting paragraphs.
After you’ve put together an outline and written the introduction, you’ve completed the hardest
parts of the task. Then you just need to write your supporting paragraphs clearly with as few
errors as possible. Begin with the idea you designated as your rst topic in Step 6 (“the conclusion
is too simplistic”). Introduce the paragraph with a topic sentence, provide a few supporting
examples, and conclude your point. The rst supporting paragraph could point out other impor-
tant considerations for corporations, such as “a duty to care for the consumer and an obligation
toperform research, that supersede the dangerous desire to make as much money as possible.”
Repeat the process for your remaining points.
9. Write a brief conclusion.
End your essay with a simple summary of the points you’ve already made. Provide a synopsis of
the conclusions you reached in each of your supporting paragraphs and end with a restatement
of your thesis. Move from specic statements to more general ones. Many people try to make
too much out of their conclusions, but this paragraph isn’t the place to introduce new ideas or
argue your position. Instead, just remind the reader of your supporting points and thesis.
10. Proofread.
When you’ve nished writing, make sure you have time left over to read through what you’ve
written. Look for spelling and punctuation errors and other careless mistakes that you may
have made in your rush to complete the assignment on time. Concentrate on errors that you
can correct in a few seconds; don’t try to rewrite entire paragraphs.
If you follow these steps in your practice writings and on test day, you’ll come away with an ana-
lytical writing assessment score to be proud of.
CHAPTER10 Deconstructing Sample GMAT Essays 133
IN THIS CHAPTER
» Clarifying GMAT AWA scores
» Analyzing sample argument essays
Deconstructing Sample
GMAT Essays
T
his chapter denes analytical writing assessment (AWA) scores for you and provides you
with some sample GMAT AWA essays so you can see what these babies look like and apply
some elements of the examples to your own writing. By deconstructing sample essays to
gure out what makes for a great essay per GMAT standards, you’ll have a much better chance of
constructing great essays of your own.
Dening GMAT AWA Scores
The dierence between an essay that’s simply adequate and one that’s outstanding comes down
to a few important factors. Here’s how the GMAT dierentiates among essays that score 4, 5, and
6, based on analysis and organization:
»
An outstanding essay (score 6) thoroughly analyzes and evaluates an argument and addresses
whether the case the author makes is logically sound. The analysis uses logical reasoning to
identify any aws in the argument and oers insight as to how to minimize or eliminate these
aws. The essay is thorough and organized.
»
A strong essay (score 5) still oers a powerful, well-reasoned analysis, but it may not be as
insightful as an outstanding (score 6) essay. The essay contains well-chosen examples for
support and is also well organized, though it’s likely not as tightly organized as an outstanding
essay.
»
An adequate essay (score 4) oers a competent analysis of an argument. This essay interprets
the strength and validity of an argument made by another and supports its points with
relevant examples. The analysis may not be particularly well developed, but the fact that the
essay shows competence in at least attempting to validate or disprove the assertions of
another distinguishes it from lower-scoring essays.
Chapter10
134 PART 3 Acing the Analytical-Writing Section
Here’s how the GMAT distinguishes among the top three scores based on quality of writing:
»
An outstanding essay (score 6) demonstrates superior control of the language and employs a
variety of grammatically accurate and detailed sentences. This essay uses eective transitions.
Although the essay may have a few minor errors, it generally reects a superior ability in
grammar, usage, and mechanics of standard written English.
»
A strong essay (score 5) is similar to an outstanding essay, but the sentences may not have
quite as much variety, and the choice of words may not convey as much detail. This essay
employs transitions but not as eectively as an outstanding essay. This essay may have a few
minor errors but reects a facility for grammar, usage, and mechanics.
»
An adequate essay (score 4) lacks sentence variety and, although the diction may be accurate,
the word choice isn’t particularly detailed or precise. This essay may employ transitions, but
they’re likely to be somewhat abrupt. The adequate essay reects a familiarity with standard
written English but may contain several minor errors or a few more-serious aws.
In addition to the top three possible scores, four lower scores reect aws of diering magni-
tudes. We give less time to describing these categories, because after you’ve read Chapters8 and9
and practiced writing essays for the exam, you aren’t likely to produce one of these lower scores
on the GMAT:
»
A limited essay (score 3) is like an adequate paper in most respects, but it’s clearly awed in
one or more areas. This essay may make an ineective interpretation of the argument; lack
organization; fail to present relevant examples; have problems in sentence structure; or
contain errors in grammar, usage, and mechanics numerous enough to interfere with
conveying meaning.
»
A seriously awed essay (score 2) demonstrates more signicant errors than a limited essay. It
may fail to properly follow the directions stated in the prompt, lack any semblance of organiza-
tion, neglect to provide any examples, have serious problems with language or sentence
structure, and contain errors in grammar, usage, or mechanics that seriously interfere with
meaning.
»
A fundamentally decient essay (score 1) provides little evidence of the ability to eectively
interpret the strength of the argument in the prompt. This essay may also have grave and
pervasive writing errors that seriously interfere with the meaning of the essay.
»
A no-score essay (score 0) is blank, completely o topic, or not written in English.
Taking a Look at Sample Essays
The task for the analytical writing assessment is to analyze an argument. The prompt asks you to
write an essay that uses logical reasoning to critique an argument made by another. Its focus is
how well you evaluate an argument instead of what your own views and opinions may be on a
particular topic. In the following sections, we provide sample essay prompts as well as sample
essay responses and walk you through the elements of an eective, well-written response. You’ll
nd more opportunities to turn your logical reasoning powers into outstanding essays in the
practice tests included with this book.
CHAPTER 10 Deconstructing Sample GMAT Essays 135
Sample essay #1
If you have an extra 30 minutes just lying around, you can take the time to analyze the essay
prompt in this section and write a full essay before you read the sample response we provide.
Ifnot, at least take ve minutes before you read the sample essay to create a quick outline, using
Steps 1 through 6 from Chapter9. Read the instructions following the argument very carefully,
and remember: The idea here is to analyze the given argument, not create your own. Here’s the
sample prompt:
The following appeared as part of an editorial in a business newsletter:
“Gasoline prices continue to hover at record levels, and increased demand from China and India
assures that the days of one dollar per gallon gasoline are over. Continued threat of unrest in the
oil-producing regions of the Middle East, Africa, and South America means a perpetual threat to the
U.S. oil supply. American leaders have acknowledged the need for new sources of power to fuel the
hundreds of millions of cars and trucks in America. Despite this acknowledgment, the U.S. govern-
ment has yet to provide substantial funding for this important research. Ocials are relying on
private industry and university researchers to undertake this research that is vital to the economy
and national security. Given the long interval before new technologies are likely to become
protable and the tremendous cost, research into new fuels will be successful only if funded by the
U.S. government using taxpayer funds.”
Examine this argument and present your judgment on how well reasoned it is. In your discussion,
analyze the author’s position and how well the author uses evidence to support the argument. For
example, you may question the author’s underlying assumptions or consider alternative explana-
tions that may weaken the conclusion. You can also provide additional support for or arguments
against the author’s position, describe how stating the argument dierently may make it more
reasonable, and discuss what provisions may better equip you to evaluate its thesis.
After you’ve attempted your own response to the prompt, read through this sample:
The author of this editorial presents the idea that the development of new technology for fueling
the automobiles of America is an absolutely necessary project and provides substantial evidence to
support this claim, for example, the rising price of gasoline, the swelling demand for oil in overseas
markets, and warning signs of turbulence and instability in oil-producing countries. However, the
author has not provided much evidence for or reasoning behind the statement that the U.S.
government should fund this research and instead relies on certain assumptions about the reader’s
level of background knowledge about the issues.
The editorial states that it will take a long time and a lot of expense to develop these new technolo-
gies, but the argument fails to include evidence of this. The author is making the assumption that
readers will know that private companies and universities have been working for decades on
projects such as hydrogen fuel cells, bio-diesel, ethanol, and electric cars. The editorial would be
much stronger if it included one or two sentences on the fact that each of these technologies is
feasible and that with increased funding could be brought rapidly to market.
Furthermore, it is suggested that the development of new fuel technologies is “vital to the economy
and national security” of the U.S., but this statement is neither explained nor substantiated. It
seems to me that if a greater amount of government funding is dedicated to scientic research, the
budgets of other programs and departments will have to be cut, which could have serious negative
impacts on national security, and possibly also the economy. If the editorial were to compare the
hundreds of millions needed to fund research into alternatives to oil with the hundreds of billions
spent each year on national security, then the argument would be stronger.
136 PART 3 Acing the Analytical-Writing Section
Clearly, the author of this editorial has made several assumptions about his/her readers, the most
important probably being that readers of this business newsletter are familiar with this issue and
will be able to provide the details of government funding and alternative fuel research lacking in the
editorial. The evidence that the author does provide is strong. The editorial’s conclusions seem
valid. However, the editorial lacks the necessary foundation of facts and reasoning that would
demonstrate, for example, why funding alternative fuel research now will allow new fuel technolo-
gies to gradually replace dependence on oil before a crisis hits.
This editorial discusses a very important issue and raises the critical subject of government funding
for research into alternative fuels. However, the author has not provided much evidence or
reasoning behind the conclusion that the U.S. government should fund this research.
Discussion of sample essay #1
This response is well developed and clearly articulated. The essay begins with a very strong intro-
ductory paragraph that develops the position, credits the editorial’s strong points, and then
clearly states the thesis that the author has made too many assumptions and not provided the
necessary evidence. From the start, this essay appears to merit at least a 4.5.
The middle three paragraphs provide specic examples of assumptions that the editorial makes
and indicate how the author could strengthen the argument. The rst example is the assumption
that the reader will know that alternative fuel technologies take a long time to develop. This essay
provides the specic examples that the editorial itself lacked. The next paragraph discusses the
claim that the economy and national security depend on alternative fuels. This is probably the
weakest paragraph in the essay. The essay sidesteps the editorial’s point when the essay turns to
the issue of reducing the budgets of other programs. Still, this is a well-written paragraph that
does oer valid suggestions for strengthening the editorial. The fourth paragraph ties everything
together by pointing out the specic assumptions that the editorial is making about its readers.
This paragraph demonstrates the sophistication of the essay by pointing out the editorial’s
intended audience, the weaknesses of the assumptions it makes, its strengths, and nally, ways
to make the editorial better.
This essay is strong because it’s specic and well developed. The essay singles out particular
points in the editorial and explains not only the weaknesses of those points but also ways to make
them stronger. It provides a clear introduction and thesis statement. The conclusion is brief and
fullls its purpose of restating the thesis. The diction used in this essay is precise and descriptive.
The sentences are simple but varied, and they mostly demonstrate active rather than passive
voice. There are no obvious errors in grammar, usage, or mechanics. This essay overall would
likely garner a 5 but denitely nothing lower than a 4.5.
Sample essay #2
Here’s another prompt for you to try. Again, if possible, attempt your own essay before you read
through the sample response; if you don’t have time to write an entire essay, take at least ve
minutes to create a quick outline, using Steps 1 through 6 from Chapter9.
The following is an excerpt from an editorial that appeared in a periodical dedicated to education
topics:
“The most important factor in choosing a career should be the potential salary. It all comes down to
quality of life. A high salary ensures that you’ll be able to pay your bills, live in a nice house, drive a
nice car, and aord a comfortable, enjoyable lifestyle that’s sure to be the envy of your friends. This
is most easily achieved by securing a job with the highest salary possible. Well-paid positions like
those of doctors, lawyers, and architects are important to society, well respected, and protable, so
CHAPTER 10 Deconstructing Sample GMAT Essays 137
these are the types of positions you should shoot for. While many believe it is important to nd a
job that you enjoy rst and foremost, if that job doesn’t pay well, you’ll be faced with numerous
stresses and hardships sure to aect your overall quality of life and you will ultimately come to
regret not prioritizing nancial stability above all else.”
Examine this argument and present your judgment on how well reasoned it is. In your discussion,
analyze the author’s position and how well the author uses evidence to support the argument. For
example, you may question the author’s underlying assumptions or consider alternative explana-
tions that may weaken the conclusion. You can also provide additional support for or arguments
against the author’s position, describe how stating the argument dierently may make it more
reasonable, and discuss what provisions may better equip you to evaluate its thesis.
Attempt your own response to the prompt, and then read through the following sample essay:
The author of this essay clearly states his belief that, when choosing a career path, earning potential
is paramount. While he oers a number of reasons as to why he feels this way, such as an
improved overall quality of life, a comfortable home, and the ability to impress your friends, his
arguments are based on generalizations and assumptions about what others value most in life and
the overall strength of his stance suers as a result.
For example, the author “ensures” the reader that a high salary will enable them to live a lavish
lifestyle and a life of little stress and strife. Yet he doesn’t take into account the fact that high-paying
jobs are also often high-demand, sometimes at the expense of a happy marriage, quality time with
the kids, or simply time to kick back and relax.
Furthermore, he is assuming that happiness is achieved through material comforts, such as a fancy
house and car, but he fails to recognize that his idea of happiness is not necessarily shared by the
rest of the population. Nor does he consider other ways of nding happiness, like, say, helping
others or nding a way to make a dierence in the world.
Throughout the essay, a fundamental problem with the author’s reasoning is his assumption that
his readers share his feelings as to what is most valuable in life. Even when he acknowledges the
fact that others feel that nding a career you enjoy should be top priority, he fails to devote any
time or attention to the notion that one can feel “rich” even without a thick wallet and ashy car if
they’re able to engage in a career that they nd fullling and gratifying.
While the author of this essay is sure to make his personal stance known in regard to what’s most
important in choosing a career, he fails to oer concrete evidence or devote sucient attention as
to why what is true for him fails to be true for the masses.
Discussion of sample essay #2
How do you think this essay would likely score? The essay asserts early on that the author in the
prompt fails to acknowledge the fundamental dierences as to what constitutes happiness and
backs this up with examples and reasoning, so it’s unlikely to receive a score below 4.
The response refutes the author’s assertions that happiness is achieved through nding a job
with the highest possible salary and backs this up with examples, such as the fact that high-
paying jobs are frequently also high-stress and that other areas of one’s life are often neglected.
The essay also argues against the claim that material goods are the key to quality of life by noting
that one person’s opinion of what constitutes a high quality of life isn’t necessarily true for
someone else. To improve the quality of the supporting examples, the author could have been
more specic, and she could have provided more compelling evidence for her point by referring
to individuals in the public spotlight. For example, the author could have talked about the recent
138 PART 3 Acing the Analytical-Writing Section
nervous breakdown of a wealthy celebrity to show that wealth doesn’t necessarily lead to a stress-
free life. And the author could have supplemented her assertion that money doesn’t buy happi-
ness by expounding on the fullling life of Mother Theresa.
Generally, the essay makes its points, using strong, concise English with few grammatical errors,
although the concluding paragraph is constructed as one long sentence that would read more
clearly if it were broken down into two. And the author includes a couple of pronouns that don’t
agree in number with their references. For example, the author uses the plural pronoun they to
refer to the singular noun one in “... one can feel ‘rich’ even without a thick wallet and ashy car
if they’re able to engage in a career that they nd fullling and gratifying.” The essay also para-
phrases the same general idea several times when it discusses the idea that the author of the
prompt’s idea of happiness diers from that of others. This essay would likely score a solid 4 or,
possibly, as high as a 5.
Compare what you’ve written in response to the prompt to the sample essay. Evaluate your mas-
terpiece and ask yourself how it measures up to— and perhaps accomplishes more than!— the
sample. Use your evaluation to perfect your writing achievement.
Sample essay #3
Read through this prompt and attempt your own essay before you read through the sample
response. If you don’t have time to write an entire essay, take at least ve minutes to create a
quick outline, using Steps 1 through 6 from Chapter9.
The following is an excerpt from an editorial that appeared in a local city newspaper:
“Some cities have enacted bans on pit bull breeds that prohibit city residents from owning dogs that
fall under the “pit bull” umbrella, and other cities across the nation should follow suit as a matter of
public safety. Given that statistics show that three-quarters of all dog-inicted deaths involve either
pit bulls or Rottweilers, which many also consider a “bully” breed, it is undeniable that these animals
are unnecessarily dangerous. They are also widely abused, which contributes, at least in part, to
their aggressive nature. Some pit bull owners say banning an entire breed is essentially racial
proling for dogs, but what if one type of person was responsible for three-quarters of all murders
in the country? Such people should not be able to roam free and endanger whomever they like, and
neither should pit bulls.”
Examine this argument and present your judgment on how well reasoned it is. In your discussion,
analyze the author’s position and how well the author uses evidence to support the argument. For
example, you may question the author’s underlying assumptions or consider alternative explana-
tions that may weaken the conclusion. You can also provide additional support for or arguments
against the author’s position, describe how stating the argument dierently may make it more
reasonable, and discuss what provisions may better equip you to evaluate its thesis.
A sample response to this prompt may read like this:
Though the argument made in the prompt starts out strong by referencing key statistics about the
dangers associated with pit bulls, it falters somewhat later on, when the author tries to consider the
arguments of those who are against implementing pit bull bans. The fact that the author references
a pit bull ban that is already in eect in a major U.S. city seems to add some validity to the overall
argument against the breed, and the statistics about the percentage of canine-inicted deaths in
America oer a solid argument about why a ban might be a good idea.
CHAPTER 10 Deconstructing Sample GMAT Essays 139
The author then falters a bit when trying to drive home the point that pit bulls are also violent and
dangerous because they are widely abused. While this may or may not be true, it would have
strengthened the author’s argument and made he or she seem more convincing if additional
statistics about abuse were included here, as they were in the section regarding canine-related
fatalities. Even without formal statistics, this section of the prompt would have benetted from
additional clarication about the connection between abusive owners and aggressive pit bulls.
The holes in the author’s argument become increasingly apparent when he or she notes that ban
opponents often compare the act of banning certain dog breeds to racial proling. The author tries
to make the point that if a certain “type” of human was responsible for the majority of all murders,
that “type” of person would likely be banned, too. But the author fails to further clarify what he or
she means by “type,” leaving it open to interpretation and scrutiny. Is the author referencing people
of a certain race, nationality or color? Or a person with a certain type of personality trait, or hair
color? Without further explanation, this argument falls at, and the author is therefore unable to
eectively refute the arguments of pit bull-ban advocates. Because of this failure to eectively
address the other side, the strength of the entire argument suers.
Discussion of sample essay #3
At rst glance, this response appears relatively strong. It has no glaring spelling errors and just a
couple grammatical problems, and each paragraph transitions well to the next. Additionally, the
author of the response takes the time to discuss both the strengths and downfalls of the editorial
and back up his opinions with thoughtful reasoning. Based o this alone, the response will likely
warrant a score that comes in somewhere around a 5.
The response summarizes its content in the rst few lines, giving the reader an idea that the
writer plans to further develop key points, such as how the initial editorial relied on statistics to
strengthen its argument, later on. The writer also mentions that while the original editorial cer-
tainly had its merits, it is not without aws, again referring to areas of the essay that would be
more closely dissected further along in the content.
This response is also likely to receive a high score because the author not only points out where
he believes the editorial is awed— such as when it fails to establish a strong connection between
abusive owners and aggressive pit bulls— but also because he oers ideas for how it might be
strengthened (by adding strong, clarifying information about the perceived connection and add-
ing additional statistics specic to abusive owners). The response to the original editorial is also
thoughtful in that it analyzes the editorial’s consideration of the other side of the argument. The
editorial notes that pit bull owners often equate breed bans to racial proling, but it makes a weak
argument about why this should not be the case. The response identies this weakness and refer-
ences it when assessing the overall strength of the original argument. Because the response’s
author carefully considered the strengths and weaknesses of the editorial and avoided grammati-
cal and spelling errors, this essay would likely score high.
Sample essay #4
Here is yet another prompt for you to analyze. Create a response and then read through the
sample essay that follows.
The following is an excerpt from a promotional brochure for an online dating service:
“Technology and social media are intended to better-connect society and enable us as humans to
maintain relationships we may otherwise not be able. However, many people try to argue that what
it is really doing is inserting more wedges between us socially by limiting face-to-face interaction
and keeping our faces in our phones. When it comes to forming strong relationships with other
140 PART 3 Acing the Analytical-Writing Section
people, though, why are relationships that develop online considered any less valid than those
conceived through in-person interaction? Some online relationships might actually prove stronger
than those that are developed by more traditional means, because people may be more apt to
reveal their true selves from behind a screen than they would otherwise. Technology also helps
those who might be shy or antisocial come out of their shells by taking away the stresses associated
with real human interaction, so it can actually strengthen rather than weaken social relationships.”
Examine this argument and present your judgment on how well reasoned it is. In your discussion,
analyze the author’s position and how well the author uses evidence to support the argument. For
example, you may question the author’s underlying assumptions or consider alternative explana-
tions that may weaken the conclusion. You can also provide additional support for or arguments
against the author’s position, describe how stating the argument dierently may make it more
reasonable, and discuss what provisions may better equip you to evaluate its thesis.
Read through the following sample essay in response to this prompt to see how it compares with
your masterpiece.
The author of the prompt is thoughtful in his or her discussion of whether technology and social
media make us less connected as a society, and he or she makes a number of strong points when
supporting the argument that these resources do not, in fact, weaken social relationships. That
being said, there are a number of areas in which I think the argument might have benetted from
some additional input or material.
One such area where the author might have strengthened the prompt would be at the beginning,
by plainly stating his or her belief that technology does not weaken social relationships. Instead, the
prompt’s author “beats around the bush,” so to speak. Rather than clearly state his or her opinion
right o the bat and then use arguments and key points to back up the assertion, the editorial
author instead starts out by refuting some of the arguments in favor of technology hindering
personal relationships. He or she begins by saying, “Technology and social media are intended ...”
which actually reveals very little about his or her own personal take on the matter. While refuting
the opposition’s arguments is certainly important, it might have been better if this was done further
on in the initial argument, after a “thesis” statement-of-sorts based on the author’s own opinions
had been clearly stated.
As for the argument’s strengths, the author made some strong points about why technology and
social media may help some people build social bridges— it’s just a little regrettable that these
points didn’t come up until almost the end of the argument. Such points included the arguments
about shy people perhaps feeling more at ease behind a computer screen, and the notion that
some people were more comfortable discussing serious, emotional matters via a computer than
through face-to-face interaction.
Discussion of sample essay #4
This essay presents a clear, concise assessment of the initial prompt’s strengths and weaknesses,
and it does so with few, if any, spelling or grammatical errors along the way. It is apparent that
the essay author took the time to consider the information provided in the original prompt and
suggest that the argument may have been stronger had it made its case earlier.
For example, the essay author points out that the editorial’s author failed to promptly state his or
her own opinion on whether technology and social media ruin relationships. Though it quickly
becomes apparent that he or she does not feel online socialization is a bad thing, the essay writer
was convinced the impact would have been greater if the prompt author’s personal opinion had
been made clear from the outset.
CHAPTER 10 Deconstructing Sample GMAT Essays 141
The essay author did, however, take the time to point out where the argument in the prompt was
particularly strong, and she called out a few key examples of such arguments, indicating strong
comprehension and a convincingness on the part of the prompt author, even if the essay author
didn’t necessarily agree with the prompt’s stance.
One area where the essay author might have beneted would have been to not only point out that
the prompt’s “... argument might have benetted from some additional input or material,” but
to actually provide some suggestions for such material. For example, the essay author could have
suggested the use of statistics or survey results pertaining to the connection between intercon-
nectedness and social media, or added additional arguments not made in the prompt to support
the same stance. Because the essay author took a thoughtful approach when writing her essay and
analyzed much of the content of the original editorial while demonstrating strong writing skills,
this essay would likely score a 3.
CHAPTER11 Sampling a Series of Writing Prompts 143
IN THIS CHAPTER
» Getting familiar with AWA
prompts
» Preparing timed prompt responses
» Evaluating sample essays
Sampling a Series of
Writing Prompts
W
e know you’re itching to create your own essay responses to some sample AWA prompts.
In this chapter, you wait no longer. Here’s your chance to create your evaluations of
sample arguments. For each of the following four sample prompts, follow this plan:
1. Open your word processor so that you duplicate the AWA’s online format.
2. Set a timer for 30 minutes.
3. Read the sample prompt.
4. Evaluate the argument and create a quick outline.
5. Based on your outline, write a well-organized essay within the 30-minute time limit.
6. Read the sample essay and dissection that follow each prompt to help you assess your
creation.
Sample Prompt #1
The following argument appeared in a plea from a politician:
“The U.S.Constitution has expressed the laws of the land for more than 225 years, and its tenets
are meant to help Americans live harmoniously in the company of one another. To date, 27
amendments have been made to it to adapt it for modern life. There are two methods under which
changes can be made to the Constitution, and one of them, known as an Article V convention, has
never taken place. Given the current divisive political climate, however, it has never been more
necessary. An Article V convention would gather states together to discuss and debate newly
proposed amendments, and the states would then vote as to whether to make the proposed
changes to the Constitution. The very fact that information about Article V appears in the original
Constitution implies that its framers knew broad changes would, one day, be necessary.
Furthermore, 38 out of 50 states would have to approve any amendments before their passage, so
any changes would truly express the wishes of the American people.”
Chapter11
144 PART 3 Acing the Analytical-Writing Section
Examine this argument and present your judgment on how well reasoned it is. In your discussion,
analyze the author’s position and how well the author uses evidence to support the argument. For
example, you may question the author’s underlying assumptions or consider alternative explana-
tions that may weaken the conclusion. You can also provide additional support for or arguments
against the author’s position, describe how stating the argument dierently may make it more
reasonable, and discuss what provisions may better equip you to evaluate its thesis.
Sample response to essay #1
The author of the prompt is trying to argue that Americans should move forward with an Article V
convention in order to make the contents of the U.S.Constitution more appropriate and relevant
for modern society. For the most part, the prompt does a good job of making the case for the
convention.
The author makes some strong points, such as when he or she notes that the Constitution has
already been changed 27 times. This statement makes it seem as if changing the document is not a
major deal, which might encourage more people to think in the same manner. Another strong point
made in the prompt is that the very existence of Article V in the original Constitution intimates that
its original creators looked ahead and foresaw necessary change on the eventual horizon.
There are, however, some areas where the prompt could have explained its arguments more
clearly or eloquently. One example of this is when the prompt author refers to the “current divisive
political climate,” but fails to explain the statement further. What makes the current political climate
divisive? Would amending the Constitution put an end to said divisiveness? The author should have
provided answers to these questions.
Additionally, the prompt might have beneted from more attention to possible arguments against
calling a convention to amend the constitution. It sounds as if this is what he or she is starting to do
near the end, where it is noted that 38 out of 50 states would have to voice their approval before
any changes could be made, but more depth and additional attention to counterarguments might
have strengthened the argument for the convention in the rst place.
Furthermore, the author references “two methods” through which the Constitution could be
amended, but then only discusses the Article V convention. This begs the question— what is the
other method, and why isn’t that one being considered as a means of adapting the Constitution for
modern-day relevancy? The argument would be more convincing if it provided answers to these
questions and the others mentioned above.
Dissection of essay #1
In reading the essay response to the prompt, it becomes clear that the author gave the initial
argument thoughtful consideration, and he was able to articulate his thoughts about the argu-
ment in thoughtful, concise prose. The author is also able to eectively refute some of the argu-
ments that would likely be raised by the opposition, and he also makes reference to areas where
the original argument may have beneted from additional material. For these reasons, this essay
would likely score at least a 4.
The essay author describes in detail the merits of the original argument, such as how it refer-
enced the fact that the Constitution has already undergone multiple revisions and that the fram-
ers seemed to have anticipated this when the document was authored. He also applauded the
author of the initial argument by foreseeing the argument about conventions possibly not
expressing the wishes of the American people by noting that at least 38 states would have to be
on board before any changes could be made.
CHAPTER 11 Sampling a Series of Writing Prompts 145
The essay author also points out where the initial argument falls short, such as when it fails to
clarify its remarks about the divisive political climate and what the other method of amending the
Constitution (as opposed to calling a convention) might be. In doing so, the essay author also
outlines his thoughts about what could be added to the essay to strengthen it, demonstrating he
gave considerable thought to the issue.
In addition to showing a solid understanding of the subject matter and the arguments that can be
made for or against it, the author’s writing is strong and consistent throughout and is largely free
of any grammatical or spelling errors. The combination of thoughtful analysis, thorough assess-
ment of the argument’s strengths and weaknesses, and strong writing skills ensures that the
essay should not score below a 4.
Sample Prompt #2
The following appeared in the editorial section of a city newspaper:
“As incidents of school violence continue to dominate American mainstream media, educators,
legislators and parents continue to seek out methods of countering it. One proposed solution is to
arm America’s teachers, so that they have what they need to act fast if the need arises. The Second
Amendment already grants Americans the right to bear arms, so why should teachers, who are in
charge of some of society’s most vulnerable, be any dierent? Our teachers already assume a
tremendous level of responsibility simply by teaching and guiding our children during the school
day, and arming them would simply make it easier for them to accept more responsibility for
protecting the nation’s children, if the need arises. Teachers undergo background checks before
working with children, and these checks should help weed out any potential dangers or violent
oenders before they get in the classroom— or get their hands on guns.”
Examine this argument and present your judgment on how well reasoned it is. In your discussion,
analyze the author’s position and how well the author uses evidence to support the argument. For
example, you may question the author’s underlying assumptions or consider alternative explana-
tions that may weaken the conclusion. You can also provide additional support for or arguments
against the author’s position, describe how stating the argument dierently may make it more
reasonable, and discuss what provisions may better equip you to evaluate its thesis.
Sample response to essay #2
The author of the prompt is trying to argue that teachers should be armed in the classroom to
enhance the safety of all students and ensure a quick response in the event of an emergency or
intruder. While some of the arguments made therein are strong points, the author fails to pay
much attention to some of the more obvious arguments against arming educators— and the
strength of the argument suers as a result.
By failing to take into account oppositional arguments— such as the fact that kids have a way of
getting their hands on just about anything, and there’s no reason to think this wouldn’t also hold
true for guns— the author doesn’t give himself or herself a chance to address, or better yet, refute
them. Another example of this is when the author notes that teachers undergo background checks,
which, he or she reasons, will keep the bad apples out of America’s schools. This, however, only
holds true if you believe the assumption that the only people out there with the potential to be
dangerous are people who have oended before. But every oender had to have a rst time, right?
So this argument falls a little at. The language the author uses “these checks should weed out any
potential dangers” makes it sound as if even he or she isn’t speaking with a whole lot of conviction.
146 PART 3 Acing the Analytical-Writing Section
Where the prompt does make you think is when it raises the point about how much responsibility
our teachers already have every day. The very nature of the job means most parents have to have a
certain amount of trust in them but the same could be said of having a babysitter— does that
mean all babysitters should be armed, too? Because the author of the prompt fails to consider,
address or refute the arguments on the other side, it ultimately fails to convince.
Dissection of essay #2
The essay response to the argument made in the prompt is thoughtful, analytical, and, for the
most part, well-written, although there are a few small errors here and there (more on that later).
The response successfully identies the prompt’s strengths and weaknesses, and the essay author
also oers some strong advice about where the argument might have been strengthened, indicat-
ing strong comprehension of the subject matter.
Among the key strengths of the essay response is that the essay author references the fact that
kids have the ability to get their hands on almost anything. This raises a very strong point against
arming teachers in America’s schools, and it also points out an area where the original argument
was lacking. The essay makes another strong point (another argument against arming teachers)
when the author mentions the fact that background checks are only going to keep out teachers
who have oended before, not every possible dangerous person out there.
The areas in which the essay response falters tend to be related to grammar and style. The essay
switches back and forth between the second- and third-person, which aects its overall strength
(and ultimately, its score, too). While the majority of the essay is written in the third person, the
author switches to second person in the second paragraph, where she says, “only holds true if
you” and again in the third paragraph, where she says, “the prompt does make you think.” The
overall strength of the essay would have been better if the essay author had picked one point of
view and stayed consistent with it throughout the copy.
There are several other grammatical errors that also distract a reader from the actual content in
the essay. For example, the second-to-last sentence in the essay is missing a comma between
“them” and “but.” If a complete sentence appears on either side of the conjunction, a comma is
needed for clarity.
Sample Prompt #3
The following argument appeared in a parenting blog:
“Americans are raising a generation of children that don’t know how to lose. Nowadays, our kids
receive praise in the form of trophies for just about anything, from participating to perfect atten-
dance. Not only does this tend to make our kids more “soft” and uneasy once they make it to the
“real world,” where they are prone to losing at least once in a while, but it also gives our children the
impression that losing is so utterly terrible that we simply cannot let it happen anymore. NOT giving
awards for any and everything teaches kids that awards must be earned, and talents have to be
honed. It teaches them that it can take some time to excel in a given area, and that that’s just ne.”
Examine this argument and present your judgment on how well reasoned it is. In your discussion,
analyze the author’s position and how well the author uses evidence to support the argument. For
example, you may question the author’s underlying assumptions or consider alternative explana-
tions that may weaken the conclusion. You can also provide additional support for or arguments
against the author’s position, describe how stating the argument dierently may make it more
reasonable, and discuss what provisions may better equip you to evaluate its thesis.
CHAPTER 11 Sampling a Series of Writing Prompts 147
Sample response to essay #3
The author of the prompt clearly believes that trophies and awards are too broadly distributed
among today’s kids and that giving awards for participation and such sends the wrong message.
After an initial read, it is safe to say the author makes some compelling arguments that might even
be strong enough to convince opponents that giving out awards too freely actually does children a
disservice.
Among the stronger arguments made in the prompt is the fact that if children do not learn how to
lose during adolescence, they may struggle with disappointment once they enter the adult world,
where most everyone tends to fail or lose at one time or another. Another key point made in the
prompt is when the author says that giving awards for everything gives children the impression that
losing is so terrible it cannot be tolerated. In both statements, the prompt’s author drives home the
point that what children are taught during childhood tends to transcend into their adult lives. Just as
a child who grows up in an abusive home may, too, perpetuate the cycle of abuse, a child who grow
up never losing may grow up to be an adult who has tremendous struggles with failure, and his or
her life may be impacted negatively as a result. The author also notes that, by NOT giving awards
for participation, kids learn the value of hard work and that it takes time and practice to be the best
at something.
The author’s argument is sound and thoughtful, and the only area where it might have beneted
from additional copy is if it had included some points that might refute arguments made on the
other side. For example, youth sports are youth sports for a reason, and not every 6-year-old is
dreaming of one day playing in the big leagues. Shouldn’t kids who will likely never pick up a bat or
ball again receive at least some level of recognition for taking part in an activity? Ultimately,
however, the argument made in the prompt is quite strong, and the author evidently took the time
to clearly articulate his or her thoughts.
Dissection of essay #3
Though the author of the essay response never clearly stated his own feelings about whether
today’s kids are awarded too many trophies just for “participating,” it sounds as if he might have
initially leaned toward the other side of the argument— that kids should be given participation
trophies— but then thought twice or reconsidered after reading the argument made in the prompt.
Evidence of this can be found in the last line of the rst paragraph, when the essay author notes
that the prompt’s compelling arguments “might even be strong enough to convince opponents.”
This demonstrates that the essay author had a strong, comprehensive understanding of the argu-
ments made in the initial prompt, and that he gave them all thoughtful consideration before
crafting the essay response. This attention is also evident when the essay author introduces the
comparison regarding children who grow up in abusive homes. While the subject matter might be
a bit of a stretch, the comparison does have merit, and some may see it as adding strength to the
original argument against giving awards for just about anything.
The essay author also points out where the original prompt might have been strengthened while
pointing out one of the main arguments the opposition might make, which again demonstrates
that the essay author took the time to carefully consider the issue and respond appropriately.
Additionally, the essay response is formulated well: It begins by briey summarizing the issue
discussed in the prompt, and then calls out the essay’s key strengths as well as the areas where
it faltered slightly before adding in some suggestions about how it might have been strengthened.
Because the essay author formulated the response well, clearly considered the arguments made
in the original prompt, and took the time to call out the strengths and weaknesses of the initial
argument, it is safe to assume this essay would score around a 5. It also is largely free from
spelling or grammatical errors or any glaring inconsistencies, which should also contribute to a
favorable score.
148 PART 3 Acing the Analytical-Writing Section
Sample Prompt #4
This argument appeared in a legal motion:
“In many states, sex oenders are not allowed to use social media sites that also allow children to
use them, such as Facebook, Twitter, Instagram and so on. Some believe the ban ought to be
enacted at the federal level. Sex oenders, however, already face a myriad of restrictions in their
day-to-day lives that impede their abilities to nd employment and housing, interact socially and
with loved ones, and stay current on the world around them. Once they have served their sen-
tences and paid their debts to society, they should be allowed to reintegrate into the outside world
in the same manner as other criminals. It is also often forgotten that sex oenders, too, have civil
rights. Banning them from modern forms of communication is a violation of free speech and the
First Amendment of the U.S.Constitution, and for that alone, it should not be tolerated.”
Examine this argument and present your judgment on how well reasoned it is. In your discussion,
analyze the author’s position and how well the author uses evidence to support the argument. For
example, you may question the author’s underlying assumptions or consider alternative explana-
tions that may weaken the conclusion. You can also provide additional support for or arguments
against the author’s position, describe how stating the argument dierently may make it more
reasonable, and discuss what provisions may better equip you to evaluate its thesis.
Sample response to essay #4
This argument sounds as if it is sympathetic to sex oenders, which is unimaginable. That being
said, there are a few important points made that really make you think. Although, not enough to
actually change your mind.
The most convincing argument made in the initial prompt is when the author suggests that
keepingsex oenders from using social media is a violation of the First Amendment. It is very
though-provoking, because when the U.S.Constitution was written, there was no internet. There
was no Facebook, Twitter or Instagram, so the Constitution’s framers couldn’t have possibly
foreseen what was coming up the pike or addressed it in any kind of appropriate manner.
However,the First Amendment is undeniably about protecting certain freedoms for all Americans,
and for that reason, the argument at least has merit.
However, the prompt’s author seems to be making excuses for sex oenders and expressing
sympathy when he or she goes on about how they already have other restrictions imposed on
them that make it hard to nd work and place to live, among other things. Of course they should
face restrictions— they are sex oenders. They shouldn’t, as the prompt states, “be allowed to
reintegrate into the outside world in the same manner as other criminals,” because they aren’t
other criminals, and many of them commit crimes against children. Therefore, the only particularly
strong argument made is the one about the First Amendment.
Dissection of essay #4
Arguably, the biggest takeaway from the essay response is that the essay’s author seemed to have
a dicult time analyzing the strength of the argument without letting her own personal feelings
about the sensitive subject matter cloud her judgment. This is apparent in statements such as,
“Of course they should face restrictions — they are sex oenders” and “they aren’t other
criminals.”
CHAPTER 11 Sampling a Series of Writing Prompts 149
The main point of drafting the essay is to thoughtfully and analytically evaluate the strength of
the argument itself— not to include your own personal opinion on the subject matter. There are
also some structural and grammatical issues that will likely aect the essay writer’s score.
Redundancy is among the issues, as the essay references the strength of the First Amendment
statement several times.
Other issues include the lack of a comma after “of course” in the nal paragraph, and the sen-
tence fragment, “Although, not enough to actually change your mind,” that appears in the intro-
ductory paragraph. It’s also worth pointing out that the author of the essay has a tendency to
switch back and forth between second (you, your, and so on) and third person throughout the
copy, which can be distracting. In the intro paragraph, the essayist makes statements such as
“really make you think,” but the entire following paragraph switches back to third person. As a
general rule, it’s best to pick a point of view and stick with it.
The essay isn’t entirely bad— the point about how the Internet wasn’t around when the Consti-
tution was drafted, for example, is a strong one. However, the other issues will likely keep it from
scoring above a 3.
4
Conquering the
Quantitative
Section
IN THIS PART ...
Dust o your basic math skills with a review of
fundamental operations, fractions, and exponents.
Take a trip down memory lane with good old algebra,
including quadratic equations and functions.
Get in shape for the GMAT geometry problems. Go over
various formulas, including area and perimeter and the
slope of a line and gain timesaving tips for nding side
lengths of triangles.
Cover the ins and outs of statistics and probability,
including data interpretation, combinations and
permutations, and sets, from the essential concepts
of mean and mode to more complex calculations of
standard deviation and probability.
Understand the two varieties of GMAT math questions:
the standard ve-answer, multiple-choice, problem-
solving kind and the less familiar data-suciency
questions.
Take a mini GMAT math test to show o your fresh
skills.
CHAPTER12 Getting Back to Basics: Numbers and Operations 153
IN THIS CHAPTER
» Refreshing your memory on types
of numbers and basic operations
» Getting the skinny on bases,
exponents, and radicals
» Keeping order of operations in mind
» Grabbing your share of fractions,
decimals, and percentages
» Making comparisons by using
ratios and proportions
» Bringing numbers down to size
with scientic notation
Getting Back to Basics:
Numbers and Operations
T
hose of you who majored in math in college probably look at the math section of the GMAT
like an old friend. Those of you who haven’t stepped into a math class since high school are
more likely dreading it. You know who you are! Don’t worry, this chapter takes you back
to the beginning with a review of the concepts you’ve learned through the years but may have
temporarily forgotten. In this chapter, you see problems that test your knowledge of the math
building blocks, such as number types, basic operations, exponents and radicals, fractions, and
ratios. These concepts form the foundation of more complicated math problems, so this stu is
important to know. For example, you could end up with a completely wrong answer if you solve
for real numbers when the question asks for integers. Some GMAT-takers may end up kicking
themselves (and that looks just plain odd) for missing relatively simple problems because they
were unfamiliar with some basic terminology. To avoid this unfortunate (and awkward) position,
make sure you’re well-heeled in math basics.
Just Your Type: Kinds of Numbers
Since the Stone Age, humans have found it necessary to rely on numbers to get through daily liv-
ing. In hunter-gatherer cultures, the people made notches in bones to count, for example, the
number of days in a lunar cycle or perhaps to indicate how long the nomadic tribe spent in a
particular location until it found food. But through the millennia, humankind soon realized that
numbers could become large and unwieldy. Hence, the advent of number classications and
operations!
Chapter12
154 PART 4 Conquering the Quantitative Section
Although understanding modern mathematical operations may have burst prehistoric man’s
cerebral cortex, it’ll surely be easier for you after you complete this review. For the GMAT, you
need to know the more common types of numbers, such as integers, rational numbers, real num-
bers, and prime numbers. And you should at least be aware of some of the less common types,
such as irrational and imaginary numbers.
»
Integers: Numbers that belong to the set of all positive and negative whole numbers with 0
included. Integers can’t be fractions or decimals or portions of a number. Integers include –5,
–4, –3, –2, –1, 0, 1, 2, 3, 4, and 5 and continue innitely on either side of 0. Integers greater than
0 are called natural numbers or positive integers. Integers less than 0 are called negative integers.
Take care when working with 0. It’s neither positive nor negative.
»
Rational numbers: Numbers that are expressed as the ratio of one integer to another; that is,
numbers that can be expressed as fractions. Rational numbers include all positive and
negative integers, zero, fractions, and decimal numbers that either end or repeat. For example,
the fraction
1
3
can be expressed as
0 3333.
. Rational numbers don’t include numbers like
orradicals like
2
because the decimal equivalents of these numbers don’t end or repeat.
They’re called irrational numbers.
»
Real numbers: All numbers that you normally think of as numbers. Real numbers belong to
the set that includes all integers, rational numbers, and irrational numbers. Think of real
numbers as those numbers represented by all the points on a number line, either positive or
negative or zero. Real numbers are also those numbers you use to measure length, volume, or
weight. So when the GMAT asks you to give an answer expressed in terms of real numbers,
just solve the problem as you normally would.
»
Imaginary numbers: Any number that isn’t a real number. So an imaginary number is a
number like
1
. Think about it: You know that when you square any positive or negative real
number, the result is a positive number. This means you can’t nd the square root of a
negative number unless the root is simply not a real number. So imaginary numbers include
square roots of negative numbers or any number containing i, which represents the square
root of –1. Won’t you be a fascinating conversationalist at your next soiree!
»
Prime numbers: All the positive integers that can be divided by only themselves and 1; 1 isn’t
a prime number. The smallest prime number is 2, and it’s also the only even prime number.
This doesn’t mean that all odd numbers are prime numbers, though. Also, 0 can never be a
prime number because you can divide 0 by every natural number there is. To determine prime
numbers, consider this series: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and so on. What makes these
numbers unique is that the only two factors for these numbers are 1 and the number itself.
You probably won’t encounter this term on the GMAT, but in case it comes up at cocktail parties,
you should know that 0 and positive numbers other than 1 that aren’t prime numbers are called
composite numbers. A composite number has more than two factors, so it’s the product of more
than simply itself and the number 1. Questions regarding prime numbers appear fairly frequently
in GMAT math sections. Here’s a sample of one you may see.
AN IRRATIONAL FEAT WITH AN
IRRATIONAL NUMBER
Recently, a team of computer engineers in Japan calculated out to over 1.24 trillion decimal digits. It
still didn’t end, meaning that
is truly irrational. And it may be irrational to attempt to prove otherwise!
Thankfully, the GMAT won’t ask you to attempt this task or anything remotely like it.
CHAPTER 12 Getting Back to Basics: Numbers and Operations 155
Which of the following expresses 60 as a product of prime numbers?
(A)
2 235
(B)
2 215
(C)
2 335
(D)
2 35
(E)
1256
This question tests your knowledge of prime numbers. Because the correct answer has to be a
series of prime numbers, eliminate any choice that contains a composite (or non-prime) number.
So Choices (B) and (E) are out (even though the product of both is 60) because 15, 1, and 6 aren’t
prime numbers. Then, eliminate any answers that don’t equal 60 when you multiply them.
Choice(C) is 90, and Choice (D) is 30, so the answer must be Choice (A). It’s the correct answer
because it contains only prime numbers whose product equals 60.
It’s Not Brain Surgery: Basic Operations
Now that you’re a bit more comfortable with some terms, it’s time to take a stab at manipulating
numbers. Figuring out how to do operations, which we discuss in the following sections, is pretty
simple, almost as simple as 1-2-3. It doesn’t take a brain surgeon to open your mind to endless
possibilities.
Adding, subtracting, multiplying, and dividing
You’re probably pretty familiar with the standard operations of addition, subtraction, multiplica-
tion, and division. But even these math basics have some tricky elements that you may need to
refresh your memory on.
Putting two and two together: Addition
Adding is pretty simple. Addition is just the operation of combining two or more numbers to get
an end result called the sum. For example, here’s a simple addition problem:
34512
Addition also has two important properties that you may remember from elementary school: the
associative property and the commutative property. Understanding these simple concepts for the
GMAT math questions is important:
»
Associative property: The associative property states that the order in which you choose to
add three or more numbers doesn’t change the result. It shows how numbers can group
dierently with one another and still produce the same answer. So regardless of whether you
add 3 and 4 together rst and then add 5 or add 4 and 5 together followed by 3, you still get an
answer of 12.
( )
()
34 512
34512
»
Commutative property: The commutative property states that it doesn’t matter what order
you use to add the same numbers. Regardless of what number you list rst in a set of
numbers, they always produce the same sum. So
2 35
is the same as
325
.
156 PART 4 Conquering the Quantitative Section
Depleting the supply: Subtraction
Subtraction, as you probably know, is the opposite of addition. You take away a value from another
value and end up with the dierence. So if
347
, then
734
.
In subtraction, order does matter, so neither the associative property nor the commutative prop-
erty applies. You get completely dierent answers for
345
, depending on what method you
use to associate the values. Here’s what we mean:
( )34 56
but
3454()
The order of the values counts in subtraction, too. For example,
34
isn’t the same as
4 3
(
34 1
, but
4 31
).
Increasing by leaps and bounds: Multiplication
Think of multiplication as repeated addition with an end result called the product:
35
is the same
as 5 + 5 + 5. They both equal 15.
On the GMAT, you may see several signs that represent the multiplication operation. A multiplica-
tion sign can be designated by
or simply with a dot, like ∙. And in many instances, especially
when variables are involved (for more about variables, see Chapter13), multiplication can be indi-
cated by just putting the factors right next to each other. So ab means the same thing as
a b
,
and 2a is the same as
2 a
. One of these back-to-back factors may appear in parentheses: 2(3)
means
2 3
.
Multiplication is like addition, in that the order of the values doesn’t matter. So it obeys the com-
mutative property:
a bba
And the associative property:
( )ab ca bc
Another property associated with multiplication is the distributive property. So you may encounter
this multiplication problem:
a bc
You solve it by distributing the a to b and c, which means that you multiply a and b to get ab and
then a and c to get ac, and then you add the results together like this:
a bc ab ac
.
Sharing the wealth: Division
Finally, there’s division, which you can consider to be the opposite of multiplication. With divi-
sion, you split one value into smaller values. The end result is called the quotient. So whereas
3515
,
15 53
, and
15 35
.
As in subtraction, order matters, so division doesn’t follow either the commutative or associative
properties. Also, just so you’re familiar with any terms you may encounter on the GMAT, the
CHAPTER 12 Getting Back to Basics: Numbers and Operations 157
number at the beginning of any equation using division (15in the last expression) is called the
dividend and the number that goes into the dividend is the divisor (3in the last expression).
The division sign may be represented by a fraction bar. For more info on fractions, see “Splitting
Up: Fractions, Decimals, and Percentages,” later in this chapter.
Checking out the real estate:
Properties of real numbers
In addition to basic operations, the GMAT expects you to know the fundamental properties of the
numbers you’re working with. These include absolute values, evens and odds, and positives and
negatives.
Absolutes do exist: Absolute value
To simplify things, just think of the absolute value of any real number as that same number with-
out a negative sign. It’s the value of the distance a particular number is from 0 on a number line.
The symbol for absolute value is | |, so the absolute value of 3 is written mathematically as |3|.
And because the number 3 sits three spaces from 0 on the number line,
33
. Likewise, because
–3 sits three spaces from 0 on the number line, its absolute value is also 3:
33
.
The GMAT loves to trip you up when dealing with multiple numbers and absolute values. Remem-
ber that absolute value pertains only to the value contained within the absolute value bars. So if
you see a negative sign outside the bars, the resulting value is negative. For example,
33
because although the absolute value of –3 is 3, the negative sign outside the bars makes the end
result a negative.
When you’re working with variables in absolute-value expressions, remember that there is likely
more than one solution for the variable because the value within the absolute value sign may be
positive or negative, as demonstrated by this sample problem.
Which of the following is the complete set of solutions for x when
x 36
?
(A)
9
(B)
99,
(C)
39,
(D)
39,
(E)
933,,
To nd one solution for x, remove the absolute-value sign and solve:
x
x
x
36
36
9
You know 9 is a solution for x, so you can eliminate Choice (E) because it doesn’t contain 9. You
can’t end with Choice (A), though; you have to consider that the value within the absolute value
158 PART 4 Conquering the Quantitative Section
signs could be negative. To accomplish this feat, multiply the terms between the bars by –1 and
then solve for x:
x
x
x
x
x
36
136
36
3
3
()
Because the value in the absolute-value signs may be either negative or positive, x may be either
–3 or 9. Choice (C) is the complete set of solutions.
A balancing act: Even and odd numbers
We’re pretty sure you know that even numbers are integers divisible by 2: 2, 4, 6, 8, 10, and so on.
And odd numbers are those integers that aren’t divisible by 2: 1, 3, 5, 7, 9, 11, and so on.
You’re probably with us so far, but what’s important to remember for the GMAT is what happens
to even or odd numbers when you add, subtract, or multiply them by one another.
Here are the rules regarding evens and odds for addition and subtraction:
»
When you add or subtract two even integers, your result is an even integer.
»
When you add or subtract two odd integers, your result is also even.
»
If you add or subtract an even integer and an odd integer, your result is an odd integer.
Here’s what you should know about multiplying even and odd integers:
»
When you multiply an even number by an even number, you get an even number.
»
When you multiply an odd number by an even number, you also get an even number.
»
The only time you get an odd number is when you multiply an odd number by another
oddnumber.
Division rules are a little more complex because the quotients aren’t always integers; sometimes
they’re fractions. Here are a few rules to know:
»
When you divide an even integer by an odd integer, you get an even integer or a fraction.
»
An odd integer divided by another odd integer results in an odd integer or a fraction.
»
An even integer divided by another even integer can result in either an odd or even quotient,
so that’s not very helpful.
»
When you divide an odd integer by an even one, you always get a fraction; because fractions
aren’t integers, the quotient for this scenario is neither odd nor even.
You may be wondering why you need to know these rules. Here’s why: Memorizing them can be
a big timesaver when it comes to eliminating answer choices. For example, if you have a multi-
plication problem involving large even numbers, you know you can eliminate any odd-number
answer choices without even doing the math! Here’s a sample question that shows you just how
valuable knowing the rules can be.
CHAPTER 12 Getting Back to Basics: Numbers and Operations 159
If a and b are dierent prime numbers, which of the following numbers must be odd?
(A) ab
(B) 4a + b
(C) a + b + 3
(D) ab– 3
(E) 4a + 4b + 3
To solve this number theory question, think of numbers for a and b that represent their possible
values. Then substitute these values into the answer choices to eliminate all that can be even.
When considering values for a and b, make sure to include 2 because it’s the only even prime
number. Neither 1 nor 0 is an option because neither is prime.
Substitute 2 for a or b in Choice (A), and you see that it can be even because the rules tell you
that any time you multiply an even number by another number, you get an even number. You
also know that Choice (B) can be even because 4 (an even number) times any number is an even
number. If b = 2 and you added that to 4a, you’d be adding two even numbers, which always
gives you an even sum. Again, if b = 2in Choice (C), then a would have to be an odd prime
number. You add a (odd) to b (even) to get an odd sum. Then you add that odd number to the
odd number 3, which results in an even number. Choice (D) can be even if both a and b are odd.
An odd number times an odd number is an odd number. When you subtract an odd number, like
3, from another odd number, you get an even number.
By process of elimination, the answer must be Choice (E). It doesn’t matter whether a or b in
Choice (E) is even or odd; 4a and 4b will always be even, because anytime you multiply an even
number by another number, you get an even number. When you add two evens, you get an even
number, so 4a + 4b is an even number. And because an even number plus an odd number is
always odd, when you add that even result to 3, you get an odd number, always. The correct
answer is Choice (E).
Half empty or half full: Positive and negative numbers
Positive and negative numbers have their own set of rules regarding operations, and they’re even
more important to remember than those for even and odd integers. Here’s what you need to know
for multiplying and dividing:
»
When you multiply or divide two positive numbers, the result is positive.
»
When you multiply or divide two negative numbers, the result is also positive.
»
Multiplying or dividing a negative number by a positive number gives you a negative result (as
does multiplying or dividing a positive number by a negative number).
As you may expect, you need to know some things about adding and subtracting positives and
negatives:
»
When you add two positive numbers, your result is a positive number.
»
When you add two negative numbers, the resulting sum is negative.
»
When you add a positive number to a negative number, the result is positive when the
number with the largest absolute value is positive and negative when the number with the
largest absolute value is negative.
»
If you subtract a negative number from another number, you end up adding the positive version
of the negative number to the other number. For example, x– (–3) is the same thing asx + 3.
160 PART 4 Conquering the Quantitative Section
Using Little Numbers for Big Values:
Bases and Exponents
Because multiplication can be thought of as repeated addition, you can think of exponents as
repeated multiplication. This means that
4
3
is the same as
4 44
or 64. In the example, you refer
to 4 as the base and the superscript 3 as the exponent. If you add a variable into this mix, such
as
4
3
b
, the base becomes b and the 4 becomes what’s known as the coecient. In our example,
the coecient 4 is simply multiplied by
b
3
.
As a high-school algebra teacher used to scream (usually when he caught his students napping):
“The power governs only the number immediately below it!” (that is, the base). So the exponent
doesn’t aect the coecient. Only the base gets squared or cubed or whatever the exponent says
to do.
This rule brings up some fascinating properties regarding positive and negative bases and even
and odd exponents:
»
A positive number taken to an even or odd power remains positive.
»
A negative number taken to an odd power remains negative.
»
A negative number taken to an even power becomes positive.
What all of this means is that any number taken to an even power either remains or becomes
positive, and any number taken to an odd power keeps the sign it began with. Another interesting
tidbit to digest is that any term with an odd power that results in a negative number will have a
negative root, and this is the only possible root for the expression. For example, if
a
3
125
, then
a 5
. That is, the cube root of –125 is –5.
On the other hand, anytime you have an exponent of 2, you have two potential roots, one positive
and one negative, for the expression. For example, if
a
2
64
, then a = 8 or –8. So 64 has two pos-
sible square roots: either 8 or –8.
In the following sections, we outline a few rules for adding, subtracting, multiplying, and divid-
ing exponents. We also clue you in on how to gure out the powers of 0 and 1 and what to do with
fractional and negative exponents.
Adding and subtracting with exponents
The only catch to adding or subtracting with exponents is that the base and exponent of each term
must be the same. So you can add and subtract like terms such as
4
2
a
and
a
2
like this:
4 5
22 2
aa a
and
4 3
22 2
aa a
. Notice that the base and exponent remain the same and that the coecient is
the only number that changes in the equation.
Multiplying and dividing with exponents
The rules regarding multiplying and dividing exponents are pretty numerous, so to keep them
straight, we’ve set up Table12-1 for you. The table describes each rule and gives you an example
or two.
CHAPTER 12 Getting Back to Basics: Numbers and Operations 161
Figuring out the powers of 0 and 1
Exponents of 0 and 1 have special properties that you’ll have to commit to memory:
»
The value of a base with an exponent of 0 (such as
7
0
) is always 1.
»
The value of a base with an exponent of 1 is the same value as the base (
33
1
).
Dealing with fractional exponents
If you see a problem with an exponent in fraction form, consider the top number of the fraction
(the numerator) as your actual exponent and the bottom number (the denominator) as the root. So
to solve
256
1
4
, simply take 256 to the rst power (because the numerator of the fraction is 1),
which is 256. Then take the fourth root of 256 (because the denominator of the fraction is 4),
which is 4, and that’s your answer. (Find out more about roots in the “Checking Out the Ancestry:
Roots” section later in this chapter.) Here’s what it looks like mathematically:
256 256 256 4
1
4
1
4
4
The GMAT may also present you with a variable base and a fractional exponent. You handle those
the same way, like this:
a a
2
3
2
3
This is what you get when you take a to the second power and then nd its cube root.
Working with negative exponents
A negative exponent works like a positive exponent with a twist. A negative exponent takes the
positive exponent and then ips the base and exponent around so that together they become the
TABLE12-1 Rules for Multiplying and Dividing with Exponents
Rule Examples
To multiply terms with exponents and the same bases, add the exponents.
a aa
23 5
If the expression contains coecients, multiply the coecients as you
normally would.
4 28
23 5
aa a
When you divide terms with exponents and the same bases, just subtract the
exponents.
a aa
52 3
Any coecients are also divided as usual.
9 33
53 2
aa a
To multiply exponential terms with dierent bases, rst make sure the exponents
are the same. If they are, multiply the bases and maintain the same exponent.
4 520
33 3
;
a bab
55 5
()
Follow the same procedure when you divide terms with dierent bases but the
same exponents.
205 4
33 3
;
( )ab ab
55 5
When you raise a power to another power, multiply the exponents.
( )55
45 20
;
( )aa
35 15
If your expression includes a coecient, take it to the same power.
( )28
23 6
aa
162 PART 4 Conquering the Quantitative Section
reciprocal (see the section “Dening numerators, denominators, and other stu you need to
know about fractions,” later in this chapter), like this:
3
1
3
1
27
3
3
When you work with negative exponents, don’t fall for the trick of assuming that the negative
exponent somehow turns the original number into a negative number. It ain’t gonna happen! For
example,
32
7
1
27
3
or .
To see how the GMAT may test exponents, check out a sample problem.
If
8 1
23x
, what is the value of x?
(A) 0
(B) 1.5
(C) 2
(D) 8
(E) 10.5
The trick to mastering this problem is to remember that a number to the power of 0 is equal to
1. So, for the expression to equal 1,
8
23x
must equal
8
0
. When you know that
8 8
23 0x
, you know
2 30x
. Solve for x.
2 30
23
3
2
15
x
x
x
x .
The simple answer to this perhaps initially confusing problem is Choice (B). If you picked
Choice (C), you may have thought the exponent was equal to 1 instead of 0.
Checking Out the Ancestry: Roots
If you like exponents, you’ll love roots, which are also known as radicals. Roots are sort of the
opposite of exponents. The square root of a number is the number that you square to get that
number. So because you square 3 to get 9, the square root of 9 is 3. What could be simpler?
There are as many roots as there are powers. Most of the time, the GMAT has you work with
square roots, but you may also see other roots. That won’t intimidate you, though. If you come
upon a cube root or fourth root, you’ll recognize it by the radical sign, √.
For example, the cube root of 27 is expressed as
27
3
. This expression asks what number, when
raised to the third power, equals 27. Of course, the answer is 3 because
327
3
.
Radicals, even the seemingly ugly ones, can often be simplied. For example, if you come up with
an answer of
98
, you’re not done yet. Just think of the factors of 98 that are perfect squares. You
know that
2 49 98
, and 49 is a perfect square:
749
2
. Put these factors under the radical sign:
49 2
. Now you can extract the 49 from the square root sign because its square root is 7. The
result is
72
. Here’s how you may see this situation on the GMAT.
CHAPTER 12 Getting Back to Basics: Numbers and Operations 163
If
512 42
n
n
, then n = ?
(A)
1
4
(B)
1
2
(C) 1
(D) 4
(E) 8
You can solve this equation most easily by simplifying the radical. The nth root of 512 is equal to
4 times the nth root of 2. Consider the factors of 512:
2 256 512
, so
256 2
n
, which also equals
4 2
n
.
256 2 256 2
nn
n
, so you know that
256 4
n
, which is the same as saying 4
n
= 256.
Because
4 444 256
,
n 4
, and Choice (D) is the correct answer.
Roots obey the same rules as exponents when it comes to performing operations. You can add and
subtract roots as long as the roots are of the same order (that is, square root, cube root, and so
on) and the same number. Here are a couple examples:
57 67 11 7
11 65aaa
When you need to multiply or divide radicals, make sure the roots are of the same order (such as
all square or all cube roots) and you’re good to go! For multiplication, just multiply what’s under
the radical signs, like this:
93 27
Divide what’s under the radical signs like this:
933
And here’s how a question about operations with radicals may appear on the GMAT.
16 9
?
(A) 5
(B) 7
(C)
12
1
2
(D) 25
(E) 625
Pay attention to the values underneath the radical. In this question, the line of the square root
symbol extends over the entire expression, so you’re supposed to nd the square root of 16 + 9,
not
16 9
. It’s a subtle but major dierence!
First, add the values under the radical sign:
16 925
. The square root of 25 is 5, so Choice (A)
is the correct answer. If you chose 7, you determined the square root of each of the values before
you added them together. For 7 to be the correct answer, your problem should have been written
with two separate square root signs,
16 9
.
164 PART 4 Conquering the Quantitative Section
Order of Operations: Please Excuse
My Dear Aunt Sally
Basic arithmetic requires that you perform the operations in a certain order from left to right.
Okay, so maybe you don’t have an aunt named Sally, but this section’s title is a helpful mnemonic
for the order you use when you have to perform several operations in one problem. What that
means is that if you have an expression that contains addition, subtraction, multiplication, divi-
sion, exponents (and roots), and parentheses to boot, it helps to know which operation you per-
form rst, second, third, and so on.
The acronym PEMDAS (Please Excuse My Dear Aunt Sally) can help you remember to perform
operations in the following order:
»
Parentheses
»
Exponents (and roots)
»
Multiplication and Division
»
Addition and Subtraction
Here’s an example:
2
04 74
9
3
3
2
x
First, evaluate what’s inside the parentheses:
2
03 43
32
x
Then evaluate the exponents:
202749 x
Then multiply:
540 36 x
Finally, do the addition and subtraction from left to right:
504 x
Splitting Up: Fractions, Decimals,
andPercentages
Fractions, decimals, and percentages are interrelated concepts; they all represent parts of a whole.
You’ll likely need to convert from one form to the other to solve several problems on the GMAT
math.
Fractions are really division problems. If you divide the value of a by the value of b, you get the
fraction
a
b
. So
14
1
4
.
CHAPTER 12 Getting Back to Basics: Numbers and Operations 165
To convert the fraction to a decimal, you simply perform the division indicated by the fraction
bar:
1
4
02
5
. .
To convert a decimal back to a fraction, you rst count the digits to the right of the decimal point;
then divide the original number over a 1 followed by the same number of zeroes as there were
digits to the right of the decimal. Then you simplify. So
0
25
25
100
1
4
. ;
0
356
356
1 000
89
250
.
,
.
Changing a decimal to a percent is really pretty easy. Percent simply means out of one hundred, or
times 100. To perform the conversion, you move the decimal two places to the right. Then you
write the resulting number as a percent. For example,
0 25 25.%
, and
0 925 92 5..%
.
To turn a percent back into a decimal, you follow the procedure in reverse. You move the decimal
point two spaces to the left and lose the percent sign, like this:
1001%.
.
The GMAT probably won’t specically ask you to express answers in all three formats (fractions,
decimals, and percentages), but you need to know that answer choices can appear in any one of
the three formats when you’re dealing with percentage problems.
You may encounter a GMAT problem that asks you to nd something like the portion of garbage
that’s paper when you know that out of 215 million tons of garbage, about 86 million tons of the
total garbage are paper products. You should be able to express the answer as a fraction, decimal,
and percent:
»
As a fraction:
86
215
2
5
or
»
As a decimal:
2
5
25
04
.
»
As a percent:
0 440.%
Don’t worry: We provide all the details you need to know about dealing with fractions and per-
centages in the following sections.
Dening numerators, denominators, and other
stu you need to know about fractions
GMAT questions may refer to the numerator or the denominator of a fraction. The numerator is
the number on top and represents the part of the whole. The denominator is the number on the
bottom and represents the whole.
To better understand these terms, picture a cherry pie sliced into eight equal pieces (see
Figure12-1) and a hungry family of seven, each of whom has a slice after dinner (or before dinner
if they’re sneaky).
The shaded pieces of pie show how much of the dessert was gobbled up by the family; the
unshaded piece shows what’s left of the pie when the family is nished.
To put this pie into terms of a fraction, the total number of pieces in the pie to begin with (the
whole) represents the denominator, and the number of pieces that were eaten (the part of the
whole) is represented by the numerator. In this case, the number of pieces that were eaten made
up
7
8
of the total pie, so 7 is the numerator and 8 is the denominator. To look at the scenario
another way, you can say that the fraction of pie that was left is
1
8
of what you started with.
166 PART 4 Conquering the Quantitative Section
Here are a few other fraction denitions you should be familiar with:
»
Proper fractions: Fractions where the numerator is less than the denominator. Examples of
proper fractions are
3
4
and
13
15
.
»
Improper fractions: Fractions where the numerator is either greater than or equal to the
denominator. An example is
15
2
.
»
Mixed fractions: Another way of formatting improper fractions is with a whole number and a
proper fraction, such as
1
2
3
.
»
Reciprocal: The ip-op of a fraction. The numerator and denominator switch places. So the
reciprocal of
3
5
is
5
3
. To get the reciprocal of a whole number, you simply divide 1 by your
number. So the reciprocal of 5 is
1
5
. The reciprocal of a variable a is
1
a
, just as long as
a 0
.
When you work with fractions on the GMAT, you may have to substitute mixed fractions for
improper fractions and vice versa. You’ll nd that changing a mixed fraction into an improper
fraction before you perform operations is often easier. To change a mixed fraction to an improper
fraction, you multiply the whole number by the denominator, add the numerator, and put that
value over the original denominator, like this:
2
2
3
8
3
You multiply the whole number (2) by the denominator (3) to get 6; add the numerator (2) to 6,
which gives you 8; and place that value over the original denominator of 3.
To convert an improper fraction to a mixed number, you divide the numerator by the denomina-
tor and put the remainder over the denominator, like this:
31
4
7
3
4
First, you divide 31 by 4: 4 goes into 31 seven times with a remainder of 3 (
4 728
and
31 28 3
). Put the remainder over the original denominator, and place that fraction next to the
whole number, 7.
Another thing you should know about fractions is how to simplify them. You may be thinking that
fractions are simple enough, that it just can’t get any easier. Simplifying a fraction means reduc-
ing it to its simplest terms. You make the larger terms smaller by dividing both the numerator
and denominator by the same value. Here’s an example of reducing or simplifying a fraction:
12
36
12
12
1
3
FIGURE12-1:
Fraction of
a pie.
© John Wiley & Sons, Inc.
CHAPTER 12 Getting Back to Basics: Numbers and Operations 167
The largest common factor of 12 and 36 is 12. When you divide the fraction by
12
12
, it’s the same as
dividing by 1. And any number divided by 1 equals the original number. You know that
1
3
has the
same value as
12
36
. It’s just in simpler terms.
Adding and subtracting fractions
Because fractions are parts of whole numbers, they’re not as easy to add together as 2 + 2. To add
or subtract fractions, you must give them the same denominator. Then all you do is either add or
subtract the numerators and put that value over the original denominator, like this:
2
7
4
7
6
7
;
6
5
4
5
2
5
.
Be careful when you’re asked to add and subtract fractions with dierent denominators. You can’t
just add or subtract the numerators and denominators. You have to change the fractions so they
have the same denominator. So you have to nd what’s called the least common denominator. For
example, if you see
2
3
1
9
, you know you have to change the denominators before you add.
To determine the least common denominator, consider values that are divisible by both 3 and 9.
When you multiply 3 by 9, you get 27. So both 3 and 9 go into 27, but that’s not the smallest num-
ber that both 3 and 9 go into evenly. Both 3 and 9 are factors of 9, so the least common denomina-
tor is 9 rather than 27.
Convert
2
3
to
6
9
by multiplying the numerator and denominator by 3. The second fraction already
has a denominator of 9, so you’re ready to add:
6
9
1
9
7
9
Multiplying and dividing fractions
Multiplying fractions is easy. Just multiply the numerators and the denominators. Reduce if you
have to:
4
5
5
7
20
35
4
7
An easier and faster (and faster is better on the GMAT) way to perform this task is to simply can-
cel out the ves that appear in the denominator of the rst fraction and the numerator of the
second one, like so:
4
5
5
7
4
7
Dividing fractions is pretty much the same as multiplying them except for one very important
additional step. Here’s what you do to divide two fractions:
1. Find the reciprocal of the second fraction in the equation (that is, turn the second
fraction upside down).
2. Multiply (yes, multiply) the numerators and denominators of the resulting fractions.
168 PART 4 Conquering the Quantitative Section
Here’s an example:
2
7
3
5
2
7
5
3
10
21
x
x
x
To test your knowledge of how to perform operations with fractions, the GMAT may present you
with a straightforward equation, such as the following.
1
2
3
8
2
5
5
6
7
8
(A)
1
8
(B)
15
16
(C)
17
24
(D)
2
1
6
(E)
5
6
To solve this problem, you need to know how to perform all four operations with fractions. Be
sure to follow the order of operations. (See the earlier section “Order of Operations: Please
Excuse My Dear Aunt Sally” for details.)
First, compute the operations inside the rst set of parentheses:
3
8
2
5
3
8
5
2
15
16
Then, gure out the value of the second set of parentheses:
5
6
7
8
35
48
Now the equation looks like this:
1
2
15
16
35
48
The least common denominator of 2, 16, and 48 is 48. To convert the denominator in the rst
fraction to 48, you multiply the fraction by
24
24
:
1
2
24
24
24
48
To convert the denominator in the second fraction to 48, you need to multiply by
3
3
:
15
16
3
3
45
48
Now you can compute the expression:
24
48
45
48
35
48
34
48
That’s not one of your answer options, so you need to simplify the fraction. Divide the numera-
tor and denominator by 2 to get
17
24
, which is Choice (C).
Knowing how to perform operations with fractions comes in handy for percent problems, too.
CHAPTER 12 Getting Back to Basics: Numbers and Operations 169
What is 75% of
7
1
4
?
(A)
37
130
(B)
5
3
4
(C)
5
7
16
(D)
7
3
4
(E)
2
1
3
16
This question asks you to determine a percent of a fraction. Note that the answers are in frac-
tion form rather than decimal form, which means you need to work out the problem so it ends
up as a fraction rather than a decimal.
Whenever you see the word of in a word problem, you know it means multiply. Therefore,
you’re multiplying 75 percent by
7
1
4
. Converted to a fraction, 75 percent is
3
4
, so you’re trying to
nd the answer to
7
1
4
3
4
. Converting
7
1
4
from a mixed fraction gives you
29
4
, so the answer is
29
4
3
4
87
16
.
Convert to a mixed fraction:
87
16
5
7
16
. The answer is Choice (C).
You can easily eliminate Choices (D) and (E). Obviously, 75 percent of
7
1
4
has to be less than
7
1
4
.
Calculating percent change
Percent change is the amount a number increases or decreases expressed as a percentage of the
original number. For example, if a store normally sells tennis shoes for $72 and has them on sale
for $60, what is the percent change of the markdown? To get the percent decrease, simply take
the dierence in price, which is $12, and divide that number by the original price:
12 72 0 1667.
or
16
2
3
%
Pay careful attention when guring percent change. For example, if the store then increases the
marked down price by
16
2
3
percent, you may think the price returns to its original value. But
that’s not right. If you increase the lower price of $60 by 0.1667, you get just about a $10 increase.
The price goes from $60 to just about $70:
6001667 10 002..
;
6010 002 70 002..
.
How can that be? The reason the numbers don’t seem to add up is because when you drop the
price the rst time, you take
16
2
3
percent of $72, which is a bigger number to take a percent from
than the lower sale price.
So what percent of the marked-down price of $60 must you increase the price by in order to get
the original price of $72? To nd out, take the dierence in price, $12, and determine what per-
cent that is of the sale price of $60:
12
60
12
60
2
10
02020
.%
So it’s a 20 percent increase from 60 to 72.
If you know what the percent increase or decrease of an original number is and want to nd out how
that increase or decrease changes the original number, keep these two important details in mind:
»
To nd the amount of increase, multiply the original number by 1 plus the rate as a decimal.
»
To nd the amount of decrease, multiply the original number by 1 minus the rate as a decimal.
170 PART 4 Conquering the Quantitative Section
So if you increase 100 by 5 percent, you multiply 100 by (1 + 0.05):
100 1005 100 105 105..
If you decrease 100 by 5 percent, you multiply 100 by (1– 0.05).
100 1005 100 09595..
Try a sample percent change problem.
A le cabinet that originally cost $52 is on sale for 15% o. If the sales tax on oce furniture is
5% of the purchase price, how much is the total cost of the le cabinet at its sale price?
(A) $7.80
(B) $40.00
(C) $44.20
(D) $46.41
(E) $48.23
This word problem asks you how to deal with two percentages, the subtraction of the percent-
age discount and the addition of the percentage sales tax. First, calculate the discount.
You can gure 15 percent in your head by knowing that 10 percent of 52 is 5.20 and half of that
(5 percent) is 2.60, so the discount is $7.80. Now subtract the discount from the original price:
$52.00– $7.80 = $44.20. The discount price for the cabinet is $44.20.
You still need to calculate the sales tax, so don’t choose Choice (C)! You know that 5 percent of
44.20 is half of 4.42 (10 percent), or 2.21. You add $2.21 to $44.20. The only answer that ends in
1 is Choice (D). You can do the math to verify your guess, but Choice (D) is the correct answer:
$44.20 + $2.21 = $46.41. Not a bad price for some much-needed organization!
Taking it further: Repeated percent change
Now suppose you want to show a percent change repeated over a period of time, such as when you
need to gure out how much interest accrues on a bank account after several years. To do so, you
take the formula for percent change a step further.
Suppose you have $100in a bank account at the end of 2012, and you want to know how much
money will be in that same account at the end of 2022 at an annual interest rate of 5 percent. No
fair pulling it out when the stock market is making a bull run! One way to gure this out is by
using the percentage increase formula. The rst step looks something like this:
100 1005 105.
So you have $105 at the end of the rst year.
Don’t make the mistake of thinking that all you have to do is multiply by 10 and you have $1,050
after 10 years. You wish! This type of question will trap anyone who isn’t paying attention every
time.
To get the correct answer, tweak the formula a bit by adding an exponent. The exponent will be
the number of times the original number changes. The formula looks like this, where n is the
number of changes:
F
inal Amount = Original Number Rate1
n
CHAPTER 12 Getting Back to Basics: Numbers and Operations 171
Plug the numbers into the formula and solve:
100
1005
100 105
100 1 6289
162 89
10
10
.
.
.
.
x
x
x
x
So after 10 years, you’d have $162.89in the bank.
To show a repeated percent decrease over time, you’d use this similar formula:
F
inal Amount Original Numbe
rR
ate1
n
Making Comparisons: Ratios and Proportions
A ratio is the relation between two like numbers or two like values. A ratio may be written as a
fraction (
3
4
), as a division expression (
34
), or with a colon (3:4), or it can be stated as “3 to 4.”
Because a ratio can be regarded as a fraction, multiplying or dividing both terms of a ratio by the
same number doesn’t change the value of the ratio. So 1:4 = 2:8 = 4:16. To reduce a ratio to its
lowest terms, simplify the ratio as you would a fraction. (See the earlier section “Dening numer-
ators, denominators, and other stu you need to know about fractions.”)
Ratios often crop up in word problems. Suppose an auto manufacturer ships a total of 160 cars to
two dealerships at a ratio of 3 to 5. This means that for every three cars that go to Dealer 1, ve
cars ship to Dealer 2. To determine how many cars each dealership receives, add the terms of the
ratio, or 3 + 5, to get the total number of fractional parts each dealership will get: 3 + 5 = 8. The
rst dealership will receive
3
8
of 160 cars, or
3
8
160
, which equals 60. The second dealership
receives
5
8
of 160 cars, or 100.
As long as the total number of items in a ratio problem can be evenly divided by the total number
of fractional parts, you can nd the total number of items that are attributable to each part.
A proportion is a relationship between two equal ratios. It may be written as the proportion sign ::
or with an equal sign. So you can read 1:4 :: 2:8 as “1 is to 4 as 2 is to 8.”
The rst and last terms in a proportion are called the extremes, and the second and third terms are
called the means. If you multiply the means together and multiply the extremes together and then
compare the products, you nd that the products are the same:
18 24
Anytime you know three terms of a proportion, you can nd the missing term rst by multiplying
either the two means or the two extremes (depending on which are known) and then dividing the
product by the remaining term. This is also known as cross-multiplying. So if you know 7:8 ::
x:104, you can solve for x by using cross-multiplication:
7
8 104
8
7 104
8
728
91
x
x
x
x
()
172 PART 4 Conquering the Quantitative Section
Be sure to keep the elements of your ratios and proportions consistent. For example, if your pro-
portion is “3 is to 4 as 5 is to x,” you must set up the problem like this:
3
4
5
x
rather than this:
3
45
x
Here’s what a GMAT ratio problem may look like.
If the ratio of 4a to 9b is 1 to 9, what is the ratio of 8a to 9b?
(A) 1 to 18
(B) 1 to 39
(C) 2 to 9
(D) 2 to 36
(E) 3 to 9
At rst, this problem may appear to be more dicult than it actually is. If 4a to 9b is a 1 to 9
ratio, then 8a to 9b must be a 2 to 9 ratio, because 8a is 2 times 4a. If 4a equals 1, then 8a must
equal 2. The answer, therefore, has to be Choice (C).
Playing the Numbers: Scientic Notation
Scientic notation is a simple way to write out humongous (technical term) or teensy weensy
(another technical term) numbers so they’re more manageable. You express a number in
scientic notation by writing it as the product of a number and a power of 10. Simply move the
decimal point so all digits except one are to the right of the decimal point; then multiply that
decimal number times 10 raised to an exponent that equals the number of places you moved
thedecimal point. If you’re working with a large number and you moved the decimal point to the
left, the exponent is positive:
1 234 567 1 234567 10
2
020 000 000 20 10
6
7
,, .
,, . million
To display very small numbers in scientic notation, you move the decimal point to the right so
one value is to the left of the decimal point. When you move the decimal point to the right, the
exponent is negative. In this example, the decimal point moved six places to the right:
0 0000037 37 10
6
..
Here’s how the GMAT may test you on scientic notation.
CHAPTER 12 Getting Back to Basics: Numbers and Operations 173
The number of organisms in a liter of water is approximately
6 010
23
.
. Assuming this number is
correct, about how many organisms exist in a covered Petri dish that contains
1
200
liters of
water?
(A) 6.9
(B)
30 10
21
.
(C)
6 010
22
.
(D)
30 10
23
.
(E)
12 10
26
.
This question uses many words to ask you to the nd the answer to
60 10
200
23
.
. If a liter of water
contains a certain number of organisms,
1
200
liter of water would contain the same number of
organisms divided by 200. Try not to let the wording of the question confuse you.
So if 6.0 divided by 200 equals 0.03, the answer is
0 03 10
23
.
, but that’s not scientic notation
because the decimal point is in the wrong place. Move the decimal point two places to the right
and decrease the power by two (remember that when you move the decimal point to the right,
the exponent is negative, so you subtract). The answer is Choice (B),
30 10
21
.
.
CHAPTER13 Considering All the Variables: Algebra 175
IN THIS CHAPTER
» Dening variables and other
fundamental algebra terms
» Solving your problems with
algebraic operations
» Simplifying your life with factoring
» Getting functions to function
» Cracking the mysteries of
solving algebraic equations and
inequalities
Considering All the
Variables: Algebra
A
lgebra is the study of properties of operations carried out on sets of numbers. That may
sound like mumbo-jumbo, but the idea is that algebra is really just a form of arithmetic
in which symbols (usually letters) stand for numbers. You use algebra to solve equations
and to nd the value of a variable. For example, how often have you heard the command, “Solve
the equation for x”?
The algebra concepts tested on the GMAT are limited to the ones you’d use in a rst-year algebra
course, so you’re at no disadvantage if you’ve never taken Algebra II.But many GMAT math prob-
lems involve basic algebra, and this chapter provides what you need to know to excel on all
of them.
Dening the Elements: Algebraic Terms
Before we jump into solving algebra problems, we dene some terms you need to know in the
following sections. Although the GMAT doesn’t specically test you on the denitions of variable,
constant, and coecient, it does expect you to know these concepts when they crop up in the
questions.
Braving the unknowns: Variables
and constants
You’ll see a lot of variables in algebra problems. They’re the symbols that stand for numbers. Usu-
ally the symbols take the form of letters and represent specic numeric values. True to their
name, variables’ values can change depending on the equation they’re in.
Chapter13
176 PART 4 Conquering the Quantitative Section
Think of variables as abbreviations for discrete things. For example, if a store charges dierent
prices for apples and oranges and you buy two apples and four oranges, the clerk can’t ring them
up together by simply adding 2 + 4 to get 6. That would be incorrectly comparing apples and
oranges! So, to express the transaction in algebraic terms, you use variables to stand in for the
price of apples and oranges, something like 2a and 4o.
In contrast, constants, as their name implies, are numbers with values that don’t change in a spe-
cic problem. Letters may also be used to refer to constants, but they don’t change their value in
an equation as variables do (for example, a, b, and c stand for xed numbers in the formula
y ax bx c
2
).
Coming together: Terms and expressions
Single constants and variables or constants and variables grouped together form terms; terms are
any set of variables or constants you can multiply or divide to form a single unit in an equation.
You can combine these single parts in an equation that applies addition or subtraction. For exam-
ple, the following algebraic expression has three terms:
axbxc
2
. The rst term is
ax
2
, the
second term is bx, and the third term is c.
Terms often form expressions. An algebraic expression is a collection of terms that are combined
by addition or subtraction and are often grouped by parentheses, such as (x + 2), (x– 3c), and
(2x –3y). Although an expression can contain just one term, it’s more common to think of expres-
sions as combinations of two or more terms. So, in the apples and oranges scenario we presented
earlier, you can make an expression for combining two apples and four oranges, which may look
something like this: 2a + 4o.
A coecient is a number or symbol that serves as a measure of a property or characteristic.
In 2a + 4o, the variables are a and o, and the numbers 2 and 4 are the coecients of the variables.
This means that the coecient of the variable a is 2 and the coecient of the variable o is 4.
In an algebraic expression, terms involving the same variable, even if they have dierent coe-
cients, are called like terms. For example, in the expression 3x + 4y– 2x + y, 3x and –2x are like
terms because they both contain the single x variable; 4y and y are also like terms because they
both contain the y variable and only the y variable.
The variables must be exact matches with the same powers; for example,
3
3
xy
and
xy
3
are like
terms, but x and
x
2
aren’t like terms, and neither are 2x and 2xy.
You can combine (add/subtract) like terms together, but you can’t combine unlike terms. So, in
the expression 3x + 4y– 2x + y, you can subtract the terms with the common x variable: 3x– 2x =
x. And you can add the like terms with the common y variable: 4y + y = 5y (if a variable has no
visible numerical coecient, it’s understood that its coecient is 1; therefore, y is understood to
be 1y). All this combining results in the nal expression of x + 5y, which is a much simpler expres-
sion to work with. We work with many more algebraic expressions in the section “Maintaining an
Orderly Fashion: Algebraic Operations,” later in this chapter.
Knowing the nomials: Kinds of expressions
Expressions carry particular names depending on how many terms they contain. On the GMAT,
you’ll work with monomials and polynomials.
A monomial is an expression that contains only one term, such as 4x or
ax
2
. A monomial is, there-
fore, also referred to as a term in an algebraic expression.
CHAPTER 13 Considering All the Variables: Algebra 177
Poly means many, so we bet you’ve already gured out that a polynomial is an expression that has
more than one term. These multiple terms can be added together or subtracted from one another.
Here are a couple of examples of polynomials:
a b
abacb
22
2
2
Polynomials can have more specic designations, depending on how many terms they contain.
For example, a binomial is a specic kind of polynomial, one that contains two terms, such as
a + b or 2a + 3. And a trinomial is a polynomial with three terms, like
4 38
2
xy
.
A famous trinomial that you should be very familiar with for the GMAT is the expression known
as a quadratic polynomial, which is this trinomial expression:
axbxc
2
We discuss this very important expression in the “Solving quadratic equations” section, later in
this chapter.
Maintaining an Orderly Fashion: Algebraic
Operations
Symbols like +, –, , and are common to arithmetic and algebra. They symbolize the operations
you perform on numbers. Arithmetic uses numbers with known values, such as 5 + 7 = 12, in its
operations (visit Chapter12 for more on basic arithmetic operations), but algebraic operations
deal with unknowns, like x + y = z. This algebraic equation can’t produce an exact numerical value
because you don’t know what x and y represent, let alone z. But that doesn’t stop you from solving
algebra problems as best you can with the given information. In the following sections, we show
you how to add, subtract, multiply, and divide expressions with unknowns.
Adding to and taking away
From arithmetic, you know that 3 dozen plus 6 dozen is 9 dozen, or
312612 912
In algebra, you can write a somewhat similar equation by using a variable to stand in for the
dozen: 3x + 6x = 9x. And you can subtract to get the opposite result: 9x– 6x = 3x.
Remember to combine positive and negative numbers according to the rules of arithmetic (see
Chapter12 if you need a refresher). If you add two or more positive numbers in an expression,
they keep the positive sign. If you add a positive to a negative number, it’s as though you’re
subtracting.
For example, to tackle the expression 7x + (–10x) + 22x, you nd the sum of the two positive num-
bers (7x and 22x) and then subtract the value of the negative number (because adding a negative
is the same as subtracting a positive), like this:
71022
2
910
19
xxx
xx
x
178 PART 4 Conquering the Quantitative Section
That’s ne for adding and subtracting like terms, you may say, but what about working with
unlike terms? You can’t combine terms with dierent symbols or variables the same way you can
when the symbols are the same. For instance, take a look at this example:
710153xyxy
If you were to simply combine the whole expression by adding and subtracting without account-
ing for the dierent variables, you’d come up with a wrong answer, something like 29xy. (And you
can bet the GMAT will oer this incorrect gure as one of the answer choices to try to trap you.)
Instead, you rst separate the x’s from the y’s and add and subtract to get something more man-
ageable, like this:
71522
10 37
xx x
yyy
which gives you this nal expression:
227xy
If you want to get tricky and add two or more expressions, you can set them up just as you would
an addition problem in arithmetic. Remember, only like terms can be combined together this way.
347
2 28
36
4 57
xyz
xyz
xy
z
xyz
Here’s how an algebra problem may look on the GMAT.
For all x and y,
4612 8124
22
22
xxyy xxyy ?
(A)
41816
22
xxyy
(B)
4616
22
xxyy
(C)
468
22
xxyy
(D)
4 616
22
xxyy
(E)
12 18 8
22
xxyy
The easiest way to approach this problem is to distribute the negative sign to the second expres-
sion (see the later section “Distributing terms”) and combine the two expressions with like terms
by following these steps:
1. Distribute the negative sign (multiply each term in the second expression by –1).
Remember that subtracting is the same as adding a negative number. So your problem is really
4612 18 12 4
22
22
xxyy xx
yy
. Distributing the negative sign changes the second
expression to
8124
22
xxyy
, because a negative times a positive makes a negative and two
negatives make a positive.
2. Combine the expressions with like terms together:
4 8612 12 4
22 22
xxxy xy yy
3. Add and subtract like terms:
48 4
6126
12 416
22 2
22 2
xx x
xy xy xy
yy y
CHAPTER 13 Considering All the Variables: Algebra 179
4. Put the terms back into the polynomial:
4616
22
xxyy
So the answer is
4616
22
xxyy
, which is Choice (B). If you chose any of the other answers,
you either distributed the negative sign improperly or you added and subtracted the like terms
incorrectly.
Eliminate wrong answers as you combine terms. For instance, once you determine that the rst
term is
4
2
x
, you can eliminate Choices (D) and (E).
After you’ve combined like terms, double-check that you’ve used the correct signs, particularly
when you change all the signs like you did in the second expression. The other answer choices
for the sample problem are very similar to the correct choice. They’re designed to trap you in
case you make an addition or subtraction error. Add and subtract carefully, and you won’t fall
for these tricks.
Multiplying and dividing expressions
Multiplying and dividing two or more variables works just as though you were performing these
same operations on numbers with known values. So if
2 222
3
, then
x xxx
3
. Likewise,
if
2 22
23 5
, then
xx x
23 5
. Similarly, if
2 22
64 2
, then
y yy
64 2
.
The process is pretty simple for monomials, but polynomials may be a little more complicated. In
the next sections, we explore the dierent methods for multiplying and dividing polynomials.
Distributing terms
You can distribute terms in algebra just like you do in arithmetic. For example, when you multiply
a number by a binomial, you multiply the number by each term in the binomial. In this example,
you multiply 4x by each term inside the parentheses:
4
34 12
2
xx
xx
With division, you do the same operation in reverse.
16 44
41
2
xx
xx
Here’s an example of a GMAT question for which you can use distribution to answer.
For all x,
12 10 310xxxx
?
(A) 10x
(B)
310
2
xx
(C)
352
2
xx
(D)
38
2
xx
(E)
38
2
xx
This question tests your ability to add, subtract, and multiply terms in an algebraic expression.
First, use distribution to multiply –3x by (–x + 10):
3103 30
2
xx xx
Now the equation looks like this:
12 10 330
2
xxxx
180 PART 4 Conquering the Quantitative Section
Combine the terms that contain the x variable:
12 10 30 8xxxx
So the answer to the equation is Choice (E):
38
2
xx
.
Stacking terms
One easy way to multiply polynomials is to stack the two numbers to be multiplied on top of one
another. Suppose you have this expression:
xxyy
xy
22
2 .
You can stack this expression just like an old-fashioned multiplication problem. Just remember
to multiply each of the terms in the second line by each term in the rst line.
xx
yy
xy
xx
yxy
xy xy y
xxyxyy
22
32 2
22
3
32
23
2
2
2
Line up like terms during the rst round of multiplication so they match up before you add the
products.
The GMAT may ask you to divide a polynomial by a monomial. Simply divide each term of the
polynomial by the monomial. Here’s how you’d divide the expression
60 20
5
43
xx
x
:
60 20
5
60
5
20
5
60
5
20
5
12
43 43
43
xx
x
x
x
x
x
x
x
x
x
x
441 31
32
4
12 4
x
xx
Taking a shine to the FOIL method
You can multiply binomials by using the FOIL method. FOIL is an acronym for rst, outer, inner, last,
which indicates the order that you multiply the terms from one binomial by the terms of the sec-
ond binomial before adding their products. Take a look at this example:
4538xx
Multiply the rst terms in each binomial— 4x and 3x.
4 312
2
xx x
Then multiply the outer terms (4x and 8) to get 32x and the inner terms (3x and –5) to get –15x.
You can add the products at this point because they’re like terms.
32 15 17xxx
Last, multiply the last terms.
58 40
Combine the products to form the resulting expression.
12 17 40
2
xx
CHAPTER 13 Considering All the Variables: Algebra 181
You may recognize this expression as the quadratic polynomial we discussed in the earlier section
“Knowing the nomials: Kinds of expressions.”
To save time on the GMAT, you may want to commit the following factors and their resulting
equations to memory:
xy xx
yy
xy xx
yy
2
22
2
22
2
2
So if you’re asked to multiply (x + 3)(x + 3), you know without using FOIL that the answer is
xx
2
23 9()
or
xx
2
69
. And
xx xx33 69
2
or
xx
2
69
.
If you’re able to keep track of the terms, you can use FOIL to multiply terms in the proper order
without taking the time to stack them. The FOIL method comes in handy for solving GMAT prob-
lems like the next one.
When the polynomials 3x + 4 and x– 5 are multiplied together and written in the form
320
2
xkx
, what is the value of k?
(A) 2
(B) 3
(C) –5
(D) –11
(E) –20
This question asks you for the constant in the middle term of the quadratic expression formed by
multiplying 3x + 4 and x– 5. Remember with FOIL, you multiply the rst, outer, inner, and last.
The problem gives you the rst term: 3x
2
. The last is also there: –20. Because the problem pro-
vides the product of the rst terms and last terms, all you have to do to get the middle term is to
multiply the outer and inner numbers of the two expressions and then add them together.
1. Multiply the outer numbers:
3515xx
2. Multiply the inner numbers:
4 4xx
So the middle term of the quadratic is –15x + 4x = –11x. The constant k must equal –11, which is
Choice (D).
Extracting Information: Factoring Polynomials
Factors are the numbers you multiply together to get a product. So, factoring a value means you
write that value as a product of its factors. For the GMAT, you should know how to pull out the
common factors in expressions and the two binomial factors in a quadratic polynomial. We show
you how to do both in the following sections.
182 PART 4 Conquering the Quantitative Section
Something in common: Finding common factors
To simplify polynomials for complex problems, extract their common factors by dividing each
term by the factors that are common to every term. You can think of the process as the opposite
of distributing terms. For example, to nd the common factors of the terms in the expression
14 35
36
xx
, follow these steps:
1. Consider the coecients.
Because –7 is common to both –14 and –35, take this factor out of the expression by dividing
both terms by –7. Then put the remaining expression in parentheses next to the common
factor:
72 5
36
()xx
.
2. Now look at the variables.
Because
x
3
or a multiple of it is common to both terms, divide both terms in parentheses by
x
3
,
multiply x
3
by the other common factor (–7), and put the remaining expression in parentheses:
725
33
xx()
.
So,
14 35 725
36 33
xxxx()
.
Two by two: Factoring quadratic polynomials
The GMAT also expects you to know how to factor quadratic polynomials. To accomplish this
task, you have to perform the FOIL operations in reverse to come up with a couple of binomial
factors that look something like this:
xaxb
.
For example, look at the following quadratic polynomial:
xx
2
56
To nd its factors, draw two sets of parentheses: ( )( ). The rst terms of the two factors have to
be x and x because
x
2
is the product of x and x. So you can add x as the rst term for both sets of
parentheses. You know that the operation in both terms must be addition because both the middle
and last terms of the quadratic expression are positive:
xx
To nd the second terms for the two factors, ask yourself which two numbers have a product of
6 (the third term of the quadratic) and add up to the number 5 (the coecient of the quadratic’s
second term). The only two factors that meet these two criteria are 2 and 3. The other factors of
6 (6 and 1, –6 and –1, –2 and –3) don’t add up to 5. So the binomial factors of the quadratic equa-
tion are (x + 2) and (x + 3).
Because you do just the opposite of what you do when you multiply binomials using the FOIL
method, you can use the FOIL method to make sure the binomial factors result in the original
quadratic when you multiply them together.
There’s a timesaving way to factor binomials that are made up of a dierence of perfect squares,
such as x
2
– 4. Factors for these types of quadratic polynomials (known as the dierence of per-
fect squares) result in the following form:
xaxa
The variable x is the square root of the rst term, and a is the square root of the second term. So
the factors of
xxx
2
422
.
CHAPTER 13 Considering All the Variables: Algebra 183
This factoring technique is very easy to memorize and can help you answer some algebra questions
much more quickly than if you were to take the time to carry out long calculations. For example, if
you’re asked to multiply factors (x– 5)(x + 5), you can use the FOIL method to gure out the
answer, but spotting that the correct answer will be the dierence of two perfect squares is much
faster. You know the correct answer is
x
2
25
without performing time-consuming calculations.
Likewise, if you need to factor
x
2
25
, all you do is gure the square root of
x
2
and the square root
of 25 and enter those values into the proper factoring form for perfect square quadratics. You
know right away that the factors are (x– 5)(x + 5).When you break down the quadratic polyno-
mial, you’ll be able to solve quadratic equations. For more about how to do this, see the section
“Solving quadratic equations,” later in this chapter.
Knowing how to multiply polynomials with variables can help you more eciently solve similar
problems that don’t contain variables, such as this one:
What is the solution for
23
23
?
(A) –1
(B) 0
(C) 1
(D)
2 3
(E)
4 3
You may look at this question and think “Gee, I wish I had a calculator to help me add and sub-
tract the stu in the parentheses.” But then you may notice that this problem looks a lot like
multiplying binomial expressions. All you need is FOIL!
1. Multiply the rst terms:
2 24
2. Notice that the inner and outer terms will cancel each other because you’re adding and
subtracting the same terms:
2 3230
3. Multiply the last terms:
33 3
2
4. Combine the remaining terms:
4
34
31
2
The answer is Choice (C)— no calculator needed.
Minding Your Ps and Qs: Functions
Some of the GMAT math questions involve functions. Simply put, functions are relationships
between two sets of numbers; each number you put into the formula gives you only one possible
answer. Functions may sound complicated, but they’re really pretty simple. A function problem
looks something like this:
fx x23
2
. What is f(2)?
We explore the terminology of functions and how to nd the domain and range of functions in the
following sections.
184 PART 4 Conquering the Quantitative Section
Standing in: Understanding function terminology
Before we show you how to solve function problems, you need to know a few denitions.
Table13-1 gives you the terms we use when we discuss functions.
Functions on the GMAT are usually displayed with the letters f or g. For example, f(x) is used to
indicate the function of x, and it simply means “f of x.”
Don’t let this language confuse you. All you really have to do is substitute the indicated value for
x in the function.
Don’t think that the parentheses in the function notation mean multiplication like they do in
algebraic operations. The expression f(x) doesn’t mean
fx
.
To see how functions work, consider the earlier example:
fx
x
23
2
. What is f(2)?
The initial expression means that the function of x is to square x, multiply the result by 2, and
then add 3. To calculate the function exercise with the number f(2), you just substitute 2 for x in
the expression and solve.
f
f
f
f
2223
22
43
283
211
2
()
()
So when x is 2, f(x) is 11. That’s all there is to it! The function notation is really just a fancy way of
telling you to perform a substitution.
Here’s another example.
If
gx
x
21
7
2
, what is g(12)?
(A) 12
(B) 17
(C) 100
(D) 288
(E) 305
TABLE13-1 Dening Terms for Functions
Term Denition
Function A rule that turns each member of one set of numbers into a member of another set.
Independent
variable (input)
The number you want to nd the function of; the x in f(x).
Dependent
variable (output)
The result of substituting the independent value into the function, f(x). (This is like your y
variable.)
Domain The set of all possible values of the independent variable.
Range The set of all possible values of the dependent variable.
CHAPTER 13 Considering All the Variables: Algebra 185
If you quickly consider the situation, you can eliminate Choices (A), (B), and (C) right away. When
you substitute 12 for x in the function, you square 12, which is 144. The answer then results from
multiplying by and adding to that number, so you know the result will be greater than 100. Fur-
thermore, the answer in Choice (D), 288, is just
2 144
. You still have to add 17, so the answer
probably isn’t Choice (D) either. Without much calculation, you can eliminate enough answers to
determine that Choice (E) is correct. But to do the calculations, just substitute 12 for x and solve:
g
g
g
g
12 21
21
7
12 2 144
17
12 288 17
12 305
2
()
()
The answer is denitely Choice (E).
That was a pretty simple problem. But functions can get more complicated on the GMAT.Check
out this example.
If
fx x()2
2
, nd the value of f(2x– 2).
(A)
4 4
2
x
(B)
4 4
2
x
(C)
4 816
2
xx
(D)
4 16 16
2
xx
(E)
4 16 16
2
xx
Don’t try to do this one in your head. Begin by plugging in (2x– 2) for x. Then solve.
fx
x
fx
x
fx xx
f
22 222
22 24
22 24
24
2
2
2
xxxx
fx
xx
24 28
16
2241
61
6
2
2
()
So the correct answer is Choice (D).
Taking it to the limit: Domain
and range offunctions
The domain of a function is the set of all numbers that can possibly be an input of a function, the x
in f(x). The range of a function is the set of all numbers that can possibly be an output of a function,
the value for f(x). In other words, if you think of the domain as the set of all possible independent
variables values you can put into a function, the range is the set of all possible dependent vari-
ables values that can come out of any particular function. Domain and range questions aren’t
dicult, but you need to be aware of some basic rules to determine the proper limits of the
domain and range. The GMAT also tests you on graphing functions on the coordinate plane, but
we discuss that in Chapter15.
Mastering the territory: Domain
Unless a problem species otherwise, the domain of a function includes all real numbers, which
means that the only numbers that aren’t included in the domain are numbers that aren’t real (see
186 PART 4 Conquering the Quantitative Section
Chapter12 for more info on imaginary and real numbers). Here are some properties of numbers
that aren’t real and, therefore, can’t be part of the domain of a function:
»
A real number can’t be a fraction with a denominator of 0, because then the number would be
undened.
»
A real number can’t be an even-numbered root of a negative number. Even-numbered roots of
negatives aren’t real numbers because any number that’s squared or has an even-numbered
power can’t result in a negative number.
For example, there’s no such thing as
4
because there’s no one number that you can square
that results in a negative 4. So
22
will always equal positive 4.
To see how the rst rule aects domain, look at this function:
fx
x
x
4
2
Normally, the domain of x in a function can contain an unlimited number of values. In the pre-
ceding example, though, you have a fraction in the function, which puts the variable x in the
denominator. Because your denominator can’t add up to 0, the denominator of x– 2 can’t equal
0. This means that x can’t equal 2. In terms of functions, the domain of f(x) is, therefore,
x 2
.
That’s all there is to it!
Here’s a function that relates to the second rule:
gn
n
32
4
In this function, you have an even-numbered radical sign with the variable n within it. You know
that the root of an even-numbered radical, in this case, the 4th root, can’t be a negative number.
Otherwise, you wouldn’t have a real number as your nal answer. Therefore, the number under
the radical sign can’t be less than 0. So
n 2
. The result is that the domain of the function g(n)
is
n 2
.
The GMAT may test your knowledge of domain with a problem such as the following.
Determine the domain of the function
fx
xx
4
2
2
.
(A)
x 12,
(B)
x 12,
(C)
x 12,
(D)
x 42,
(E)
x 42,
This problem involves simple algebra. You know the denominator can’t equal 0, so set the trino-
mial in the denominator equal to 0, and solve for x to nd out what x can’t be. We show you how
to solve trinomials later in the “Solving quadratic equations” section.
xx
xx
xx
xx
2
20
120
10 1
20 2
;
;
You’re not nished! If you picked Choice (C) as your answer, your factoring would have been
absolutely right, but your answer would be absolutely wrong. Answer Choice (C) gives you only
the values for x that make the denominator equal to 0. You’re trying to nd the values that
make the denominator not equal to 0.
CHAPTER 13 Considering All the Variables: Algebra 187
So, the correct answer is Choice (A); x can be any real number other than –1 and 2 because if x
were equal to –1 or 2, the denominator would be 0, and the value would be undened. If you
chose Choice (B), you switched the signs of the factors. If you chose Choices (D) or (E), you
found the correct factors of the denominator but mistakenly divided the numerator by each root
of the denominator.
Roaming the land: Range
Just as the domain of a function is limited by certain laws of mathematics, so, too, is the range.
Here are the rules to remember when you’re determining the range of a function:
»
An absolute value of a real number can’t be a negative number.
»
An even exponent or power can’t produce a negative number.
Check out some situations where these rules come into play. Look at the following functions:
gx x
gx
x
2
Each of these functions can result only in an output that’s a positive number or 0. So in each case,
the range of the function of g is greater than or equal to 0. Here’s a question that puts the range
rules to work.
What is the range of the function
gx x12
?
(A)
gx 2
(B)
gx 2
(C)
gx 2
(D)
gx 1
(E)
gx 1
First, you have to make the radical a real number. The value within the square root sign has to be
equal to or greater than 0. So, x has to be equal to or greater than 2, because any value less than 2
would make the radical a negative value. To check the possible outputs, consider several values
for x.
If x is the lowest value, 2, you’d gure the output of the function like this:
gx
gx
gx
gx
12
2
10
10
1
So you know that g(x) can be equal to 1.
If x is a higher value than 2, say 6, then you’d calculate the output like this:
gx
gx
gx
gx
16
2
14
12
1
Now you know that any value for x that’s higher than 2 results in a lower value for the output of
the function. Therefore, g(x) has to equal 1 or be less than 1, and the correct answer is Choice (E).
188 PART 4 Conquering the Quantitative Section
Getting confused and looking for the domain when you should be nding the range is very easy.
If you chose Choice (C), you solved for the domain of x. If you chose Choices (A) or (B), you’re
hung up trying to make the number under the radical a positive number. If you chose Choice (D),
you simply don’t know how to solve for range, so be sure to review this section.
Putting On Your Thinking Cap: Problem-Solving
You may be wondering how the GMAT tests your knowledge of algebra concepts. Well, wonder no
more. The following sections present you with many of the ways you’ll use algebra to solve GMAT
math problems.
Isolating the variable: Linear equations
A linear equation is an algebra equation that contains an unknown variable and no exponent
greater than 1. In other words, these equations are fairly easy.
In its simplest form, a linear equation is expressed as
axb y
, where x is the variable and a and
b are constants. Here are two things to keep in mind when you’re solving linear equations:
»
Isolate the variable in the equation you’re trying to solve, which means you work to get it all by
itself on one side of the equation. In other words, you’re solving for x.
»
Whatever operation you perform on one side of the equation, you must do to the other side.
This easy question asks you to solve a linear equation: If
4 10 38x
, what is the value of x?
Solve for x by isolating the variable on one side of the equation:
1. Eliminate 10 from the left side of the equation by subtracting it.
(Remember that if you do something to one side of the equation, you need to do the same
thing to the other side. Otherwise, your math teacher is liable to rap you on the knuckles with a
slide rule.) Here’s what happens when you subtract 10 from both sides:
4 10 10 38 10
448
x
x
2. Next, divide both sides by 4, and you have your answer.
4
4
48
4
12
x
x
The value of x is –12.
You tackle division problems the same way. So if you’re asked to solve for x in the problem
x
4
5
,
you know what to do. Isolate x to the left side of the equation by multiplying both sides of the equa-
tion by 4:
x
x
4
45
4
20
CHAPTER 13 Considering All the Variables: Algebra 189
If the equation includes multiple fractions, you can simplify things and save precious time by
eliminating the fractions. Just multiply each fraction by the least common denominator (which is
the lowest positive whole number that each fraction’s denominator divides into evenly). For
example, you may have to solve for x in a problem like this:
3
5
8
15 10
xx
The lowest number that 5, 15, and 10 go into evenly is 30, so that’s your least common denomina-
tor. Multiply each fraction by a fraction equivalent to 1 that will give you 30in the denominators,
like this:
3
5
6
6
8
15
2
210
3
3
18
30
16
30
3
30
xx
xx
Now you can eliminate the fractions by multiplying both sides of the equation by 30:
18 16 3xx
Then just solve for x:
18 16 3
18
18 16
31
8
16 15
16
15
15
15
16
15
xx
xx
xx
x
x
x
Bringing in the substitution: Simultaneous
equations
Solving for x is simple when it’s the only variable, but what if your equation has more than one
variable? When you have another equation that contains at least one of the variables, you can
solve for either variable. These two equations are called simultaneous equations. You just solve one
of the equations for one of the variables and then plug the answer into the other equation and
solve. Here’s a simple example.
If
4 530xy
and
y 2
, what is the value of x?
Because the second equation tells you that y is 2, just substitute 2 for the value of y in the rst
equation and you’re on your way:
4530
4
52
30
41
030
420
5
xy
x
x
x
x
()
That’s all there is to it!
190 PART 4 Conquering the Quantitative Section
You can also solve simultaneous linear equations by stacking them. This method works when you
have as many equations as you have possible variables to solve for. So you can stack these two
equations because they contain two variables:
6466
228
xy
xy
Your goal is to nd a way to remove one of the variables. Here’s how:
1. Examine the equations to determine what terms you can eliminate through addition or
subtraction.
If you multiply the entire second equation by 3, you can eliminate the x terms in both equations
because
2 36xx
, and
6 60xx
. Just be sure to multiply each term in the equation by the
same value. So the second equation becomes
6624xy
.
2. Stack the equations, combine like terms, and solve for y.
6466
6624
01
09
0
9
xy
xy
y
y
3. Plug the value of one variable into one of the equations and solve for the other value.
You’ve found that y = 9, so substitute 9 for the value of y in one of the equations to solve for x.
228
22
98
21
88
210
5
xy
x
x
x
x
()
Therefore, the solutions, also referred to as roots, to the simultaneous equations are x = 5 and
y = 9.
Knowing that you can nd solutions for variables when you have as many separate linear equa-
tions as the number of distinct variables they contain can help you answer some data suciency
questions, such as this example.
What is the value of x?
1.
2 928xy
2.
4 342yx y
(A) Statement 1 is sucient.
(B) Statement 2 is sucient.
(C) The two statements are sucient together.
(D) Each of the statements is sucient alone.
(E) Neither statement nor both together is sucient.
You can’t solve for x using either of the statements by itself. The best you can do is solve for x in
terms of y in either case. So the answer is either Choice (C) or (E). Without lifting a pencil, you
know that the answer is Choice (C); the statements are sucient together. Each of the two dis-
tinct equations contains the same two variables, so the conditions are met to reach a clear value
for x. You don’t have to take the time to actually solve for x during the exam, but we’ll take you
through the process in case you aren’t convinced.
CHAPTER 13 Considering All the Variables: Algebra 191
Combine like terms in Statement 2:
4342
3342
yx y
xy
Multiply all terms in the Statement 2 equation by 3 so you can eliminate the y value when you
stack the two equations:
33 342
99126
()xy
xy
Stack the equations and solve:
2928
99
126
7
154
22
xy
xy
x
x
Not playing fair: Inequalities
An inequality is a statement such as “x is less than y” or “x is greater than or equal to y.”
In addition to the symbols for add, subtract, multiply, and divide, mathematics also applies stan-
dard symbols to show how the two sides of an equation are related. You’re probably pretty famil-
iar with these symbols, but a little review never hurts. Table13-2 gives you a rundown of the
symbols you’ll deal with on the GMAT.
Here are some of the more common symbols used in algebra to signify equality and inequality.
Performing operations with inequalities
You treat inequalities a lot like equations. Isolate the variable to one side and perform the same
operations on both sides of the inequality. The only dierence is that if you multiply or divide by
a negative number, you need to reverse the direction of the inequality sign. So, here’s how you
solve this inequality:
210
5
x
x
TABLE13-2 Mathematical Symbols for Equality and Inequality
Symbol Meaning
=
Equal to
Not equal to
Approximately equal to
>
Greater than
<
Less than
Greater than or equal to
Less than or equal to
192 PART 4 Conquering the Quantitative Section
Working with ranges of numbers
You can also use inequalities to show a range of numbers. For example, the GMAT may show the
range of numbers between –6 and 12 as an algebraic inequality, like this:
612x
To show the range between –6 and 12 including –6 and 12, you use the sign:
612x
You can add or subtract values within a range. For example, you add 5 to each part of
612x
,
like this:
65 5125
1517
x
x
And you can perform operations between dierent ranges, such as 4 < x < 15 and –2 < y < 20. To
nd the sum of these two ranges, follow these steps:
1. Add the smallest values of each range:
4 + (–2) = 2
2. Add the largest values of each range:
15 + 20 = 35
3. Create a new range with the sums:
2 < x + y < 35
This means that the range of values of x + y is 2 < x + y < 35.
Here’s an example of how the GMAT may ask you to deal with inequalities.
If
x
2
18
, what is the smallest real value x can have?
(A) –9
(B) –6
(C) –3
(D) 0
(E) 3
This problem asks you to determine the smallest real value of x if
x
2
1
is less than or equal to 8.
Solve the inequality for x:
x
x
2
2
18
9
9
x
Or
9 x
because the product of two negative numbers is also positive.
So,
33x
. Remember that the square root of a number may be positive or negative. The square
root of 9 is either 3 or –3. Because –3 is less than 3, –3 must be the smallest real value of x.
To make sure you’re right, you can eliminate answer choices by using common sense. For exam-
ple, –9in Choice (A) would make
x
2
1
equal 80, and –6in Choice (B) would make
x
2
1
equal
35. So neither Choices (A) nor (B) can be a solution for x. In Choice (D), 0 is a solution for x, but it
isn’t the smallest solution, because you know that –3 is a possibility. Choice (E) can’t be right
because it’s larger than two other possible solutions, –3 and 0. So Choice (C) is the correct answer.
CHAPTER 13 Considering All the Variables: Algebra 193
Solving quadratic equations
When you set a quadratic polynomial equal to 0, you get what’s called a quadratic equation. An
example of the classic quadratic form is
axbxc
2
0
, where a, b, and c are constants and x is a
variable that you have to solve for. Notice that 0 is on one side of the equation, and all non-zero
terms are on the other side.
Quadratic equations may appear in slightly dierent forms. For example, all the following equa-
tions are quadratic equations because they contain a squared variable and equal 0:
x
x
xx
2
2
2
0
40
3650
Factoring to nd x
The GMAT may give you a quadratic equation and ask you to solve for x. The simplest way to solve
a quadratic equation is to try to factor the equation into two binomials, just like you did earlier in
the section “Two by two: Factoring quadratic polynomials.”
xx
2
650
To factor this trinomial, consider what numbers multiply together to become 5 that also have a
sum of –6.
The two factors of 5 are 5 and 1 or –5 and –1. To get a sum of –6, you need to go with the negative
values. Doing so gives these two binomial factors: (x– 5) and (x– 1). So the resulting equation is
(x– 5)(x– 1) = 0.
To solve for x, you set each of the binomial factors equal to 0. You can do so because you know that
one of the factors must equal 0 if their product is 0.
x– 5 = 0
x = 5
and
x– 1 = 0
x = 1
Now the solutions (or roots) to the equation are clear: x = 1 and x = 5. Both 1 and 5 are possible
solutions for x in this quadratic equation.
Quadratic equations usually have two possible solutions.
Determining solutions for the dierence of perfect squares
Finding the solution set for a quadratic equation made up of the dierence of perfect squares (like
xy
22
0
) is simple if you remember that
xy xyxy
22
. If the GMAT presents you with
the task of solving for x in an equation where the dierence of perfect squares is equal to 0, you
know that x equals the positive and negative values of the square root of y
2
(which is the second
term).
194 PART 4 Conquering the Quantitative Section
So, if you were told to nd the solution set for
x
2
49 0
, you’d determine the square root of the
second term (49), which is 7. The factors, then, are (x + 7) and (x– 7). Therefore, the solution set
for this problem is x = –7 and x = 7, which are indeed the positive and negative values of the sec-
ond term’s square root!
Using the quadratic formula
Solving quadratic equations is easy when the solutions come out to be nice, round numbers. But
what if the ultimate solutions are harsh-looking radicals or perhaps not even real roots? For the
rare GMAT occasions when you can’t simply solve a quadratic equation by factoring, you may
have to use the quadratic formula, which is a rearrangement of the classic equation:
axbxc
2
0
.
It looks like this:
x
bb ac
a
2
4
2
Although this formula may look mighty unmanageable, it may be the only way to nd the solu-
tion to x for quadratic equations that aren’t easily factored. Here’s how you’d apply the formula
when asked to solve
3760
2
xx
for x. In this equation, a = 3, b = 7, and c = –6. Plug these
numbers into the quadratic formula:
x
x
x
x
x
7743 6
23
74972
6
7 121
6
711
6
18
6
2
()
or
44
6
3
2
3
x
or
The solutions for x are
2
3
and –3. Whew! Luckily, the GMAT won’t give you many quadratic equa-
tions that require you to apply this formula. But you’ll know what to do if you encounter one of
the few.
Reading between the lines: Word problems
The GMAT tests algebra and arithmetic concepts in word problems as well as mathematical equa-
tions. In fact, word problems are more common on the GMAT than straightforward equation-
solving. So you have to know how to translate the English language into mathematical expressions.
(You’ll probably see a few geometry word problems, too, but algebra is more common on the
GMAT.)
To help you with the translation, Table13-3 provides some of the more common words you’ll
encounter in word problems and tells you what they look like in math symbols.
Here’s an example of how you play foreign language interpreter on GMAT word problems.
CHAPTER 13 Considering All the Variables: Algebra 195
On the rst day of an alpine slalom competition, the total combined time of Grace’s two runs
was 1 minute and 57 seconds. If twice the number of seconds in her rst run was 30 seconds
more than the number of seconds in her second run, what was her time in seconds for the
rstrun?
(A) 15
(B) 30
(C) 49
(D) 68
(E) 147
Focus on what you’re supposed to gure out. The question asks for the time of Grace’s rst run
in seconds. So you know you have to convert her total time to seconds so you’re working in the
correct units. A minute has 60 seconds, which means that Grace’s total time was 60 + 57, or 117
seconds.
You can immediately eliminate Choice (E) because Grace’s rst run couldn’t have been longer
than the sum of her two runs. Now apply your math translation skills. You have two unknowns:
the time of Grace’s rst run and the time of her second run. Let x stand for the rst unknown and
y for the second.
You can solve a problem with two variables when you know two equations that involve those two
variables. So search the problem for two equations.
For the rst equation, the problem tells you that the total time of the two runs is 117 seconds.
According to the English-to-math-translation dictionary, that means x + y = 117. You’ve got one
equation!
You also know that 2 times (×) the number of seconds in her rst run (x) was (=) 30 seconds more
(+) than her time for the second run (y). Translation please? 2x = 30 + y.
TABLE13-3 Common Words and Their Math Equivalents
Plain English
Math
Equivalent
More than, increased by, added to, combined with, total of, sum of Plus (+)
Less than, fewer than, decreased by, diminished by, reduced by, dierence between,
taken away from
Minus (–)
Of, times, product of Multiply (
)
Ratio of, per, out of, quotient Divide (
or /)
x percent of y (x
100) y
Is, are, was, were, becomes, results in Equals (=)
How much, how many, a certain number Variable (x, y)
196 PART 4 Conquering the Quantitative Section
After you have the two equations, you can use substitution or stacking to solve for x. For this
problem, stacking is faster. Notice that 2x = 30 + y is the same as 2x– y = 30. When you stack and
add the two equations, you can eliminate the y variable because y– y = 0.
xy
xy
x
x
117
23
0
3 147
49
So, Grace ran her rst race in 49 seconds, which is Choice (C). If you chose Choice (D), you
solved for y instead of x. Grace’s second run was 68 seconds.
Burning the midnight oil: Work problems
Work problems ask you to nd out how much work gets done in a certain amount of time. You use
this formula for doing algebra work problems:
Production = Rate of Work Time
Production means the amount of work that gets done. Because you get that quantity by multiply-
ing two other numbers, you can say that production is the product of the rate times the time.
Here’s how you’d apply the formula on a GMAT work problem.
There are two dock workers, Alf and Bob. Alf can load 16 tons of steel per day, and Bob can load
20 tons per day. If they each work eight-hour days, how many tons of steel can the two of them
load in one hour, assuming they maintain a steady rate?
(A) 2.5
(B) 4.5
(C) 36
(D) 160
(E) 320
This question asks you to nd the amount of production and gives you the rate and the time. But
to calculate the rate properly, you must state the hours in terms of days. Because a workday is
eight hours, one hour is
1
8
of a day. Figure out how much Alf loads in one hour (
1
8
of a day) and
add it to what Bob loads in one hour.
Total Production AlfsProduction BobsProduction
T
otal Pr
’’
ooduction
T
otal Production
T
otal Produ
16
1
8
20
1
8
225
.
cction 45.
So, Alf and Bob load 4.5 tons of steel in one hour (
1
8
of a day), which is Choice (B). If you chose
Choice (C), you gured out the total production for one day rather than one hour.
CHAPTER 13 Considering All the Variables: Algebra 197
Going the distance: Distance problems
Distance problems are a lot like work problems. The formula for computing distance or speed
problems is this:
DistanceRateTime
Any problem involving distance, speed, or time spent traveling can be boiled down to this equa-
tion. The important thing is that you have your variables and numbers plugged in properly. Here’s
an example.
Abby can run a mile in seven minutes. How long does it take her to run
1
10
of a mile at the same
speed?
(A) 30 seconds
(B) 42 seconds
(C) 60 seconds
(D) 360 seconds
(E) 420 seconds
Before you do any calculating, you can eliminate Choice (E) because 420 seconds is 7 minutes, and
you know it takes Abby less time to run
1
10
of a mile than it does for her to run a mile.
The problem tells you that Abby’s distance is
1
10
of a mile. You can gure her rate to be
1
7
because
she runs 1 mile in 7 minutes. The problem is asking how long she runs, so you need to solve for
time. Plug the numbers into the distance formula:
DistanceRateTime
t
1
10
1
7
You need to isolate t on one side of the equation, so multiply both sides by 7:
1
10
7
7
10
t
t
So, Abby runs
1
10
of a mile in
7
10
of a minute. Convert minutes to seconds. There are 60 seconds in
a minute, and
7
10
60
42
seconds. The correct answer must be Choice (B).
CHAPTER14 Getting the Angle on Geometry: Planes and Solids 199
IN THIS CHAPTER
» Looking at lines and angles
» Taking a crack at triangles
» Questing after quadrilaterals
» Pondering polygons
» Circumnavigating circles
» Reaching out to touch three-
dimensional gures
Getting the Angle on
Geometry: Planes and
Solids
G
eometry starts with the basics— plane geometry— which is the study of lines and shapes
in two dimensions. From that foundation, geometry constructs increasingly complex
models to more accurately portray the real world. Three-dimensional, or solid, geometry
is almost as simple as plane geometry, with the added dimension of depth.
The GMAT tends to have fewer math questions about planes and solids than about algebra and
statistics. Those of you who aren’t particularly fond of manipulating shapes and gures can
rejoice! But 20 percent of GMAT math questions cover geometry concepts, and this chapter is
designed to make sure you’re ready for them.
Fishing for the Answers: Lines and Angles
The building blocks for geometric forms are lines and angles, so we start by dening these fun-
damental elements. Understanding the meanings of these terms is an important part of solving
problems on the GMAT.Here are the common terms that pop up on the test:
»
Line: A straight path of points that extends forever in two directions. A line doesn’t have any
width or thickness. Arrows are sometimes used to show that the line goes on forever. See line
AB in Figure14-1.
»
Line segment: The set of points on a line between any two points on the line. Basically, it’s just
a piece of a line from one point to another that contains those points and all the points
between. See line segment CD in Figure14-1.
Chapter14
200 PART 4 Conquering the Quantitative Section
»
Ray: A ray is like half of a line; it starts at an endpoint and extends forever in one direction. You
can think of a ray as a ray of light extending from the sun (the endpoint) and shining as far as it
can go. See ray EF in Figure14-1.
»
Midpoint: The point halfway (equal distance) between two endpoints on a line segment.
»
Bisect: To cut something exactly in half, such as when a line, or bisector, cuts another line
segment, angle, or polygon into two equal parts.
»
Intersect: Just like it sounds— intersect simply means to cross; that is, when one line or line
segment crosses another line or line segment.
»
Collinear: A set of points that lie on the same line.
»
Vertical: Lines that run straight up and down.
»
Horizontal: Lines that run straight across from left to right.
»
Parallel: Lines that run in the same direction, always remaining the same distance apart.
Parallel lines never cross one another.
»
Perpendicular: When two lines intersect to form a square corner. The intersection of two
perpendicular lines forms a right, or 90-degree, angle.
»
Angle: The intersection of two rays (or line segments) sharing a common endpoint. The
common endpoint is called the vertex. The size of an angle depends on how much one side
rotates away from the other side. An angle is usually measured in degrees or radians.
»
Acute angle: Any angle measuring less than 90 degrees. Like an acute, or sharp, pain, the
acute angle has a sharp point. See Figure14-2.
»
Right, or perpendicular, angle: An angle measuring exactly 90 degrees. It makes up a square
corner. See Figure14-3.
»
Obtuse angle: An angle that measures more than 90 degrees but less than 180 degrees. The
opposite of an acute angle, an obtuse angle is dull rather than sharp. See Figure14-4.
»
Straight angle: An angle that measures exactly 180 degrees. A straight angle appears to be a
straight line or line segment.
FIGURE14-1:
Line, line
segment,
and ray.
© John Wiley & Sons, Inc.
FIGURE14-2:
Acute angle.
© John Wiley & Sons, Inc.
CHAPTER 14 Getting the Angle on Geometry: Planes and Solids 201
»
Complementary angles: Two angles that add together to total 90 degrees. Together, they
form a right angle.
»
Supplementary angles: Two angles that add together to total 180 degrees. They form a
straight angle.
»
Similar: Objects that have the same shape but may have dierent sizes.
»
Congruent: Objects that are equal in size and shape. Two line segments with the same length,
two angles with the same measure, and two triangles with corresponding sides of equal
lengths and angles that have equal degree measures are congruent.
Two important rules for lines and angles arise from these basic denitions. You can read all about
them in Table14-1.
FIGURE14-3:
Right angle.
© John Wiley & Sons, Inc.
FIGURE14-4:
Obtuse
angle.
© John Wiley & Sons, Inc.
TABLE14-1 Rules for Lines and Angles
Condition Rule Sample Figure
Intersecting
lines
When two lines intersect, the opposite angles (across from each other)
are always congruent or equal, and the adjacent angles are always
supplementary. Opposite angles are also known as vertical angles.
Adjacentangles have a common side, so they’re right next to each other.
Inthe sample gure,
ABC
and
DBE
are congruent;
ABC
and
CBD
forma straight line and are, therefore, supplementary.
Parallel lines
intersected
by a transversal
When parallel lines are crossed by a third line that’s not perpendicular
to them (called a transversal), the resulting small and large angles share
certainproperties. Each of the small angles is equal to the other; the large
angles are also equal to each other. These equal smaller and larger angles
are called corresponding angles. The measurement of any small angle
addedto that of any large angle equals
180
.
202 PART 4 Conquering the Quantitative Section
Here’s how lines and angles may be tested on the GMAT math section.
In the preceding gure, line m is parallel to line n and line t is a transversal crossing both lines
m and n. Given the information contained in this gure, what is the value of e?
(A)
30
(B)
60
(C)
100
(D)
120
(E) It cannot be determined from the information provided.
Because lines m and n are parallel, you know that the value of e is equal to the value of c. The angle
with a value of c lies along a straight line with the angle with a measure of a, so
a c 180
.
Because a equals 60 degrees, c must equal 120 degrees. And because c equals e, e must also equal
120 degrees. The correct answer is Choice (D).
Trusting Triangles
Lines and angles form gures, and one of the most commonly tested GMAT gures is the triangle.
A triangle has three sides, and the point where two of the sides intersect is called a vertex. You
name triangles by their vertices, so a triangle with vertices A, B, and C is designated as
ABC
.
Many geometry questions on the GMAT involve triangles, so pay particular attention to their
properties and rules.
Triple treat: Types of triangles
You can identify triangle types by the measurements of their sides and angles:
»
A scalene triangle has no equal sides and no equal angles.
»
An isosceles triangle has at least two equal sides, and the measures of the angles opposite
those two sides are also equal to each other.
»
An equilateral triangle has three sides of equal lengths and three 60-degree angles.
»
A right triangle has one angle that measures 90 degrees. The side opposite the right angle is
called the hypotenuse.
These rules hold true for all types of triangles:
»
The measures of the three angles add up to 180 degrees.
»
The sum of the lengths of two sides is always greater than the length of the third side.
CHAPTER 14 Getting the Angle on Geometry: Planes and Solids 203
»
The side that’s opposite of a given angle in a triangle is proportionate to that angle, as you can
see in Figure14-5. So the smallest angle faces the shortest side of the triangle. If two or more
angles have the same measurement, their opposite sides are also equal.
Here’s an example of how this information may be tested on the GMAT.
In the preceding gure, line SA is parallel to line TB. If the measure of
BTU
is 60 degrees, what
is the measure of
ATB
?
(A)
30
(B)
40
(C)
50
(D)
60
(E)
80
Like a bridge over troubled water, line RU traverses the parallel lines SA and TB. Therefore,
BTU
and
AST
are corresponding angles and have the same measurement. Because the value of
BTU
is 60 degrees,
AST
must also measure 60 degrees.
You also know that line segment SA equals line segment TA, so
SAT
is isosceles, and the angles
opposite these two line segments have the same measure. One of these angles is
AST
.
AST
measures 60 degrees, and
STA
has the same measurement as
AST
. Therefore,
STA
also mea-
sures 60 degrees.
The measures of the angles along a straight line add up to 180 degrees, so the measure of
ATB
equals 180 less the value of
BTU
less the value of
ATS
.
BTU
and
ATS
each measure
60 degrees, so the measure of
ATB 180 60 60
, which is also 60. The correct answer is
Choice (D).
FIGURE14-5:
Angles of a
triangle are
in propor-
tion to their
opposite
sides.
© John Wiley & Sons, Inc.
204 PART 4 Conquering the Quantitative Section
The area of a triangle
The GMAT will likely ask you to determine the area of a triangle, so you better be ready. Memorize
this formula:
Ab
h
1
2
A stands for (what else) area, b is the length of the base or bottom of the triangle, and h stands
for the height (or altitude), which is the distance that a perpendicular line runs from the base to
the angle opposite the base. For a visual, check out Figure14-6.
Notice that, as shown in Figure14-6, the height is always perpendicular to the base and that the
height can be placed either inside or outside the triangle. Because the legs of a right triangle are
perpendicular, you can use one leg as the triangle’s height and the other leg as the triangle’s base
(handy to remember if the triangle’s ipped on its hypotenuse).
The Pythagorean theorem and other
cool stu about right triangles
You can solve GMAT problems for the lengths of the sides of right triangles by using a groovy
little formula called the Pythagorean theorem and by memorizing some common right-triangle
side lengths.
Digging Pythagoras and his theorem
The Pythagorean theorem simply states that the sum of the squares of the legs of a right triangle
is equal to the square of the hypotenuse, or
a bc
222
, where a and b represent the two legs of
the right triangle and c is the hypotenuse. The legs of a right triangle are simply the sides that
form the right angle, and the hypotenuse is the side opposite it. (It’s always the biggest side of
the right triangle.) If you know the lengths of two sides of a right triangle, you can easily nd the
length of the other side by using this handy formula.
Keep in mind that the Pythagorean theorem works only with right triangles. You can’t use it to
nd the lengths of sides of triangles that don’t have a right angle in them.
Which of the following is the length, in inches, of the remaining side of a right triangle if one
side is 7 inches long and the hypotenuse is 12 inches long?
(A)
5
(B) 5
(C) 7
(D) 12
(E)
95
FIGURE14-6:
The base
and height
of a triangle.
© John Wiley & Sons, Inc.
CHAPTER 14 Getting the Angle on Geometry: Planes and Solids 205
You may nd it helpful to draw a right triangle on your paper to visualize the problem, but doing
so isn’t necessary. If the hypotenuse is 12 inches and one side is 7 inches, you gure the measure-
ment of the remaining side by applying the formula:
a bc
b
b
b
b
222
22 2
2
2
71
2
49
144
95
95
Pick Choice (E).
Getting hip to the common ratios of right triangles
You may nd it handy to memorize some ratios based on the Pythagorean theorem. That way, you
don’t have to work out the whole theorem every time you deal with a right triangle.
The most common ratio of the three sides of a right triangle is 3:4:5 (3 is the measure of the short
leg, 4 is the measure of the long leg, and 5 is the measure of the hypotenuse). Related multiples
are 6:8:10, 9:12:15, and so on. As soon as you recognize that two sides t the 3:4:5 ratio or a mul-
tiple of the 3:4:5 ratio, you’ll automatically know the length of the third side.
The hypotenuse of the triangle is always the longest side, so the largest value of the ratio (5in
this case) always corresponds to the hypotenuse when you apply this shortcut.
Other proportions of right triangles you should try to remember are 5:12:13, 8:15:17, and 7:24:25.
Knowing these proportions may allow you to more quickly solve problems like the following one
on the GMAT.
In the preceding gure, AB is 6 units long, AC is 8 units long, and BD is 24 units long. How
many units long is CD?
(A) 26
(B) 32
(C) 80
(D) 96
(E) 100
This problem would be time consuming to solve if you didn’t know the common ratios of right tri-
angles. To determine the length of line segment CD, you rst need to know the length of CB. You
could use the Pythagorean theorem, but you know an easier, faster way. Because
AB 6
and
AC 8
,
ABC
is a 3:4:5 triangle times 2— a 6:8:10 triangle. Therefore, the length of hypotenuse BC is 10.
206 PART 4 Conquering the Quantitative Section
Therefore,
BCD
is a 5:12:13 triangle times 2— a 10:24:26 triangle. So the length of CD = 26, and
the correct answer is Choice (A).
Knowing what’s neat about the 30:60:90-degree triangle
Some other handy right triangles exist. One is the 30:60:90-degree triangle. When you bisect any
angle in an equilateral triangle, you get two right triangles with 30-, 60-, and 90-degree angles.
In a 30:60:90-degree triangle, the hypotenuse is 2 times the length of the shorter leg, as shown
in Figure14-7. The ratio of the three sides is
ss s::32
, where s = the length of the shortest side.
Feeling the equilibrium of a 45:45:90-degree triangle
If you bisect a square with a diagonal line, you get two triangles that both have two 45-degree
angles. Because the triangle has two equal angles (and, therefore, two equal sides), the resulting
triangle is an isosceles right triangle, or a 45:45:90-degree triangle. Its hypotenuse is equal to
2
times the length of a leg. It’s important to recognize this also means that the length of a leg is
equal to the length of the hypotenuse divided by
2
. The ratio of sides in an isosceles right tri-
angle is, therefore,
sss:: 2
(where s = the length of one of the legs) or
ss
s
22
::
(where s = the
length of the hypotenuse). Figure14-8 shows the formula.
This example question shows just how helpful your knowledge of special triangles can be.
FIGURE14-7:
The
30:60:90-
degree
triangle.
© John Wiley & Sons, Inc.
FIGURE14-8:
The
45:45:90-
degree
triangle.
© John Wiley & Sons, Inc.
CHAPTER 14 Getting the Angle on Geometry: Planes and Solids 207
In
STR
,
TSR
measures 45 degrees and
SRT
is a right angle. If SR is 20 units long, how many
units is TR?
(A) 10
(B)
10 2
(C) 20
(D)
202
(E) 40
You could draw the triangle, but with what you know about 45:45:90-degree triangles, you don’t
need to.
Because
SRT
is a right angle, you know that the triangle in this question is a right triangle. If
TSR
measures 45 degrees, then
RTS
must also measure 45 degrees, and this is a 45:45:90-degree
triangle. So SR must equal TR. The length of line segment
SR 20
, so
TR 20
. The correct answer
is Choice (C).
A striking resemblance: Similar triangles
Triangles are similar when they have exactly the same angle measures. Similar triangles have the
same shape, even though their sides may have dierent lengths. The corresponding sides of
similar triangles are in proportion to each other. The heights of the two triangles are also in pro-
portion. Figure14-9 provides an illustration of the relationship between two similar triangles.
Knowing the properties of similar triangles helps you answer GMAT questions like the next one.
FIGURE14-9:
Similar
triangles.
© John Wiley & Sons, Inc.
208 PART 4 Conquering the Quantitative Section
RTS
and
ACB
in the preceding gure are similar right triangles with side lengths that mea-
sure as indicated. What is the area of
ACB
?
(A) 10
(B) 15
(C) 30
(D) 37.5
(E) 75
To nd the area of
ACB
, you need to know the measurements of its base and height. The gure
gives you the length of its height (5), so you need to nd the base.
Because the two triangles are similar (and proportionate to each other), you can use what you
know about
RTS
to nd the base measurement of
ACB
. TR is proportionate to CA, and RS is
proportionate to AB. Set up a proportion with x representing the measure of AB, cross-multiply,
and solve:
2
5
6
2 65
2
30
15
x
x
x
x
The base of
ACB
is 15 inches.
Don’t stop there and choose Choice (B). The question asks for the area of
ACB
, not the length
of AB.
Substitute the base and height measurements for
ACB
into the formula for the area of a triangle
Abh
1
2
and solve:
Ab
h
A
A
A
1
2
1
2
515
1
2
75
37 5
()
()
()
.
The correct answer is Choice (D).
Playing Four Square: Quadrilaterals
A quadrilateral is a four-sided polygon, and several types of quadrilaterals exist. Your primary
concern on the GMAT will be to nd the measurement of a quadrilateral’s area and perimeter. The
following sections review what you need to know to accomplish this goal.
These two rules apply to all quadrilaterals:
»
The perimeter measure of any four-sided gure is always the sum of its side lengths.
»
The sum of the angle measures of a quadrilateral is always 360 degrees.
CHAPTER 14 Getting the Angle on Geometry: Planes and Solids 209
Drawing parallels: Parallelograms
Most of the quadrilaterals that appear on the GMAT are parallelograms.
Parallelograms have properties that are very useful for solving GMAT problems:
»
The opposite sides are parallel and equal in length.
»
The opposite angles are equal in measure to each other.
»
The measures of the adjacent angles add up to 180 degrees, so they’re supplementary to each
other.
»
The diagonals (designated by d
1
and d
2
) of a parallelogram bisect each other. In other words,
they cross at the midpoint of both diagonals.
Figure 14-10 provides a visual representation of the very important properties of
parallelograms.
The area of any parallelogram is its base times its height (
Abh
). You determine the height pretty
much the same way you determine the height of a triangle. The dierence is that you draw the
perpendicular line from the base to the opposite side (instead of to the opposite angle, as in the
case of a triangle). See Figure14-11.
You can use the Pythagorean theorem to help you nd the height of a parallelogram. When you
drop a perpendicular line from one corner to the base to create the height, the line becomes the
leg of a right triangle. If the problem gives you the length of other sides of the triangle (or infor-
mation you can use to determine the length), you can use the formula to nd the height
measurement.
Parallelograms come in various types:
»
A rectangle is a parallelogram with four right angles. The formula for the area of a rectangle is
Abh
, where the base and height are the measures of the rectangle’s length and width.
»
A square is a rectangle with four equal sides, which means you can easily nd its area when
you know the length of only one side. Keep these formulas in mind:
•
The area is
As
2
, where s is the length of a side.
•
The perimeter is 4s.
FIGURE14-10:
A parallelo-
gram.
© John Wiley & Sons, Inc.
FIGURE14-11:
Finding the
area of a
parallelo-
gram.
© John Wiley & Sons, Inc.
210 PART 4 Conquering the Quantitative Section
»
A rhombus has four equal sides but not necessarily four right angles. Find the area of a
rhombus by multiplying the lengths of its two diagonals (designated as d
1
and d
2
) and then
dividing by 2:
Ad
d
1
2
12
Raising the roof: Trapezoids
A trapezoid is a quadrilateral with just one set of parallel sides. The parallel sides are called the
bases, and the other two sides are called the legs. In an isosceles trapezoid, the legs of the quad-
rilateral are the same length. It looks kind of like an A-frame with the roof cut o. Check out
Figure14-12 for an example. You can nd the area of a trapezoid as long as you know the length
of both bases and the height. Take the average of the two bases and multiply by the height:
Abbh
1
2
12
()
GMAT questions about quadrilaterals, such as the following, often require you to apply the for-
mulas for area and perimeter and what you know about triangles.
In the preceding gure, square ABCD has sides the length of 4 units, and M and N are the mid-
points of AB and CD, respectively. What is the perimeter, in units, of AMCN?
(A) 6
(B)
6 5
(C)
2 23
(D)
4 45
(E)
8 5
This question asks you to determine the perimeter of parallelogram AMCN. To solve it, rely on
what you know about triangles and simplifying radicals.
If M and N are the midpoints, then
AM 2
(which is
4
2
) and
NC 2
. Now you know the short sides
of
AMCN 2
. You can see that each of the long sides of the parallelogram is the hypotenuse of the
right triangles within the square. The lengths of the legs of the right triangles measure 2 and 4,
FIGURE14-12:
The bases
and height of
a trapezoid.
© John Wiley & Sons, Inc.
CHAPTER 14 Getting the Angle on Geometry: Planes and Solids 211
which doesn’t t with any of the special ratios associated with right triangles. So use the Pythag-
orean theorem:
2 4
416
20
20
45
25
222
2
2
c
c
c
c
c
c
Each of the short sides of AMCN measures 2 units and each long side measures
2 5
. Add the
sides to get its perimeter:
P
P
22 22 5
445
()
()
This is the answer provided by Choice (D).
Showing Their Good Sides: Other Polygons
The GMAT may throw in some other types of polygons to make things interesting. Here are some
of the common ones:
»
Pentagon: A ve-sided gure
»
Hexagon: A six-sided gure (the x makes it sound like six)
»
Heptagon: A seven-sided gure
»
Octagon: An eight-sided gure (like octopus)
»
Nonagon: A nine-sided gure
»
Decagon: A ten-sided gure (like decathlon)
In general, GMAT polygons will be regular polygons, which means that all the sides are the same
length and all the angles are equal. Polygons with exactly the same shape and same angle mea-
surements have proportional corresponding side lengths.
No set formula exists for determining the area of a polygon. You need to create quadrilaterals and
triangles within the polygon, nd their areas, and add them together to get the total area of the
polygon. In addition to determining its area, you may have to come up with the sum of a poly-
gon’s interior angles.
The formula for determining the sum of the interior angles of any polygon is simple:
SA n()2 180
, where n is equal to the number of sides.
Works every time! If the polygon’s regular, you can also determine the measure of each of the
angles. You divide the sum of the angles by the total number of angles. So each angle in a regular
pentagon measures
540
5
108 .
212 PART 4 Conquering the Quantitative Section
The method for determining the measure of an angle in a polygon works only if the GMAT tells
you that the polygon is regular.
Eating Up Pieces of Pi: Circles
A circle, by technical denition, is a set of points in a plane that are at a xed distance from a
given point. That point is called the center. The following sections go into detail about the kinds of
questions the GMAT will ask you about circles, from knowing the measures of the circle’s radius,
diameter, and circumference to working with arcs, chords, inscribed gures, and tangents.
Ring measurements: Radius, diameter,
and circumference
Almost any GMAT problem regarding a circle requires you to know or nd its radius, diameter,
circumference, and area.
»
The radius of a circle is the distance from the center of the circle to any point on the circle. The
radius is usually indicated by the letter r, as shown in Figure14-13.
»
The diameter of a circle is the length of a line that goes from one side of the circle to the other
and passes through the center. The diameter is twice the length of the radius, and it’s the
longest possible distance across the circle. Diameter usually is indicated by the letter d, as
shown in Figure14-13.
»
The circumference of a circle is the distance around the circle. The formula for nding circum-
ference is 2 times the radius times pi:
C r2
. Because twice the radius is the measure of the
diameter, you can also gure circumference by multiplying the diameter by pi:
C d
.
»
The area of a circle is the measure of the space inside the circle. The formula for nding area is
Ar
2
.
Blueprints for Noah: Arcs
When it comes to angles and arcs on a circle, you should have a basic understanding of the fol-
lowing terms so you aren’t running in circles on the GMAT math section:
»
An arc of a circle is a portion along the circumference of the circle. See Figure14-14.
•
A minor arc is less than 180 degrees.
•
A semicircle is equal to 180 degrees.
•
A major arc is greater than 180 degrees. In fact, the arc of the entire circle is 360 degrees.
You’re more likely to work with minor arcs than major ones on the GMAT.
FIGURE14-13:
Radius and
diameter
of a circle.
© John Wiley & Sons, Inc.
CHAPTER 14 Getting the Angle on Geometry: Planes and Solids 213
»
A central angle of a circle is an angle that’s formed by two radii; it’s called a central angle
because its vertex is the center of the circle. The measurement of the central angle is the same
as that of the arc formed by the endpoints of its radii. So a 90-degree central angle (like the
one in Figure14-14) intercepts one-quarter of the circle, or a 90-degree arc.
Line ’em up: Chords, inscribed and
circumscribed gures, and tangents
The GMAT may toss in some extra lines and gures when it questions you about circles. The extra
features may appear within or outside the circle. The next sections describe each of these extras.
Striking a chord
A chord is a line segment cutting across a circle that connects two points on the edge of a circle.
Those two points at the end of the chord are also the endpoints of an intercepted arc. See
Figure14-15.
Moving in: Inscribed and circumscribed gures
An inscribed gure is any gure (angle, polygon, and so on) that’s drawn inside another gure. For
example, you could draw a triangle inside a circle so that all its vertices touch at points on the
circle, just like Figure14-16.
A circumscribed gure is one that is drawn around the outside of another shape, such as a circle
drawn around a triangle so that all the vertices of the triangle touch the circle. You’d say the circle
in Figure14-16 is circumscribed around the triangle.
The only dierence between an inscribed and a circumscribed gure hinges on the reference. You
refer to the gure on the outside of another gure as a circumscribed gure and the gure on the
inside of another gure as an inscribed gure.
FIGURE14-14:
An arc and
central
angle.
© John Wiley & Sons, Inc.
FIGURE14-15:
A chord.
© John Wiley & Sons, Inc.
214 PART 4 Conquering the Quantitative Section
The GMAT may use circumscribed and inscribed gures to ask you to calculate the area of a
shaded area. When you get a “shaded area” problem, calculating the area of both gures and then
subtracting the area of one from the other is often the best way to solve the problem.
Going o on a tangent
A tangent line is one that intersects the circle at just one point. A good way to think of a tangent
line in the real world is like a wheel rolling along a road. The road is tangent to the wheel.
Figure14-17 shows line AB tangent to the circle. The line is also perpendicular to the radius that
touches the circle where the tangent intersects. To continue the wheel analogy, if that wheel had
an innite number of spokes coming from its center, only one spoke would touch (be perpendicu-
lar to) the ground at any one time.
The GMAT may test your knowledge of circles with a question such as this:
FIGURE14-16:
Inscribed
and circum-
scribed
figures.
© John Wiley & Sons, Inc.
FIGURE14-17:
Tangent line.
© John Wiley & Sons, Inc.
CHAPTER 14 Getting the Angle on Geometry: Planes and Solids 215
In the preceding gure, A and B lie on the circle with center C. CA is 9 units long, and the mea-
sure of
ACB
is 40 degrees. How many units long is minor arc AB?
(A)
(B)
2
(C)
9
(D)
18
(E)
36
First, determine how many degrees are in arc AB. Because CA and CB are radii of the circle, the
degree measurement of the central angle ACB is the same as the measurement of the arc the ends
of the radii form on the circle. So the minor arc AB is 40 degrees. How does that help you deter-
mine the length of the arc? Well, you know that a circle is 360 degrees, and 40 degrees is
1
9
of
360 degrees. That means that arc AB is
1
9
of the circumference of the circle. Determine the
circumference:
C r
C
C
2
29
18
()
()
Then gure out
1
9
of that length:
1
9
18
2
x
x
The correct answer must be Choice (B).
Getting a Little Depth Perception:
Three-Dimensional Geometry
Three-dimensional geometry, or solid geometry, adds some depth to plane geometrical gures.
You’ll likely encounter no more than a handful of solid geometry questions on the GMAT, and
they’ll likely concern only rectangular solids and cylinders, which we discuss in the following
sections.
Chipping o the old block: Rectangular solids
You make a rectangular solid by taking a simple rectangle and adding depth. Good examples of
rectangular solids are bricks, cigar boxes, or boxes of your favorite cereal. A rectangular solid is
also known as a right rectangular prism because it has 90-degree angles all around. Prisms have two
congruent polygons on parallel planes that are connected to each other by their corresponding
points. The two connected polygons make up the bases of the prism, as shown in Figure14-18.
A rectangular solid has three dimensions: length, height, and width. You really need to worry
about only two basic measurements of rectangular solids on the GMAT: total surface area and
volume.
216 PART 4 Conquering the Quantitative Section
Finding volume
The volume (V) of a rectangular solid is a measure of how much space it occupies, or to put it in
terms everyone can appreciate, how much cereal your cereal box holds. You measure the volume
of an object in cubic units. The formula for the volume of a rectangular solid is simply its length (l)
times its width (w) times its height (h):
V lwh
.
Another way of saying this formula is that the volume is equal to the base times the height (
V Bh
),
where B is the area of the base. See what we mean in Figure14-18.
Determining surface area
You can nd the surface area (SA) of a rectangular solid by simply guring out the areas of all six
sides of the object and adding them together.
First you nd the area of the length (l) times height (h), then the area of length times width (w),
and nally width times height (see Figure14-19). Now multiply each of these three area measure-
ments times 2 (after you nd the area of one side, you know that the opposite side has the same
measurement). The formula for the surface area of a rectangular solid is
SA lh lw wh22 2
.
You can visualize the surface area of a rectangular solid, or any solid gure for that matter, by
mentally attening out all the sides and putting them next to each other. It’s sort of like taking
apart a cardboard box to get it ready for recycling; only now you get to measure it. Lucky you!
Working with cubes
You can use the same formulas you used with rectangular solids to nd the area and volume of a
three-dimensional square, called a cube, shown in Figure14-20. Because all the faces on a cube
are perfect squares, you can nd its measurements with some simple formulas.
»
The volume of a cube with an edge a is
a
3
:
V a
3
.
»
The surface area of a cube is simply the area of one side times 6:
SA a6
2
.
»
The diagonal of a face on a cube (a square) measures
a 2
, as shown in Figure14-20.
»
Figure14-20 also shows that the diagonal of a cube itself measures
a 3
.
FIGURE14-19:
Surface area
of a rectan-
gular solid.
© John Wiley & Sons, Inc.
FIGURE14-18:
Volume of a
rectangular
solid.
© John Wiley & Sons, Inc.
CHAPTER 14 Getting the Angle on Geometry: Planes and Solids 217
Sipping from soda cans and other cylinders
A cylinder is a circle that grows straight up into the third dimension to become the shape of a can
of soda. The bases of a cylinder are two congruent circles on dierent planes. The cylinders you
see on the GMAT are right circular cylinders, which means that the line segments that connect
the two bases are perpendicular to the bases. Figure14-21 shows a right circular cylinder. All the
corresponding points on the circles are joined together by line segments. The line segment con-
necting the center of one circle to the center of the opposite circle is called the axis.
A right circular cylinder has the same measurements as a circle. That is, a right circular cylinder
has a radius, diameter, and circumference. In addition, a cylinder has a third dimension: its
height, or altitude.
To get the volume of a right circular cylinder, rst take the area of the base (a circle), which
is
r
2
, and multiply by the height (h) of the cylinder:
V rh
2
.
If you want to nd the total surface area of a right circular cylinder, you have to add the areas of
all the surfaces. Imagine taking a soda can, cutting o the top and bottom sections, and then slic-
ing it down one side. You then spread out the various parts of the can. If you measure each one of
these sections, you get the total surface area.
When you measure the surface area of a right circular cylinder, don’t forget to include the top and
bottom of the can in your calculation.
Here’s the formula for the total surface area (SA) of a right circular cylinder— the diameter (d) is
2 times the radius (r):
SA dh r2
2
FIGURE14-20:
A cube.
© John Wiley & Sons, Inc.
FIGURE14-21:
A right
circular
cylinder.
© John Wiley & Sons, Inc.
218 PART 4 Conquering the Quantitative Section
Here’s a sample question that shows how the GMAT may try to nd out how much you know
about three-dimensional shapes.
The preceding gure shows a cube with an edge that measures 10 inches. If points B and D are
midpoints of two of the edges, what is the measure in inches of the straight line that joins point
A to point C?
(A)
55
(B)
10 2
(C)
10 3
(D)
205
(E) 125
Answering this question is easy when you know the formula for the diagonal of a cube. Each edge
of the cube measures 10 inches, and the diagonal of a cube is the edge length times
3
. So line AC
measures
10 3
inches, which is Choice (C).
Make sure you apply the correct formula. If you pick Choice (B), you’re using the formula for the
diagonal of a square.
CHAPTER15 Keeping in Step: Coordinate Geometry 219
IN THIS CHAPTER
» Taking o on the coordinate plane
» Using formulas to nd slope, graph
lines, and determine midpoints
and distances
» Evaluating functions
Keeping in Step: Coordinate
Geometry
C
oordinate geometry involves working with points on a graph that’s ocially known
as the Cartesian coordinate plane. This perfectly at surface has a system that allows
you to identify the position of points by using pairs of numbers. In this chapter, you
gure out how equations and numbers relate to geometric forms and shapes, such as a straight
lineor a parabola, and review the formulas you need to know to y high on questions about the
coordinate plane.
You can expect to encounter coordinate geometry in roughly 10 percent of the math problems on
the GMAT.So if you’re not particularly savvy about coordinate geometry, it won’t signicantly
aect your GMAT math score.
Taking Flight: The Coordinate Plane
The coordinate plane doesn’t have wings, but it does have points that spread out innitely. You
may not have encountered the coordinate plane in a while (it isn’t something most people deal
with in everyday life), so take just a minute to refresh your memory about a few relevant terms
that may pop up on the GMAT.Although you won’t be asked to dene the terms in the following
sections, knowing what they mean is absolutely essential to answering GMAT math questions.
Line dancing: Understanding coordinate
geometry
Before you get too engrossed in the study of coordinate geometry, ground yourself with an under-
standing of these essential terms:
»
Coordinate plane: The coordinate plane is a perfectly at surface where points can be
identied by their positions, using ordered pairs of numbers. These pairs of numbers
Chapter15
220 PART 4 Conquering the Quantitative Section
represent the points’ distances from an origin on perpendicular axes. The coordinate of any
particular point is the set of numbers that identies the location of the point, such as (3, 4)
or (x, y).
»
x-axis: The x-axis is the horizontal axis (number line) on a coordinate plane. The values start at
the origin, which has a value of 0. Numbers increase in value to the right of the origin and
decrease in value to the left. The x value of a point’s coordinate is listed rst in its ordered pair.
»
y-axis: The y-axis is the vertical axis (number line) on a coordinate plane. Its values start at the
origin, which has a value of 0. Numbers increase in value going up from the origin and decrease
in value going down. The y value of a point’s coordinate is listed second in its ordered pair.
»
Origin: The origin is the point (0, 0) on the coordinate plane. It’s where the x- and y-axes
intersect.
»
Ordered pair: Also known as a coordinate pair, this duo is the set of two values that expresses
the distance a point lies from the origin. The horizontal (x) coordinate is always listed rst, and
the vertical (y) coordinate is listed second.
»
x-intercept: The value of x where a line, curve, or some other function crosses the x-axis. The
value of y is 0 at the x-intercept. The x-intercept is often the solution or root of an equation.
»
y-intercept: The value of y where a line, curve, or some other function crosses the y-axis. The
value of x is 0 at the y-intercept.
»
Slope: Slope measures how steep a line is and is commonly referred to as the rise over the run.
What’s the point? Finding the coordinates
You can identify any point on the coordinate plane by its coordinates, which designate the point’s
location along the x- and y-axes. For example, the ordered pair (2, 3) has a coordinate point
located two units to the right of the origin along the horizontal (x) number line and three units up
on the vertical (y) number line. In Figure15-1, point A is at (2, 3). The x-coordinate appears rst,
and the y-coordinate shows up second. Pretty simple so far, huh?
On all fours: Identifying quadrants
The intersection of the x- and y-axes forms four quadrants on the coordinate plane, which just so
happen to be named Quadrants I, II, III, and IV (see Figure15-1). Here’s what you can assume
about points based on the quadrants they’re in:
»
All points in Quadrant I have a positive x value and a positive y value.
»
All points in Quadrant II have a negative x value and a positive y value.
»
All points in Quadrant III have a negative x value and a negative y value.
»
All points in Quadrant IV have a positive x value and a negative y value.
»
All points along the x-axis have a y value of 0.
»
All points along the y-axis have an x value of 0.
Quadrant I starts to the right of the y-axis and above the x-axis. It’s the upper-right portion of
the coordinate plane. As shown in Figure15-1, the other quadrants move counterclockwise around
the origin. Figure15-1 also shows the location of coordinate points A, B, C, and D:
CHAPTER 15 Keeping in Step: Coordinate Geometry 221
»
Point A is in Quadrant I and has coordinates (2, 3).
»
Point B is in Quadrant II and has coordinates (–1, 4).
»
Point C is in Quadrant III and has coordinates (–5, –2).
»
Point D is in Quadrant IV and has coordinates (7, –6).
The GMAT won’t ask you to pick your favorite quadrant, but you may be asked to identify which
quadrant a particular point belongs in.
Slip-Sliding Away: Slope and Linear Equations
One of the handiest things about the coordinate plane is that it graphs the locations of lines and
linear equations. In fact, questions that expect you to know how to graph lines and equations are
some of the most common GMAT coordinate geometry questions. You should know the formulas
for nding the slope and the slope-intercept equation and for determining the midpoint and the
distance between two points on the plane. Lucky for you, we discuss all those formulas in the fol-
lowing sections.
Taking a peak: Dening the slope of a line
If a line isn’t parallel to one of the coordinate axes, it either rises or falls from the left-hand side
of the coordinate plane to the right-hand side. The measure of the steepness of the line’s rising
or falling is its slope. In the following sections, we explain how to nd the slope of a line and
explore the dierent types of slopes on a coordinate plane.
The formula for slope
You can think of the slope as the value of the rise over the value of the run. In more mathematical
terms, the slope formula looks like this:
slope
m()
Change in Vertical Coordinates
Change in Horizonta
ll Coordinates
yy
xx
12
12
FIGURE15-1:
Points
on the
coordinate
plane.
© John Wiley & Sons, Inc.
222 PART 4 Conquering the Quantitative Section
The x and y values in the equation stand for the coordinates of two points on the line. The formula
is just the ratio of the vertical distance between two points and the horizontal distance between
those same two points. You subtract the y-coordinate of one point from the y-coordinate of
theother point to get the numerator. Then you subtract the x-coordinate of one point from the
x-coordinate of the other point to get the denominator.
When you subtract the values, remember to subtract the x and y values of the rst point from the
respective x and y values of the second point. Don’t fall for the trap of subtracting
xx
21
to get
your change in the run but then subtracting
y y
12
for your change in the rise. That kind of back-
ward math will mess up your calculations, and you’ll soon be sliding down a slippery slope.
The graph in Figure15-2 shows how important it is to perform these operations in the right
order.
Figure15-2 shows coordinate point (0, 2) as
xy
11
,
, and the coordinate point (4, 0) as
xy
22
,
.
You may be tempted to subtract the 0in each coordinate point from the corresponding greater
number in the other coordinate point, but doing that switches the order of how you subtract the
x and y values in the two coordinate points.
For the slope formula to work, you calculate 0– 2 for your
y y
21
operation (which gives you –2),
and then you take 4– 0 for your
xx
21
(which gives you 4). The resulting ratio, or fraction, is
2
4
,
or
1
2
. This gives you a slope of
1
2
.
Types of slope
The line in Figure15-2 falls from left to right. This nice ski-slope image is your visual clue that
the line has a negative slope. Figure15-3 shows how you can quickly eyeball a line to get a good
idea of what kind of slope a line has.
In Figure15-3, line m has a negative slope; line n has a positive slope; a line on the horizontal
x-axis has a slope of 0; and a line on the vertical y-axis has an undened slope.
»
A line with a negative slope falls from left to right (its left side is higher than its right), and its
slope is less than 0.
»
A line with a positive slope rises from left to right (its right side is higher than its left), and its
slope is greater than 0.
FIGURE15-2:
Finding
slope.
© John Wiley & Sons, Inc.
CHAPTER 15 Keeping in Step: Coordinate Geometry 223
»
A horizontal line has a slope of 0; it neither rises nor falls and is parallel to the x-axis.
»
The slope of a vertical line is undened because you don’t know whether it’s rising or falling; it
has no slope and is parallel to the y-axis.
Using the slope-intercept form to graph lines
The characteristics of a line can be conveyed through a mathematical formula. The equation of a
line (also known as the slope-intercept form) generally shows y as a function of x, like this:
y mx b
In the slope-intercept form, the coecient m is a constant that indicates the slope of the line, and
the constant b is the y-intercept (that is, the point where the line crosses the y-axis). The equa-
tion of the line in Figure15-2 is
y
x
1
2
2
, because the slope is
1
2
and the y-intercept is 2. The
equation
y 2
indicates a horizontal line that intersects the y-axis at point (0, 2). The equation
x 3
indicates a vertical line that intersects the x-axis at point (3, 0). A line with the formula
y x41
has a slope of 4 (which is a rise of 4 and run of 1) and a y-intercept of 1. The line is
graphed in Figure15-4.
The GMAT may give you an equation of a line and ask you to choose the graph that correctly grids
it. You can gure out how the line should look when it’s graphed by starting with the value of the
y-intercept, marking points that t the value of the slope, and then connecting these points with
a line.
Whenever you get an equation for a line that doesn’t neatly t into the slope-intercept format, go
ahead and play with the equation a little bit (sounds fun, doesn’t it?) so it meets the
y mx b
format that you know and love. For instance, to put the equation
1
3
3
yx
in slope-intercept
form, you simply manipulate both sides of the equation and solve for y, like this:
1
3
3
1
3
3
33
39
yx
yx
yx
yx
()
FIGURE15-3:
Types of
slope.
© John Wiley & Sons, Inc.
224 PART 4 Conquering the Quantitative Section
The new equation gives you the slope of the line, 3, as well as the y-intercept, 9. Pretty handy!
Here’s a sample question to give you a taste of how the slope-intercept form may be tested on
the GMAT.
What is the equation of a line with a slope
3
4
and a y-intercept of 8?
(A)
4 332xy
(B)
3416xy
(C)
3432xy
(D)
3416xy
(E)
3432xy
In the slope-intercept form,
y mx b
, m is the slope, and b is the y-intercept. Plug the values
the problem gives you into the equation:
y
x
3
4
8
This isn’t an answer choice, but all options have the same format of
axbyc
. So you need to
convert your equation to that format. Move the terms around by multiplying all terms on both
sides by 4 and adding 3x to both sides, like this:
yx
yx
yx
3
4
8
43
32
4 332
Choice (E) is the correct answer.
Graphing a linear inequality is almost exactly the same as graphing the equation of a line, except
a linear inequality covers a lot more ground on the coordinate plane. While the graph of an equa-
tion for a line simply shows the actual line on the coordinate plane, the graph of a linear inequal-
ity shows everything either above or below the line on the plane. The graph appears as a shaded
area to one side of the line. Figure15-5 shows the graphs of several inequalities.
FIGURE15-4:
The graph of
y = 4x + 1.
© John Wiley & Sons, Inc.
CHAPTER 15 Keeping in Step: Coordinate Geometry 225
Meeting in the middle
If the GMAT asks you for the midpoint coordinates of a line segment on the coordinate plane, you
simply apply the midpoint formula:
M
xx
yy
12
12
22
,
M stands for midpoint and the x and y variables are the x and y coordinates of the line’s two end-
points. So, to gure out the midpoint of a line segment that ends at points A (2, 3) and B (–1, 4),
use the formula:
M
M
M
21
2
34
2
1
2
7
2
1
2
3
1
2
,
,
,
To help you remember the midpoint formula, think of it as the average of the two x coordinates
and the average of the two y coordinates of the line segment’s endpoints.
FIGURE15-5:
Graphing
lines and
inequalities.
© John Wiley & Sons, Inc.
226 PART 4 Conquering the Quantitative Section
Going the distance
Some of the questions on the GMAT may ask you to calculate the distance between two points on
a line. You can solve these problems with coordinate geometry.
To answer these questions, use the distance formula. Assume you have two points, A
xy
11
,
and
B
xy
22
,
, on a line. The formula to nd the distance between A and B is this:
AB
xx
yy
21
2
21
2
Look at the graph in Figure15-6 to see how the distance formula actually works.
Notice that Point A has coordinates (2, 1) and Point B has coordinates (6, 4). To nd the distance
between these two points, you plug these numbers into the distance formula:
AB
xx
yy
AB
AB
AB
AB
21
2
21
2
22
22
62 41
43
16 9
225
5AB
If you’re thinking this formula looks familiar, you’re absolutely right. It’s another use for the
good old Pythagorean theorem:
c ab
22
. (If this theorem is only vaguely familiar to you, check
out Chapter14.) Connecting points A and B to a third point, C, as shown in Figure15-5, gives
youaright triangle, which in this case happens to be your tried-and-true 3:4:5 right triangle.
Here’s a sample problem that asks you to nd the distance between two points.
What is the distance in units of a line segment that connects the origin to the coordinate point
(–2, –3)?
(A)
5
(B)
13
(C) 5
(D) 8.94
(E) 13.42
FIGURE15-6:
Finding the
distance
between
two points.
© John Wiley & Sons, Inc.
CHAPTER 15 Keeping in Step: Coordinate Geometry 227
Use the distance formula to gure out the distance between the coordinates of the origin (0, 0)
and the endpoint (–2, –3):
AB
xx
yy
AB
AB
AB
21
2
21
2
22
22
20 30
23
49
AAB 13
Choice (B) is the answer. If you chose Choice (C), you simply took the coordinates for the end-
point, (–2, –3), and added them together to get distance, which, of course, isn’t the proper
method. Choice (A) results from failing to square the dierences of the coordinates. You can
guess that Choices (D) and (E) are probably incorrect because uncovering their values requires
using a calculator, which you won’t have available on the GMAT quantitative section.
Notice that order doesn’t matter when you subtract the x- and y-coordinate points from each
other— you end up squaring their dierence, so your answer will always be a positive number.
Keep in mind that, in the end, the distance between two points is always a positive number. If you
ever see zero or a negative number as an answer choice for a distance question, just let your
mouse scoot on by.
Considering other shapes on the
coordinate plane
Occasionally, the GMAT may ask you coordinate geometry questions that deal with shapes other
than straight lines.
»
Circles: The equation of a circle is
xh yk r
22
2
, where the center of the circle is
point (h, k) and r is the circle’s radius. If the origin is the center of the circle, the equation
would be
xyr
222
.
»
Parabolas: When you graph a quadratic equation, it appears as a parabola, a curve shape that
opens either upward or downward. Two important properties of parabolas are
•
The axis of symmetry: This is the vertical line that bisects the parabola so that each side is a
mirror image of the other.
•
The vertex: This is the rounded end of the parabola, which is the lowest point on a curve
that opens upward and the highest point on a curve that opens downward. It’s where the
parabola crosses the axis of symmetry.
The equation for a parabola is
y
ax
hk
2
, where the coordinate point (h, k) is the vertex.
The vertical line x = h is the axis of symmetry. If a is a positive number, the parabola opens
upward. If a is negative, it opens downward. Figure15-7 shows the graph of
y x
2
. The values
for h and k are 0, so the vertex is at the origin. The parabola opens upward because a is 1, a
positive number.
228 PART 4 Conquering the Quantitative Section
Here’s a sample question that requires to you apply the parabola formula.
What is the vertex of the graph of the equation
y x23
4
2
?
(A) (–3, –4)
(B) (3, 4)
(C) (3, –4)
(D) (–3, 4)
(E) (–6, –4)
Remember the equation of a parabola:
y ax
hk
2
. The vertex of the parabola is (h, k). The h
value in the equation is 3, and the k value is –4. So the vertex of the graph of the equation in the
question is (3, –4). The correct answer is Choice (C).
Choice (D) is a trap answer. Note that the value of h is 3 and not –3. The only way that the value
of h could be –3 is if the original equation were
y
x
23
4
2
. Then you’d have to switch
the sign to put the equation into the correct form for the equation of a parabola.
Fully Functioning: Graphing Functions
Coordinate geometry and functions are connected. You can actually evaluate functions on the
coordinate plane. By looking at a graph of a function, you can tell something about the function
and its domain and range. The GMAT may give you a graph of a function and ask you to determine
whether a statement about the function is true or false. In the following sections, we give you the
info you need to know to get these questions right.
When you graph a function f(x) on the coordinate plane, the x value of the function (the input, or
the domain, of the function) goes along the horizontal (x) axis, and the f(x) value of the function
goes along the vertical (y) axis. Anytime you see a coordinate pair that represents a function, for
example (x, y), the x value is the domain, or input, of the function and the y value is the output, or
range, of the function. (For more info on functions, see Chapter13.)
Passing the vertical line test
A function is a distinct relationship between the x (input) value and the y or f(x) (output) value.
For every x value, there’s a distinct y value, and only one y value, that corresponds to the x value.
FIGURE15-7:
A parabola
with its
vertex on
the origin.
© John Wiley & Sons, Inc.
CHAPTER 15 Keeping in Step: Coordinate Geometry 229
The vertical line test is one way to look at a graph and tell whether it’s a graph of a function. This
test states that no vertical line intersects the graph of a function at more than one point.
For example, the graphs in Figure15-8 show two straight lines that pass the vertical line test and,
therefore, represent functions.
The two lines in Figure15-8 go on innitely in both directions. Any vertical line you draw on the
graph intersects the graphed line at only one point. For every x value along the line in each of
these graphs, a separate and distinct y value corresponds to it. These lines pass the vertical line
test, which means they represent functions.
You probably already know that most lines are functions— after all, the equation of a line is
y mx b
. Now you can see it for yourself graphically. The only straight line that isn’t a graph of
a function is a vertical line. A bazillion y values exist along a vertical line, but the line has only one
x value.
Not all lines are straight. Sometimes you see graphs of curved lines. Take a look at the two graphs
in Figure15-9 and determine which of them graphs a function.
The curves in Figure15-9 are parabolas, a shape we discuss in more detail in the upcoming sec-
tion about graphing domain and range. The curve in the left graph opens downward, so it goes on
innitely downward and outward. For every x value on that curve, there’s a separate and distinct
y value. This curve passes the vertical line test and, therefore, graphs a function. The curve in the
right graph is almost like the rst one, except that it opens sideways. One vertical line can cross
the path of this curve in more than one place. Therefore, this curve isn’t the graph of a function.
FIGURE15-8:
Straight
lines that
pass the
vertical
line test.
© John Wiley & Sons, Inc.
FIGURE15-9:
Graphs of
curved lines
(parabolas).
© John Wiley & Sons, Inc.
230 PART 4 Conquering the Quantitative Section
Questions that ask you to recognize the graph of a function appear rarely on the GMAT, but if you
see one, you’ll know what to do.
Which of the following graphs is not a graph of a function?
This question is easy when you’re familiar with the vertical line test. Choice (E) has to be the cor-
rect answer because it’s a curve that sort of doubles back from right to left. A vertical line can
intersect that curve at more than one point. The other graphs in this question show curves, lines,
or some other shape that a vertical line wouldn’t pass through at more than one point. All the
graphs except Choice (E) pass the test and are graphs of functions.
Feeling at home with domain and range
The GMAT expects you to be able to look at a graph of a function and have a pretty good idea of
what the domain and the range of that particular function are. Figures15-10,15-11, and15-12 are
examples of what some of these graphs may look like.
FIGURE15-10:
Domain
and range
demonstrated
by a parabola.
© John Wiley & Sons, Inc.
CHAPTER 15 Keeping in Step: Coordinate Geometry 231
Figure15-10 shows you a parabola. Its vertex is the coordinate point (0, 2). The graph extends
outward innitely from side to side, so this function contains all possible values of x, which means
its domain is all real numbers. The graph also extends downward innitely, but because the y
value in this function is limited on the upward side and doesn’t extend above the point (0, 2), its
range is
yy: 2
.
In Figure 15-11, you see a straight line that goes on forever from left to right. This line also
extends innitely upward on the left side and innitely downward on the right side. The domain
and range of this linear function are also all real numbers. There’s no articial limit to the x and
y values in this graph.
In Figure15-12, the horizontal line extends innitely from right to left, but it has only one value
on the y-axis. Its y value is limited to –3, so the equation for this line is y = –3, and the range is
limited to simply
yy: 3
. Because the line goes on forever from left to right, it includes every
possible x value, which means the domain of this linear function is all real numbers.
That’s really all there is to it. See how easy determining domain can be with the following
question.
FIGURE15-11:
Domain
and range
demonstrated
by a sloping
straight line.
© John Wiley & Sons, Inc.
FIGURE15-12:
Domain
and range
demonstrated
by a
horizontal
line.
© John Wiley & Sons, Inc.
232 PART 4 Conquering the Quantitative Section
Which of the following answers could be the domain of the function of the gure?
(A)
xx: 0
(B)
xx: 3
(C)
xx: 0
(D)
xx: 3
(E)
xx x: 0
This question asks for the domain, not the range, so don’t let the fact that the upper limit of
they value is just shy of 3 distract you from looking for all the possible x values that make up
the domain. You should toss out any answer choice that refers to the value 3, so get rid of
Choices (B) and (D) right away.
The empty circle point (0, 3) means that you don’t count that point in your answer. So
Choice(C) is exactly the opposite of what you’re looking for. Also, Choice (C) limits your domain
to only one value: 0. Because the value of 0 is actually excluded from the function, Choice (C)
simply can’t be right. The way Choice (E) is formatted doesn’t make sense at all. Set your sights
on Choice (A) as the answer of the hour. The domain, or x value, isn’t equal to 0.
CHAPTER16 Manipulating Numbers: Statistics and Sets 233
IN THIS CHAPTER
» Getting a grip on group problems
» Excelling with sets and Venn
diagrams
» Arranging groups with
permutations and combinations
» Managing means, modes, and
medians
» Solving standard deviations
» Prospering on probability
problems
Manipulating Numbers:
Statistics and Sets
F
rom the time you mastered the ability to tie your shoes, you had to gure out how to work
and play in groups. The GMAT tests what you know about groups of numbers, or sets. These
question types are usually pretty easy, so you could probably work out the answers to most
of the GMAT set questions given enough time. But, of course, you don’t have all the time in the
world on the GMAT, so in this chapter, we provide some shortcuts to help you answer set ques-
tions quickly.
You may nd the statistics and probability questions on the GMAT a little more challenging. But
don’t worry: In this chapter, we go over the concepts you need to know, which include determin-
ing probability, statistical averages, and variations from the average. The statistics questions
you’ll encounter on the GMAT aren’t particularly complex, but giving this subject your full atten-
tion will pay o.
Joining a Clique: Groups
Group problems regard populations of persons or objects and the way these populations are
grouped together into categories. The questions generally ask you to either nd the total of a
series of groups or determine how many people or objects make up one of the subgroups.
You can nd the answer to most group problems by using your counting skills, but counting is
time-consuming, and you want to work smarter, not harder, to solve these questions. Solving
group problems comes down to applying simple arithmetic in a handy formula and nothing else.
Chapter16
234 PART 4 Conquering the Quantitative Section
Here’s the formula for solving group problems:
GroupGroup Both Groups NeitherGroup Grand Total12
So if you’re told that out of 110 students, 47 are enrolled in a cooking class, 56 take a welding
course, and 33 take both cooking and welding, you can use the formula to nd out how many
students take neither cooking nor welding. Let Group 1 be the cooks and Group 2 the welders. The
variable is the group that doesn’t take either the cooking or welding class. Plug the known values
into the formula and set up an equation to solve:
GroupGroup Both Groups NeitherGroup Grand Total
x
12
47 56 33 110
70 110
40
x
x
Of the 110 students, 40 take neither the cooking class nor the welding class. Here’s an example of
how group problems may appear on the GMAT.
One-third of all U.S. taxpayers may deduct charitable contributions on their federal income tax
returns. Forty percent of all taxpayers may deduct state income tax payments from their federal
returns. If 55 percent of all taxpayers may not deduct either charitable contributions or state
income tax, what portion of all taxpayers may claim both types of deductions?
(A)
3
20
(B)
9
50
(C)
1
5
(D)
7
25
(E)
17
60
Use the formula to determine the correct percentage of taxpayers who may claim both deductions.
Group 1 can be the
1
3
who claim charitable deductions, and Group 2 can be those who deduct state
income tax payments. The unknown is those who make up both groups.
Before you begin calculating, check the answer choices. Every answer appears as a fraction.
Because your nal answer will be in the form of a fraction, change references to percentages into
fractions. Converting percentages to fractions is easy; put the value of the percentage over a
denominator of 100.
So 40 percent is the same as
40
100
, which reduces to
2
5
. Fifty-ve percent is the same as
55
100
, which
equals
11
20
. Plug in the values and solve the formula:
GroupGroup Both Groups NeitherGroup Grand Total
x
12
1
3
2
5
11
220
1
CHAPTER 16 Manipulating Numbers: Statistics and Sets 235
To add and subtract fractions, you have to nd a common denominator for all fractions and then
convert the fractions so all have the same denominator (see Chapter12 for more about performing
operations with fractions). The common denominator for this problem is 60.
20
60
24
60
33
60
60
60
77
60
60
60
17
60
x
x
x
The correct answer is Choice (E).
Compute accurately. Another reason for working with fractions instead of percentages in this
problem is that it helps you perform accurate calculations. You may be fooled into thinking that
the one-third of the taxpayers who can claim charitable contributions equals 33 percent of tax-
payers. Although
1
3
is very close to 33 percent, it isn’t exactly that amount. If you used 33 percent
instead of one-third, you may have calculated the group as
0 33 04 0551... x
and incorrectly
chosen Choice (D). If you convert
1
3
to 33 percent, you’re sacricing accuracy to save time.
Setting Up Sets
Groups are related to sets. A set is a collection of objects, numbers, or values. The objects in a set
are the elements, or members, of the set. An empty set, or null set, means that nothing is in that set.
GMAT questions about sets are usually pretty simple to answer as long as you know a little ter-
minology and how to read a Venn diagram. The following sections explore all you need to know
about sets.
Set terminology
The terms union, intersection, disjoint sets, and subset describe how two or more sets relate to one
another through the elements they contain.
»
A union of two sets contains the set of all elements of both sets. For example, the union of
sets A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and B = {2, 4, 6, 8, 10} is S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
»
An intersection of two sets is the set of the elements that are common to both sets. For
example, the intersection of sets A = {0, 1, 2, 3, 5, 6, 7, 8, 9} and B = {2, 4, 6, 8, 10} is S = {2, 6, 8}.
»
Disjoint sets are two or more sets with no elements in common. For example, set A and set
B are disjoint sets if set A = {0, 2, 6, 8} and set B = {1, 3, 5, 7}.
»
A subset is a set whose elements appear in another, larger set. If all the elements of set B =
{2, 3, 5, 7} also appear in set A = {0, 1, 2, 3, 5, 6, 7, 8, 9}, you’d say that set B is a subset of set A.
Getting a visual: Venn diagrams
The GMAT often illustrates the concept of sets with Venn diagrams, such as those presented in
Figure16-1. Venn diagrams provide visual representations of union, intersection, disjoint sets,
and subsets. You can draw Venn diagrams to help you answer GMAT questions about sets.
236 PART 4 Conquering the Quantitative Section
GMAT quantitative reasoning questions regarding sets are usually pretty straightforward. Here’s
an example.
Given the Venn diagram, what are the number of elements in the intersection of sets A and B?
(A) 0
(B) 3
(C) 4
(D) 16
(E) 53
The number of elements in the intersection of sets A and B is the number of elements that are
common to both sets. The portion of the diagram that represents the intersection is where the A
circle and the B circle overlap. When you add the values in this intersection, you nd that the
number of elements that are common to both set A and set B is 4. The correct answer is Choice(C).
If you chose Choice (B), you ignored the one element that’s common to all three sets. You must
include that one element, however, because it’s a common element of sets A and B. Choice (E)
conveys the number of elements in the union of sets A and B rather than their intersection.
FIGURE16-1:
Venn
diagrams
showing the
union and
intersection
of sets.
© John Wiley & Sons, Inc.
CHAPTER 16 Manipulating Numbers: Statistics and Sets 237
Making Arrangements: Permutations and
Combinations
The GMAT may test you on the arrangement of groups and sets, so you’re likely to see some per-
mutation and combination problems. When you calculate permutations, you gure out the number
of ways the elements of a set can be arranged in specic orders. Determining combinations is
similar to nding permutations, except that the order of the arrangements doesn’t matter. In the
following sections, we provide explanations and examples of each type of problem.
Positioning with permutations
Permutations problems ask you to determine how many arrangements of numbers are possible
given a specic set of numbers and a particular order for the arrangements. For example, guring
out the number of possible seven-digit telephone numbers you can create is a permutation
problem. And the answer is huge (
10
7
) because you have 10 possible values (the integers between0
and 9) to ll each of the seven places.
Order matters when you set up permutations. Even though two dierent phone numbers may
have the same combination of numbers, such as 345-7872 and 543-7728, the numbers ring two
dierent phones because you input them in a dierent order.
Consider the elements of S = {a, b, c}. You can arrange these three elements in six dierent ways:
a b c
a c b
b a c
b c a
c a b
c b a
Even though each group contains the same elements, these groupings are completely dierent
permutations because they convey dierent orderings of the three elements. Writing out the
number of possible orderings of a set of three letters isn’t too dicult, but what if you had to
gure out the number of orderings for a set of 11 numbers? That problem would take more time
than anyone would care to spend and certainly more time than you have to nish the GMAT.Luck-
ily, you can rely on factorials to gure out permutations.
A factorial is the product of all natural numbers in the set of numbers from 1 through a particular
number (n), which is the number of the factorial. The number of permutations of n objects is
expressed as n!. The ! symbol indicates a factorial, and you read the expression as “n factorial.”
So5! is a way of expressing
54321
.
Instead of writing the possible permutations for the set of three letters {a, b, c}, use a factorial.
Three dierent elements (the letters in the set) arranged in as many dierent orders as possible
look like this: 3!, which is equal to
321
, which is equal to 6. So
36!
. The three elements have
six permutations.
Suppose you have more than three elements. Maybe a photographer wants to know how many
dierent ways she can arrange ve people in a single row for a wedding photo. The number of
possible arrangements of the ve-person wedding party is 5! or
554321120!
.
238 PART 4 Conquering the Quantitative Section
The factorial of 0 is written as 0!, which always equals 1.
As you can see, more possible arrangements exist as the number of objects in the arrangement
increases. That’s the information you need to know to answer basic permutation questions, such
as the following one. Give it a shot!
Alice received a bracelet with four distinct removable charms. How many dierent ways can she
arrange the four charms on her new bracelet?
(A) 4
(B) 8
(C) 24
(D) 100
(E) 40,320
Because the bracelet has four charms, the number of arrangements or permutations is 4!:
4 321
.
Then just multiply the numbers to get the number of possible arrangements (the order you
multiply them in doesn’t matter):
4 312
and
12 224
. Because
241 24
, the correct answer
is Choice (C).
You can eliminate Choices (A) and (B) because they’re too small. You know that more than four
arrangements must exist, because you have four charms. Choice (B) is
4 2
, which isn’t much
better. In permutations, you know the number gets pretty large in a hurry, but not as large as
Choice (E), which is 8!.
Permutations get a little more challenging when you have a xed number of objects, n, to ll a
limited number of places, r, and you care about the order the objects are arranged in.
For example, consider the predicament of the big-league baseball coach of a 20-member baseball
team who needs to determine the number of dierent batting orders that these 20 ball players can
ll in a 9-slot batting lineup. The coach could work this permutation out by writing all the factors
from 20 back 9 places (because 20 players can ll only 9 slots in the batting order), like this:
201918171615141312 x
But this time-consuming process isn’t practical in the middle of a game. Luckily, the coach can
rely on a permutation formula.
The number of permutations of n things taken r at a time is stated as
nr
P
. (To help you remember
the formula, think of a certain public radio station that has these call letters.) The permutation
formula for n objects taken r at a time looks like this:
nr
P
n
nr
!
!
Apply the formula to gure out the possible number of batting orders:
nr
nr
nr
P
n
nr
P
P
!
!
!
!
!
!
20
20 9
20
11
CHAPTER 16 Manipulating Numbers: Statistics and Sets 239
The GMAT doesn’t allow you to use calculators, so it won’t expect you to calculate the permu-
tation beyond this point. Here’s an example of how complex permutations may appear on
theGMAT.
A lawn care company has ve employees that it schedules on a given day to work the lawns of
any ten possible homes. How many dierent ways can the company assign the ve employees
to the ten homes if each employee provides lawn care service for just one home?
(A) 50
(B)
2
1
!
!
(C) 120
(D)
10
5
!
!
(E) 10!
This question may seem counterintuitive to the formula, which calculates n number of things
taken r at a time to get the number of permutations. This problem appears to be taking a smaller
number of things, r (the number of employees), and nding out how many times they can be
spread around a greater number of places. That’s what makes this question a little tricky.
This problem may look backward, but it really follows the same formula. Rather than thinking of
how to spread ve workers over ten houses, think of how many ways you can arrange the ten
houses over the more limited number of workers and apply the formula:
nr
nr
nr
P
n
nr
P
P
!
!
!
!
!
!
10
10 5
10
5
The correct answer is Choice (D). With a calculator, you can gure out that 30,240 ways exist to
assign employees. If you chose Choice (A), you simply multiplied the number of workers times the
number of houses. But that’s not the correct calculation. Choice (C) is what you get if you calcu-
lated 5!, which isn’t the complete answer. Likewise, Choice (E) is incomplete.
Don’t let Choice (B) trip you up. You can’t simplify factorials like you can common fractions:
10
5
2
1
!
!
!
!
If this problem was dicult for you, take heart: You won’t see too many of these kinds of ques-
tions on the GMAT.
Coming together: Combinations
Combinations are a lot like permutations, only easier. You form a combination by extracting a
certain number of persons or things from a larger total sample of persons and things. Unlike
permutations, the order doesn’t matter with combinations, so combinations result in fewer pos-
sibilities than permutations.
A combination problem may ask you to nd how many dierent teams, committees, or other
types of groups can be formed from a set number of persons. For example, if you’re asked to
select as many teams as you can from a set number of people and the order of the team members
doesn’t matter, you’re nding the total number of combinations of dierent teams.
240 PART 4 Conquering the Quantitative Section
Consider how many three-member committees you can form with Tom, Dick, and Harry. Tom,
Dick, and Harry don’t line up in any particular order while they’re convening, so the way you list
them doesn’t matter. A committee composed of Tom, Dick, and Harry is the same as a committee
composed of Tom, Harry, and Dick or one composed of Dick, Tom, and Harry. So only one possible
combination exists of this three-member committee. If Tom, Dick, and Harry were asked to par-
ticipate in a lineup, you’d have a permutation and six dierent possible arrangements, but
because order doesn’t matter when you’re forming the committee, you have only one possible
combination.
You can apply a formula to gure out the number of combinations. The formula is the number of
ways to choose r objects from a group of n objects when the order of the objects doesn’t matter,
and it looks like this:
nr
C
n
rnr
!
!!
You can see right away that this formula is dierent from the one for permutations. Because you
have a larger number in the denominator than you’d have with a permutation, the nal number
will be smaller.
Suppose a pollster randomly approaches three dierent people from a group of ve mall walkers.
To gure out how many possible combinations of three dierent people the pollster can annoy,
use the combination formula:
nr
nr
C
n
rnr
C
!
!!
!
!!
5
353
The factorial of 5! is 120 (
54321
), and the factorial of 3! is 6 (
321
). So here’s the resulting
equation:
nr
C
120
65
3!
Subtract the values in the parentheses to get 2!. The value of 2! is 2 (because
2 12
):
nr
nr
nr
nr
C
C
C
C
120
65 3
120
62 1
120
12
10
!
()
Therefore, from the ve mall walkers, the pollster can create ten dierent combinations of three
people to poll.
Because you can’t use a calculator, GMAT combination problems won’t get too complex. The test-
makers won’t make you perform overly complex calculations on your low-tech noteboard.
Here’s an example of what you can expect from GMAT combination problems.
CHAPTER 16 Manipulating Numbers: Statistics and Sets 241
Some fourth-graders are choosing foursquare teams at recess. What is the total possible
number of combinations of four-person teams that can be chosen from a group of six children?
(A) 6
(B) 15
(C) 120
(D) 360
(E) 98,280
Apply the formula for combinations and see what happens:
nr
nr
nr
nr
C
n
rnr
C
C
C
!
!!
!
!!
!
!!
(
6
464
6
42
6543
21
44321
21
65
21
30
2
15
)
nr
nr
nr
C
C
C
After you perform the calculations, you nd that the correct answer is Choice (B).
If you went for Choice (D), you calculated a permutation instead of a combination.
Meeting in the Middle: Mean,
Median, and Mode
At least a few GMAT math problems will require you to evaluate sets of numbers. To evaluate data
correctly, you need to know the central tendency of numbers and the dispersion of their values.
A measurement of central tendency is a value that’s typical, or representative, of a group of
numbers or other information. Common tools for describing a central tendency include average
(arithmetic mean), median, mode, and weighted mean.
»
Average (also referred to as arithmetic mean) is the most commonly tested tendency
value. To nd the average (arithmetic mean) of a set of numbers, add the numbers and divide
by the quantity of numbers in the group:
Averag
e
SumofAll Numbersinthe Set
Number of Membersinthe Set
You can plug known values into this formula to solve for the other values. For example, if the
GMAT gives you the average and the sum of a group of numbers, you can use the formula to
gure out how many numbers are in the set.
»
The median is the middle value among a list of several values or numbers. To nd the
median, put the values or numbers in order, usually from low to high, and choose the value
that falls exactly in the middle of the other values. If you have an odd number of values, just
242 PART 4 Conquering the Quantitative Section
select the middle value. If you have an even number of values, nd the two middle values and
average them. The outcome is the median.
»
The mode is the value that occurs most frequently in a set of values. Questions about
mode may contain words like frequency or ask you how often a value occurs. For example, you
may be asked what income occurs most frequently in a given population or sample. If more
people in the population or sample have an income of $30,000 than any other income
amount, the mode is $30,000.
»
You determine a weighted mean when some values in a set contribute more to the nal
average than others. Multiply each individual value by the number of times it occurs in a set
of numbers. Then, you add these products together and divide the sum by the total number of
times all the values occur.
For example, suppose you’re asked to calculate Becky’s overall grade point average from
Table16-1, which charts the grades in all her classes and the number of credits for each.
First, you multiply the individual values (the grades) by the number of times they each occur
(the credits) to get total grade points for each class. Then, you add the total grade points for all
classes (41.7) and divide by the total number of times they all occur (which is the number of
total credits, 15):
41 7
15
278
.
. GPA.
You’ll likely see a bunch of questions on the GMAT that ask you to gure out the central tendency
of a set of values. Here’s an example of one that asks for mean.
George tried to compute the average (arithmetic mean) of his 8 statistics test scores. He mistak-
enly divided the correct sum of all his test scores by 7 and calculated his average to be 96. What
was George’s actual average test score?
(A) 80
(B) 84
(C) 96
(D) 100
(E) 108
The question asks you for George’s average score on eight tests and gives the average of those
eight scores when they’re divided by 7. You know that his average must be less than 96 because
you’re dividing by a larger number, so you can automatically eliminate Choices (C), (D), and (E).
Just use the formula for averages to determine George’s average score for eight tests.
TABLE16-1 The Weighted Mean of Grade Point Averages
Class Number of Credits Grade Total Grade Points
Statistics 5 3.8 19
English 5 1.9 9.5
Speech 4 2.3 9.2
Bowling 1 4.0 4
Total 15 2.78 GPA 41.7
CHAPTER 16 Manipulating Numbers: Statistics and Sets 243
1. Figure out the sum of all George’s test scores, using what you know from his incorrect
calculation.
96
7
672
x
x
2. Find George’s actual average based on the sum of all his scores.
A
A
672
8
84
The correct answer is Choice (B).
Straying from Home: Range and
StandardDeviation
Besides knowing the main concepts of central tendency, you also need to know about variation or
dispersion of values in statistics. The two types of dispersion you’ll deal with on the GMAT are
range and standard deviation, which we explore in the following sections. Dispersion tells you how
spread out the values are from the center. If dispersion is small, the values are clustered around
the mean. But a wide dispersion of values tells you that the mean average isn’t a reliable repre-
sentative of all the values.
Scouting out the range
The easiest measure of dispersion to calculate is the range. You can say that the range is the dif-
ference between the highest and lowest values in the set of data. The range of values in statistics
can come from either a population or a sample. The population is the set of all objects or things,
that is, the total amount of all data considered. A sample is just a part of the population.
Here’s an example of how to nd the range of a set of values: If the highest test score in a math
class was 94 percent and the lowest was 59 percent, you’d subtract the low from the high to get
the score range (94– 59 = 35). The range of test scores is 35. Simple as that!
Watching out for wanderers:
Standard deviation
Another form of dispersion you need to know for the GMAT is standard deviation. The standard
deviation expresses variation by measuring how spread out the distribution is from the mean.
Although the range (see preceding section) can give you an idea of the total spread, standard
deviation is a more reliable indicator of dispersion because it considers all the data, not just the
two on each end. Standard deviation is the most widely used gure for expressing how much the
data is dispersed from the mean.
For example, suppose you get a grade of 75 on a test where the mean grade is 70 and the vast
majority of all the other grades fall between 60 and 80. Your score is comparatively better in this
situation than if you get a 75 on the same test, where the mean grade is still 70, but most of the
grades fall between 45 and 95. In the rst situation, the grades are more tightly clustered around
the central tendency. A standard deviation in this case is a small number. Your grade is higher
compared to all the other test-takers’ grades in the rst group than your grade would be in the
244 PART 4 Conquering the Quantitative Section
second scenario. In the second scenario, the standard deviation is a bigger number, and a grade
of 75 isn’t as good relative to the others.
You’ve probably had a statistics class by this time in your career, and you probably had to calcu-
late standard deviation in that class. The GMAT won’t ask you to actually calculate standard
deviation, but it will expect you to know how to use standard deviation.
It’s a good idea to be able to recognize that a normal distribution creates a symmetrical bell curve
such as the one in Figure16-2. The standard deviation in a normal distribution is a constant. The
average (arithmetic mean) appears as an x with a line over it and appears in the exact middle of
all the values. If you stray 1 standard deviation in either direction from the mean, you’ll have net-
ted 68 percent of all the values. Going another standard deviation away from the center, you pick
up another 27 percent of all values, giving you about 95 percent of all values. Finally, when you
go
3
standard deviations from the mean, you now have about 99.7 percent of all the values in
your population or sample.
If the curve in Figure16-2 showed a group of test scores, it would mean that more than a majority
of test-takers scored within 1 standard deviation of the mean (68 percent is more than 51 percent).
The vast majority scored within 2 standard deviations, and virtually everyone scored within
3standard deviations. Say that the mean test score is 80, and one standard deviation may be
10points on either side. This means that 68 percent of the students scored between 70 and 90. If
the second standard deviation was another 5 test points in either direction, you could say that
95percent of the students scored between 65 and 95 on the test. Finally, you could say that the
third standard deviation is another 4 points away from the mean, which means that 99.7 percent
of the students scored between 61 and 99.
A small value for the standard deviation means that the values of the group are more tightly clus-
tered around the mean. A greater standard deviation means that the numbers are more scattered
away from the mean. The greater the standard deviation for a group of values, the easier deviating
from the center is. The smaller the standard deviation, the harder it is to deviate from the center.
FIGURE16-2:
Distribution
of the
standard
deviation
from the
mean.
© John Wiley & Sons, Inc.
CHAPTER 16 Manipulating Numbers: Statistics and Sets 245
Here’s what a standard deviation question on the GMAT may look like.
(I) {55, 56, 57, 58, 59}
(II) {41, 57, 57, 57, 73}
(III) {57, 57, 57, 57, 57}
Which of the following lists Sets I, II, and III in order from least standard deviation to greatest
standard deviation?
(A) I, II, III
(B) I, III, II
(C) II, III, I
(D) III, I, II
(E) III, II, I
The set with the least standard deviation is the one that has the least amount of dierence from
the highest to the lowest values. The values in Set III are all the same, so Set III has the least
standard deviation and should be listed rst. Eliminate Choices (A), (B), and (C) because they
don’t list Set III rst.
Set II (41 and 73) has a greater dierence between the high and low values than Set I (55 and 59).
So the set with the greatest standard deviation is Set II, which means it should be listed last.
Choice (D) lists the sets in their proper order from least standard deviation to greatest standard
deviation, so it’s the correct answer.
Predicting the Future: Probability
Probability is the measure of how likely a particular event will occur, but guring probability is a
bit more scientic than telling fortunes and reading tarot cards. You express probability as a per-
centage, fraction, or decimal. You’d say that the probability of an event’s occurring falls between
0 percent and 100 percent or between 0 and 1. If the probability of an event’s occurrence is 0, or
0 percent, it’s impossible for the event to occur. If the probability is 1, or 100 percent, the event is
certain to occur. Few things in life are certain, other than death and taxes. For an event to be
impossible is also rare. Therefore, the probability of the occurrence of an event usually falls
somewhere between 0 and 1, or 0 and 100 percent.
Probability questions may ask you to determine the probability of one event or multiple events.
We show you how to determine the probability for each type of question in the following
sections.
Finding the probability of one event
Probability deals with outcomes and events. For situations where all possible outcomes are equally
likely, the probability (P) that an event (E) occurs, represented by P(E), is dened as
PE
E
Number of Outcomes Involving Occurrences of
Total Po
sssible Number of Outcomes
Because you express probability as a fraction, it can never be less than 0 or greater than 1. Getting
both heads and tails with one ip of a coin is impossible, so the probability of that particular event
occurring is 0. If you used a coin with heads on both sides, the probability of getting heads on one
ip would be 1, because the number of possible outcomes is exactly the same as the number of
outcomes that will occur.
246 PART 4 Conquering the Quantitative Section
Finding the probability of many events
You can nd the probability of multiple events by following several rules. Table16-2 lists and
describes each rule, shows the corresponding formula, and provides an example of when you’d
use it.
Applying the special rule of addition
You use the special rule of addition to gure out the probability of rolling a die and coming up
with either a 1 or a 2. You can’t get both on one roll, so the events are mutually exclusive. There-
fore, the probability of rolling a 1 or a 2in one roll is
PA PB
:
PA
or B
PA
or B
PA
or B
1
6
1
6
2
6
1
3
Applying the general rule of addition
You use the general rule of addition to gure probability in the case of choosing sodas from a
cooler. Imagine that three types of sodas are in a cooler. Colas are numbered consecutively 1
through 5, orange sodas are numbered 1 through 7, and grape sodas are numbered 1 through 8.
Let event A stand for when a cola is taken out of the cooler and event B represent when a can with
a number 2 is taken out. You want to know the probability of picking out either a cola or a can with
the number 2 on it but not specically a cola with the number 2 on it. Five of the 20 cans are colas,
TABLE16-2 Finding the Probability of the Occurrence of Multiple Events
Rule Circumstance Formula Example
Special Rule
of Addition
The probability of the occurrence
of either of two possible events
that are mutually exclusive
PAorBP(A)P(B)
The probability of
rolling a 5 or 6 on one
roll of one die
General Rule
of Addition
The probability of the occurrence
of either of two possible events
that can happen together
PAorBP(A)P(B)P(A and B)
The probability of
drawing a playing card
that displays a club
or a queen
Special Rule of
Multiplication
The probability of the occurrence
of two events at the same
time when the two events are
independent of each other
PAand BP(A)P(B)
The probability of
rolling a 5 and a 6 on
one roll of two dice.
General Rule of
Multiplication
The probability of the occurrence
of two events when the
occurrence of the rst event
aects the outcome of the
second event
PAand BP(A)P(B/A)
The probability of rst
drawing the queen
of clubs from a pack
of 52 cards, keeping
the queen of clubs
out of the pack, and
then drawing the
jack of diamonds on
the next try
CHAPTER 16 Manipulating Numbers: Statistics and Sets 247
three display the number 2, and only one can is a cola with the number 2. So P(A) is
5
20
, P(B) is
3
20
, and P(A and B) is
1
20
. Plug the values in to the formula and solve:
PAor BPAPBPA and B
PA
or B
PA
or B
() () ( )
5
20
3
20
1
20
7
20
You can also express this probability as 0.35 or as 35 percent.
Applying the special rule of multiplication
The probability of multiple events occurring together is the product of the probabilities of the
events occurring individually. For example, if you’re rolling two dice at the same time, here’s how
you nd the probability of rolling a 1 on one die and a 2 on the other:
PA
and B
PA
and B
1
6
1
6
1
36
Applying the general rule of multiplication
Suppose the outcome of the second situation depends on the outcome of the rst event. You then
invoke the general rule of multiplication. The term P(B|A) is a conditional probability, where the
likelihood of the second event depends on the fact that A has already occurred. For example, to
nd the odds of drawing the ace of spades from a deck of 52 cards on one try and then drawing
the king of spades on the second try— with the ace out of the deck— apply the formula, like this:
PAand BPAPBA() (/)
.
The line between the B and A stands for “B given A”; it doesn’t mean divide!
PAand BPAPBA
PA
and B
PA
and B
() (/)
,
1
52
1
51
1
2 652
We wouldn’t bet against the house on that outcome! The probability of drawing the king of spades
on the second draw is slightly better than the probability of drawing the ace on the rst draw,
because you’ve already removed one card from the deck on the rst draw. Here’s a sample of how
the GMAT may test your knowledge of probability rules.
A candy machine contains gumballs: three blue, two red, seven yellow, and one purple. The
machine distributes one gumball for each dime. A child has exactly two dimes with which she
will purchase two gumballs. What is the chance that the child will get two red gumballs?
(A)
2
169
(B)
1
13
(C)
2
13
(D)
1
156
(E)
1
78
248 PART 4 Conquering the Quantitative Section
You need to treat getting the two red gumballs as two events. The occurrence of the rst event
aects the probability of the second because after the child extracts the rst red gumball, the
machine has one fewer gumball. So you apply the general rule of multiplication.
The chance of getting a red gumball with the rst dime is 2 (the number of red gumballs) divided
by 13 (the total number of gumballs in the machine), or
2
13
. If the child tries to get the second
gumball, the rst red gumball is already gone, which leaves only 1 red gumball and 12 total gum-
balls in the machine, so the chance of getting the second red gumball is
1
12
. The probability of
both events happening is the product of the probability of the occurrence of each event:
PAand BPAPBA
PA
and B
PA
and B
PA
and B
() (/)
2
13
1
12
2
156
11
78
Choice (E) is the correct answer. Choice (A) is
2
13
1
13
, which would look right if you didn’t sub-
tract the withdrawn red gumball from the total number on the second draw. Choice (B) is the
chance of drawing one red gumball from a machine with 13 gumballs and only 1 red gumball. In
this problem,
1
13
is also the chance of drawing the purple gumball. If you picked Choice (C), you
found the chance of drawing the rst red gumball.
CHAPTER17 It’s All in the Presentation: GMAT Quantitative Question Types 249
IN THIS CHAPTER
» Diving into data suciency
questions
» Probing problem-solving questions
It’s All in the Presentation:
GMAT Quantitative
Question Types
Y
ou need more than just math skills to excel on the quantitative section; you also need to
know how to approach the questions. This chapter tells you what to expect from the math
sections and how to work through the unique ways the GMAT presents the questions.
The kinds of math questions that appear on the GMAT test your ability to reason and think on
your feet as you make use of the information you’re given.
Two basic types of questions are intermingled throughout the quantitative section of the GMAT:
data-suciency questions and problem-solving questions. Both types of questions require simi-
lar skills, but they demand dierent approaches. In this chapter, we show you how to ace both
kinds of questions.
Enough’s Enough: Data-Suciency Questions
The quantitative section has 37 questions, and about half of them are presented in a unique form
called data suciency. These questions aren’t particularly hard if you understand how to approach
them before you walk into the testing center. However, if you don’t know much about these ques-
tions, getting confused and making careless mistakes are easy. Fortunately, you’ve decided to
read this book to get a sneak peek. Your knowledge should be more than sucient for data
suciency!
Chapter17
250 PART 4 Conquering the Quantitative Section
You don’t need the solution to nd the answer
Unlike the traditional math problems you’ve seen throughout your life, data-suciency ques-
tions don’t actually require you to solve the problem. Instead, you have to evaluate two state-
ments and determine which of those statements provides sucient information for you to answer
the question.
For each data-suciency problem, you have a question and two statements, labeled (1) and (2).
Your job is to decide whether each of the statements gives you enough information to answer the
question with general math skills and everyday facts (such as the number of days in a month and
the meaning of clockwise). If you need a refresher in the math concepts tested on the GMAT, read
Chapters12,13,14,15, and16.
Don’t make foolish assumptions when you answer data-suciency questions. Keep in mind that
your job is to determine whether the information given is sucient, not to try to make up for the
lack of data! You’re used to having to come up with an answer to every math problem, so if the
statements lack just a little information, you may be tempted to stretch the data to reach a solu-
tion. Don’t give in to temptation. For example, if a data-suciency question provides a four-
sided gure, don’t assume that it’s a square unless the data tells you it’s a square— even if
knowing that the gure is a square would allow you to solve the problem. Deal only with the
information expressly as it’s stated without making unwarranted assumptions.
The answer choices for data-suciency questions are the same for each question:
(A) Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the
question asked.
(B) Statement (2) alone is sucient, but Statement (1) alone is not sucient to answer the
question asked.
(C) Both Statements (1) and (2) together are sucient to answer the question asked, but nei-
ther statement alone is sucient.
(D) Each statement alone is sucient to answer the question asked.
(E) Statements (1) and (2) together are not sucient to answer the question asked, and addi-
tional data are needed.
The computer doesn’t actually designate the answer choices with the letters A through E, but
the choices appear in this order (you choose the correct one with your mouse or keyboard), and
we refer to them as A, B, C, D, and E to make the discussion simpler.
It’s possible that just one of the statements gives enough data to answer the question, that the
two statements taken together solve the problem, that both statements alone provide sucient
data, or that neither statement solves the problem, even with the information provided by the
other one. That’s a lot of information to examine and apply in two minutes! Don’t worry. You can
eliminate brain freeze by following a step-by-step approach to these questions.
Steps to approaching data-suciency problems
Take a methodical approach to answering data-suciency questions, and follow this series
of steps:
1. Evaluate the question to make sure you know exactly what you’re supposed to solve,
and, if you can, decide what kind of information you need to solve the problem.
CHAPTER 17 It’s All in the Presentation: GMAT Quantitative Question Types 251
2. Examine one of the statements and determine whether the data in that one statement
is enough to answer the question.
Start with the rst statement or whichever one seems easier to evaluate. Record your conclu-
sion on the noteboard.
3. Examine the other statement and determine whether it has enough information to
answer the question.
Record your conclusion on the noteboard.
4. Evaluate what you’ve written on your noteboard.
•
If you recorded yes for both statements, pick the fourth answer, which we designate as
Choice (D).
•
If you recorded yes for (1) and no for (2), select the rst answer, Choice (A) in this book.
•
If you recorded no for (1) and yes for (2), choose the second answer, Choice (B) for our
purposes.
•
If you’ve written no for both statements, go on to the next step.
5. Examine the statements together to determine whether the data given in both is enough
information to answer the question.
•
If the answer is yes, select the third answer, our Choice (C).
•
If the answer is no, choose the last answer, the one we’ve designated as Choice (E).
You can boil this method down to a nice, neat chart, like the one shown in Figure17-1.
FIGURE17-1:
Data
sufficiency
answer
elimination
chart.
© John Wiley & Sons, Inc.
252 PART 4 Conquering the Quantitative Section
Don’t think too hard about whether an answer provides sucient information to solve a problem.
Data-suciency questions aren’t necessarily designed to trick you. For example, you deal only
with real numbers in these questions, and if a line looks straight, it is.
A statement is sucient to answer the question if it provides only one possible answer for the
question. If the information in a statement allows for two or more answers, the statement isn’t
sucient.
David and Karena were among a group of runners who were raising money for a local charity. If
David and Karena together raised $1,000in the charity race, how much of the money did Karena
raise?
1. David raised
4
5
as much money as Karena did.
2. David raised 5 percent of the total money raised at the event.
Use the steps and/or the chart in Figure17-1 to solve the problem:
1. Know what you have to solve for.
The question asks you to gure out how much money Karena raised for charity. The question
gives you the total money raised by David and Karena together
( $, )DK 1 000
but doesn’t
specify how much David raised. Check out the statements to see whether either or both of
them let you know how much David came up with. If you have David’s gure, you only need to
subtract it from $1,000 to get Karena’s gure.
2. Consider Statement (1) to determine whether it lets you solve for Karena’s total.
You determined that you needed data that would allow you to separate the money raised by
Karena from that raised by David. Knowing that David raised
4
5
as much money as Karena
allows you to set up a formula to solve for Karena’s portion. Let K stand for Karena’s contribu-
tion and substitute
4
5
K for D in the equation
DK$,1 000
. Your new equation is
4
5
1
000
KK$, . This equation has only one variable, and that variable stands for how much
Karena raised. Therefore, you know you can solve the problem by using just the data from
Statement (1). You don’t need to actually gure out what K stands for. Just write
1 yes
on your
noteboard. You know that the correct answer is either Choice (A) or Choice (D), but you have to
look at Statement (2) to know which.
If a question like this one appears at the end of the section and you’re pressed for time, you can
guess between Choices (A) and (D), knowing that you have a 50 percent chance of answering
correctly without even reading Statement (2).
3. Examine Statement (2).
Statement (2) tells you that David raised 5 percent of the total money raised at the event. The
question doesn’t tell you how much total money was raised at the event, so you can’t use this
information to gure out how much David raised. And if you don’t know how much David
raised, you can’t gure out how much Karena raised. Jot down
2 no
on the noteboard.
Because (1) is a yes and (2) is a no, the answer has to be Choice (A).
CHAPTER 17 It’s All in the Presentation: GMAT Quantitative Question Types 253
If you’ve read both statements and determined that either Statement (1) or Statement (2) is suf-
cient alone, two things are true:
»
You’re done with the question and can move on the next one.
»
The answer can’t be Choice (C) or Choice (E).
Both Choices (C) and (E) apply to the statements when they’re considered together. You don’t
need to consider the statements together if either statement is sucient alone. Your only possible
choices if either statement is sucient are Choice (A) if only Statement (1) is sucient, Choice (B)
if only Statement (2) is sucient, and Choice (D) if each statement alone is sucient.
Don’t evaluate whether both statements together answer the problem unless you’ve determined
that neither is sucient alone. The only time you consider (1) and (2) together is when you’ve
answered no to both statements. For instance, say the example question replaced Statement (1)
with this data: “The event raised a total of $10,000.” Statement (1) wouldn’t be enough to answer
the question. But because Statement (2) tells you that David raised 5 percent of the total event
money, you can answer the question using the data from both statements. Statement (1) provides
the total amount, and Statement (2) allows you to gure out how much David raised based on that
amount. If you subtract that amount from $1,000, you’ll have Karena’s total.
Choice (E) would be correct if Statement (1) said, “The event raised more money this year than
last year.” In this case, neither statement, nor the two together, could answer the question.
Don’t waste time trying to come up with the actual numeric answer if you don’t have to. When
you look at a question like the example, you may be tempted to solve the equation and gure out
how much Karena raised. Don’t give in! Finding the number just wastes precious time, and no one
gives you extra credit for solving the problem! Instead, use your valuable time to solve other
questions in the quantitative section.
Taking a Look at Data-Suciency
Practice Problems
The best way to master the steps for solving data-suciency questions is to practice on sample
problems. Use the set of questions in this section to hone your skills. Make sure you have a piece
of scratch paper nearby to simulate the noteboard. You can check your answers by reading through
the explanations that follow the questions.
Practice questions
The GMAT gives you about two minutes to answer each quantitative question. So set your timer
for ten minutes to get a feel for the time limit you’ll be facing on the actual test. Follow the chart
in Figure17-1 to work your way through the answer choices. If you need to refresh your memory
of the answer choices before you begin, see the earlier section “You don’t need the solution to nd
the answer.”
254 PART 4 Conquering the Quantitative Section
1. What’s the value of the two-digit integer x?
1. The sum of the two digits is 5.
2. x is divisible by 5.
(A) Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the question
asked.
(B) Statement (2) alone is sucient, but Statement (1) alone is not sucient to answer the question
asked.
(C) Both Statements (1) and (2) together are sucient to answer the question asked, but neither state-
ment alone is sucient.
(D) Each statement alone is sucient to answer the question asked.
(E) Statements (1) and (2) together are not sucient to answer the question asked, and additional data
are needed.
2. Oce Solutions employs both male and female workers who work either full time or part time. What
percentage of its employees work part time?
1. Twenty percent of the female employees at Oce Solutions work part time.
2. Thirty percent of the workforce at Oce Solutions is male.
(A) Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the question asked.
(B) Statement (2) alone is sucient, but Statement (1) alone is not sucient to answer the question asked.
(C) Both Statements (1) and (2) together are sucient to answer the question asked, but neither state-
ment alone is sucient.
(D) Each statement alone is sucient to answer the question asked.
(E) Statements (1) and (2) together are not sucient to answer the question asked, and additional data
are needed.
3. What is the value of
2()xy
in the preceding gure?
1.
y 120
2. BC || AD
(A) Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the question
asked.
(B) Statement (2) alone is sucient, but Statement (1) alone is not sucient to answer the question
asked.
(C) Both Statements (1) and (2) together are sucient to answer the question asked, but neither
statement alone is sucient.
(D) Each statement alone is sucient to answer the question asked.
(E) Statements (1) and (2) together are not sucient to answer the question asked, and additional data
are needed.
CHAPTER 17 It’s All in the Presentation: GMAT Quantitative Question Types 255
4.
Joe uses three dierent modes of transportation to travel a total of 225 kilometers to visit his aunt. How
many kilometers does Joe travel by bus?
1. Joe rides his bike 5 kilometers to the bus station where he boards the bus to take him to the train
station. He then takes the train 10 times the distance he has traveled by bus.
2. The distance Joe travels by bike is
1
4
the distance he travels by bus, and his train ride is 40 times
longer than his bike ride.
(A) Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the question
asked.
(B) Statement (2) alone is sucient, but Statement (1) alone is not sucient to answer the question
asked.
(C) Both Statements (1) and (2) together are sucient to answer the question asked, but neither state-
ment alone is sucient.
(D) Each statement alone is sucient to answer the question asked.
(E) Statements (1) and (2) together are not sucient to answer the question asked, and additional data
are needed.
5. If x and y are real numbers and
( )()aa
xy22
81
, what is the value of
xy
?
1.
a 3
2.
xy
(A) Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the question
asked.
(B) Statement (2) alone is sucient, but Statement (1) alone is not sucient to answer the question
asked.
(C) Both Statements (1) and (2) together are sucient to answer the question asked, but neither state-
ment alone is sucient.
(D) Each statement alone is sucient to answer the question asked.
(E) Statements (1) and (2) together are not sucient to answer the question asked, and additional data
are needed.
Answer explanations
The following answer explanations provide not only the correct answer for the data-suciency
practice questions in the preceding section but also additional insight into how to approach this
unique question type. So be sure to read all the info provided here.
1. C. Apply the steps:
1. Find out what to solve for.
This short question gives you little information about x; all you know is that it’s a two-
digit integer.
2. Examine Statement (1).
Statement (1) tells you that the sum of the digits is 5. Several two-digit numbers are com-
posed of digits that when added together equal 5: 14, 23, 32, 41, and 50. Statement (1)
narrows the eld of two-digit numbers down to just these ve possibilities, but that’s not
good enough. Because you don’t have a single answer, Statement (1) isn’t sucient. Write
down
1 no
. You’ve just eliminated Choices (A) and (D).
256 PART 4 Conquering the Quantitative Section
3. Evaluate Statement (2).
Statement (2) says that x is divisible by 5. You probably realize immediately that every
two-digit number ending in 0 or 5 is divisible by 5, so the possibilities are 10, 15, 20, 25, and
so on. Clearly, Statement (2) isn’t sucient, because
1
5
of all two-digit numbers are divisible
by 5. Write down
2 no
. You’ve just eliminated Choice (B).
4. Check out what you’ve written.
You have double nos, so you have to consider both statements together.
5. Evaluate the two statements together.
Statement (1) narrows the two-digit numbers down to ve possibilities: 14, 23, 32, 41, and 50.
Statement (2) narrows the list to those numbers that are divisible by 5. The only possibility
from Statement (1) that ends in 0 or 5 is 50. Because 50 is divisible by 5 and the digits add up
to 5, it answers the question. The two statements together provide enough information to
answer the question. Correct answer: Choice (C).
You’ll notice that, for this question, you had to nd the actual answer to the question to
determine whether the information was sucient. Sometimes doing so is the quickest way
to determine whether statements provide enough data. An equation may exist that you
could’ve set up (and not solved) that would have told you that you had sucient informa-
tion. However, on questions like this one, just applying the information to the question is
often simpler and quicker. Solving the actual problem is okay if it’s the quickest way to deter-
mine that you have enough information. Just remember to stop solving the problem as soon as
you determine whether the information is sucient!
2. E. Here’s an example of how word problems may appear as data-suciency questions.
Apply the steps in the same way you do for solving linear equations:
1. Find out what to solve for.
The question asks you to nd the percentage of part-time employees at Oce Solutions. You
know two facts at this point: (1) Oce Solutions employs a certain number of males (m) and a
certain number of females (f ), and (2) a certain number of employees work either full time (F )
or part time (P). That creates four unknown variables. The question doesn’t tell you anything
about how many total people (T) Oce Solutions employs, so you have another unknown.
Here’s what you know in mathematical terms:
FPT
and
fmT
.
2. Examine Statement (1).
The rst statement gives you the percentage of female part-time employees but tells you
nothing about the percentage of male part-time employees. It takes care of only two of the
unknown variables; you’re missing half of what you need to solve the problem. Statement (1)
isn’t sucient. Write down 1 = no, and eliminate Choices (A) and (D).
3. Evaluate Statement (2).
This statement concerns male employees at Oce Solutions, but not females, so it’s insuf-
cient by itself. Record your nding as
2 no
. The answer can’t be Choice (B).
4. Check out what you’ve written.
You have double nos, so consider Statement (2)’s suciency when paired with Statement (1).
5. Evaluate the two statements together.
One statement provides a percentage for females and the other oers a percentage for
males. You may be on your way to nding the percentage for both.
CHAPTER 17 It’s All in the Presentation: GMAT Quantitative Question Types 257
Read the statements carefully. You may be tempted to think that Statement (2) oers the
other half of the solution, but this statement tells you the percentage of all males who work
at the company, not just the ones who work part time.
You can’t determine the total percentage of part-time workers if you don’t know the ratio of
male full-time to male part-time workers. Neither statement is sucient and the two
together don’t cut it. Correct answer: Choice (E).
3. B. For this problem, you evaluate a four-sided geometric gure:
1. Find out what to solve for.
You know that the sum of the interior angles of four-sided gures is 360 degrees and that
xand y are the measures of two of these interior angles, but that’s not enough to determine
the value of
2()xy
. But you knew that. Data suciency questions never give you enough
information to solve them without considering the statements. So check out what they
have to oer.
2. Examine Statement (1).
Statement (1) gives you the value of y. You may have examined the gure, assumed that it
was a parallelogram, and deduced that x and y are, therefore, angles formed by parallel lines
cut by a transversal. That makes them supplementary angles that add to 180 degrees. So if
y 120
,
x 60
, and
2 360()xy
. Problem solved!
Not so fast. You can’t assume information about a GMAT gure by looking at it. If the gure is
supposed to be a parallelogram, the GMAT will give you the information you need to know
that. Nothing to this point has indicated that BC and AD are parallel lines, so you have to write
no next to Statement (1).
3. Evaluate Statement (2).
Well, here you go. Now you know expressly that AB is a transversal that passes through two
parallel lines. The two angles x and y are supplementary.
Were you tempted at this point to pick Choice (C)? It’s true that both statements together give
you the value of x, but you aren’t looking for the value of x. You’re asked to nd the value of
2(x + y). All you need is Statement (2). If the value of x + y is 180, the value of 2(x + y) is 360.
Write yes next to Statement (2) on your noteboard and pick Choice (B). You’re done!
You only pick Choice (C) if neither of the two statements by itself solves the problem. After
you’ve determined that one of the statements works and the other doesn’t, you know the
answer can’t be Choice (C). Follow the line of questions in the chart in Figure17-1 and
you’ll be ne.
4. D. This data-suciency question is essentially a simple addition problem.
1. Find out what to solve for.
You know the total distance Joe travels to his aunt’s is 225 kilometers and that he takes
dierent types of transportation, one of which is a bus. Lucky guy! The question asks for the
length of Joe’s bus ride. That’s your unknown, so designate the bus ride as x.
2. Examine Statement (1).
From the rst statement, you learn that the other modes of transportation are bike (b) and
train (t). Great news! It also tells you the exact length of Joe’s bike ride (5 kilometers) and that
his train ride is 10 times his bus ride. So
tx10
. You can set up an equation with this informa-
tion:
510 225xx
. The equation has only one variable, the unknown length of the bus
ride. You know you can solve a linear equation with only one variable, so Statement (1)
is sucient. Write yes next to (1) on your noteboard and eliminate Choices (B), (C), and (E).
258 PART 4 Conquering the Quantitative Section
3. Evaluate Statement (2).
Create an equation from the information in the second statement. If Joe’s bike ride (b) is
1
4
as
long as his bus ride (x), then
b
x
1
4
. If the train trip (t) is 40 times the length of the bike ride (b),
then
tb40
. This gives simultaneous equations. Substitute
1
4
x for t in the train ride equation:
tx
40
1
4
. So the equation for the bike ride plus the bus ride plus the train trip is this:
1
4
40
1
4
225
xx x
This equation has only one variable, so you know you can solve for x. You don’t have to
actually solve for x; you just need to know that you can to know that Statement (2) is also
sucient. Write yes next to (2). Correct answer: Choice (D).
5. A. The last question in the practice set contains a bunch of unknown variables, so you may
think you can’t solve for much. You may be surprised!
1. Find out what to solve for.
Take a few seconds to evaluate the equation. You’re given two factors with exponents, and
their product is equal to a perfect square. Both factors have the same base (a), and both
contain an exponent with a factor of 2. The problem asks you to nd the sum of the other
two factors in the exponents of the terms.
2. Examine Statement (1).
From the information in the rst statement, you can substitute 3 for a in the equation:
( )()33 81
22xy
The terms have the same base, so you add the exponents when you multiply the terms:
381
22xy
Now extract the common factor in the exponent:
381
2( )xy
Square 3 to get 9:
9 81
()xy
Because
9 81
2
, you know that the exponent (x + y) must equal 2.
You could also nd the value of x + y by rewriting 81 as a base and exponent:
33
22 4xy
When the bases are equal, the exponents are equal:
2 24
2
xy
xy
Either way, the information in Statement (1) is sucient to tell you the value of x + y. Write yes
next to (1) on your noteboard and eliminate Choices (B), (C), and (E).
3. Evaluate Statement (2).
This statement tells you that x and y are equal, so you may be tempted to draw from the
information in the last statement and assume that x and y each equal 1. Well, that could be
true if a = 3. But you no longer know that a = 3.
CHAPTER 17 It’s All in the Presentation: GMAT Quantitative Question Types 259
You can’t carry over the information from one statement to evaluate the suciency of the
other. It’s true that x and y could each equal 1, but they could also each equal 0.5. Start fresh
with each statement.
If x and y are equal, then you can substitute x for y in the equation, simplify, and solve for a:
( )()aa
a
a
a
a
xx
x
x
x
x
22
4
44
81
81
3
3
3
Since a is equal to the xth root of 3, the possible values of x, y, a, and, of course, x + y, are
innite. For example, if x = 2, then so does y, and
a 3
. If x and y each equal 3, then
a 3
3
,
and so on. Because Statement (2) results in more than one value for x + y, it can’t be sucient
to answer the question. Write no next to (2) on your noteboard. Correct answer: Choice (A).
Houston, We Have a Problem:
Problem-Solving Questions
About half of the 37 math problems on the GMAT quantitative section are data suciency. The
other half are problem-solving questions, which (not surprisingly!) require you to apply your
mathematical skills to solve a problem. These questions are more like the ones you’ve seen on
other standardized tests, like the SAT and ACT.They present you with a question and provide ve
possible answer choices from which you select the correct answer.
The approach to regular old problem-solving questions is less clear-cut than the one for data-
suciency problems, but you should still follow an approach. Arriving at the test center with a
practice problem-solving plan not only provides you with a groovy little alliteration but also gives
you a real edge for answering standard math questions. These techniques apply more directly to
some questions than others, but learn all of them so you’re prepared for all types of problem-
solving questions:
»
Examine all the data the question provides to make sure you know exactly what you’re
asked to do. Some problems present you with gures, graphs, and scenarios, and some with
just an equation with an equal sign. Don’t jump into the answer choices until you’ve given the
question a little thought. Isolate exactly what the problem asks you to solve for and what
information the problem provides you. Especially for more complex questions and word
problems, use your noteboard to keep track of what you know and what you have to nd out.
»
Eliminate obviously incorrect answer choices if possible. Before you begin solving a more
complex math problem, look at the answer choices to root out any clearly illogical options. You
can then focus your problem-solving, and you won’t pick these answers later through mistaken
calculations. You can nd more tips for eliminating answer choices in Chapter2.
»
Use the information in the problem. The GMAT rarely presents you with the answer choice
that states, “It cannot be determined from the information.” Almost every problem-solving
question contains enough information for you to gure out the correct answer. But you need
to use what you’re given. Pull out the numbers and other terms in a problem and write them
on your noteboard in a way that makes the numbers meaningful. Depending on the problem,
you may show relationships between quantities, draw simple diagrams, or organize informa-
tion in a quick table.
260 PART 4 Conquering the Quantitative Section
»
Find the equation. Some GMAT problems provide the equation for you. Others, such as word
problems, require you to come up with an equation using the language in the problem.
Whenever possible, formulate an equation to solve from the information provided in the
problem and write it down on your noteboard.
»
Know when to move on. Sometimes you may confront a question that you just can’t solve.
Relax for a moment and reread the question to make sure you haven’t missed something. If
you still don’t know what to do or if you can’t remember the tested concept, eliminate all the
answers you can and record your best guess.
Apply the process to a sample problem.
A survey reveals that the average income of a company’s customers is $45,000 per year.
If50customers respond to the survey and the average income of the wealthiest 10 of those
customers is $75,000, what is the average income of the other 40 customers?
(A) $27,500
(B) $35,000
(C) $37,500
(D) $42,500
(E) $50,000
Scan the question to get an idea of what it’s asking of you. The word problem talks about surveys
and averages, so it’s a statistics question. It asks for the average income of 40 out of 50 customers
when the average of the other 10 is $75,000 and that the average of all 50 is $45,000.
You can eliminate Choice (E) o the bat because there’s no way that the 40 customers with
lowerincomes have an average income that’s more than the average income of all 50 customers.
Choice (D) is probably wrong, too, because the top ten incomes carry such a high average
compared to the total average. You know the answer is either Choice (A), (B), or (C), and you
haven’t even gotten down to solving yet!
Quickly eliminating answers before you begin can save you from choosing an answer that comes
from making a math error. Sometimes, the test-makers are tricky; they anticipate the kinds of
little mistakes you’ll make and oer the resulting wrong answers as distracters in the answer
choices. So be sure to eliminate illogical answers before you begin a problem.
You can nd the total income of all 50 customers and the total income of the wealthiest 10 cus-
tomers by using the formula for averages. The average equals the sum of the values in a group
divided by the number of values in the group. Apply the formula to nd the total income for the
group of 50. Then nd the total income for the group of 10. Subtract the total income of the 10
from the total income of the 50 to nd the total income of the 40. Then you can divide by 40 to
get the average income for the group of 40. Here’s how you do it:
Your calculations may be easier if you drop the three zeroes from the salaries. For this problem,
shorten $45,000 to $45 and $75,000 to 75. Just remember to add the zeroes back on to your solu-
tion when you nd it!
CHAPTER 17 It’s All in the Presentation: GMAT Quantitative Question Types 261
1. Find the total income for the group of 50.
The average income is $45 and the number of group members is 50, so use the formula to nd
the sum of all incomes (x):
Average
Sum of Values
Number of Values
45
50
2 250
x
x,
2. Find the total income for the group of 10.
The average income is $75 and the number of group members is 10, so use the formula to nd
the sum (y):
75
10
750
y
y
3. Find the total income for the group of 40.
Subtract the total income of the group of 10 (y) from the total income for the group of 50 (x):
2 250 750 1 500,,
4. Find the average income of the group of 40.
The sum of the incomes in the group is $1,500, and the number of group members is 40, so
apply the average formula:
Average
Average
1 500
40
37 5
.
.
Add three decimal places for the three zeroes you excluded in your calculations, and you have your
answer. The average income of the 40 customers is $37,500, which is Choice (C).
Trying Out Some Problem-Solving
Practice Problems
Here are a few practice questions to help you master the approach to problem-solving questions
in the quantitative section. When you’re nished answering them, read through the answer
explanations to see how you’ve fared.
Practice questions
Try to answer these practice problems in the same amount of time you’ll experience on the actual
GMAT (give yourself about ten minutes to answer all ve questions). Remember to keep track of
the information you know and the information you have to gure out as you work through the
problems. Use a piece of scratch paper to simulate the noteboard as you work out the answers.
262 PART 4 Conquering the Quantitative Section
1. An electronics rm produces 300 units of a particular MP3 player every hour of every day. Each unit
costs the manufacturer $60 to produce, and retailers immediately purchase all the produced units. What
is the minimum wholesale price (amount the manufacturer receives) per unit that the manufacturer
should charge to make an hourly prot of $19,500?
(A) $60
(B) $65
(C) $95
(D) $125
(E) $145
2. If
x 0
, what is the value for x in the equation
2
42
6
86
x
x
x
x
?
(A) –3
(B) 1
(C) 2
(D) 3
(E) 6
3.
gr
rr
rr
42
2
if
if
Given the above, evaluate
gr
if
r 7
.
(A) –28
(B) –14
(C) –7
(D) 7
(E) 28
4. In the preceding gure, the circle centered at B is internally tangent to the circle centered at A.The
smaller circle passes through the center of the larger circle, and the length of AB is 4 units. If the
smaller circle is removed from the larger circle, how many square units of the area of the larger circle
will remain?
(A)
16
(B)
36
(C)
48
(D)
64
(E)
800
CHAPTER 17 It’s All in the Presentation: GMAT Quantitative Question Types 263
5.
A line with the equation
y x230
for all real numbers would pass through which quadrants on the
coordinate plane?
(A) I, II, and III only
(B) III and IV only
(C) I, II, III, and IV
(D) I, III, and IV only
(E) II and IV only
Answer explanations
1. D. Note what the question gives and what it’s asking for. It provides units per hour and cost
per unit. It also tells you the total desired hourly prot. You’re supposed to nd the
price per unit.
The rst thing to do is eliminate obviously incorrect answer choices. You know that you’re
looking for the wholesale price that will yield a prot (which results from price minus cost
to produce) of $19,500 per hour. Because the answers given are wholesale prices, you can
eliminate Choices (A) and (B). The cost to produce each unit is $60. If the company charged
the same amount for the MP3 players as it spent to produce them, it would make no prot,
so Choice (A) is obviously incorrect. Choice (B) isn’t much better. At a prot of just $5 per
unit and 300 units per hour, the rm would make only $1,500 per hour.
You’ve eliminated two answer choices. Evaluate the data to nd the correct answer from
the remaining three. You know that 300 units are produced every hour and that those
300units have to net a prot of $19,500. If you knew the amount of prot per unit, you
could add that to the amount each unit costs to produce and get the minimum wholesale
price. Set up an equation with x as the prot per unit. Remember that per means to divide:
x
x
$,19 500
300
65
The rm needs to make a prot of $65 per unit.
You can’t stop here and pick Choice (B). You’re not done yet, but you know that because
you’ve already eliminated Choice (B).
You have to add prot to the per-unit production cost to get the nal wholesale price:
$$$60 65 125
Correct answer: Choice (D).
You could use estimation to solve this problem by rounding $19,500 up to the nearest con-
venient multiple of 300, which is $21,000, and then dividing 21 by 3in your head and get-
ting 7. This would tell you that you need a little less than $70 prot from each unit, or a
little under $130 as the wholesale price (because
$$$60 70 130
).
2. D. Here’s a relatively simple question that asks you to solve for x. The only element that
makes it a little complex is that you’re dealing with variables in fractions. Take a moment
to consider the equation. The numerator in the fraction on the right is 3 times the numera-
tor in the fraction on the left. Multiplying the numerator of the left-side fraction would
make it equal to the numerator on the right side.
When the numerators of two fractions are equal, their denominators are also equal, so cre-
ating equal numerators allows you to set the denominators equal to each other. Then just
solve for x.
264 PART 4 Conquering the Quantitative Section
1. Multiply the left-side fraction by
3
3
.
This doesn’t change the value of the fraction, because multiplying by
3
3
is the same as
multiplying by 1.
2
42
3
3
6
12 6
x
x
x
x
2. Set the denominators equal to each other and solve for x:
12 686
68
6
26
3
xx
xx
x
x
Correct answer: Choice (D).
You can also solve this question by cross-multiplying opposite numerators and
denominators:
2 86642
16
12 24 12
412
3
3
22
2
2
xx xx
xx
xx
xx
xx
x
()()
You can solve many GMAT problems by using more than one method. Go with the one
that’s easiest for you.
3. E. This function problem provides you with two outputs depending on the value of the
input. If the input is greater than or equal to 2, the output is 4 times the absolute value of
the input. If the input is less than 2, the output is the negative of the absolute value of the
input.
Don’t let the negative signs mess you up. If
r 7
, then g(–r) is the same as saying g(7),
because –(–7) is 7. So the value of the input in this problem is 7.
Because 7 is greater than 2, you’ll look to the rst rule of the function g(r). The solution to
gr() 47
is simply
4 728
. Correct answer: Choice (E).
If you confuse the signs, you’ll come up with the negative version of the correct answer,
which is Choice (A). You get the other answer choices when you use the incorrect rule.
4. C. This geometry question asks you to nd the area of the large circle less the area of the
small circle. Apply the formula for nding the area of a circle:
Ar
2
.
Because the smaller circle passes through the center of the larger one, the radius of the larger
circle is two times the radius of the smaller one: The radius of the larger circle equals 8.
Apply the area formula to the larger circle:
A
A
8
64
2
Determine the area of the smaller circle in the same way:
Ar
A
A
2
2
4
16
()
CHAPTER 17 It’s All in the Presentation: GMAT Quantitative Question Types 265
Now subtract the two areas:
641648
Correct answer: Choice (C).
5. D. This coordinate geometry problem requires you to know the slope-intercept form:
y mx b
. But before you do any calculations, go ahead and eliminate Choice (C). No way
can a straight line pass through all four quadrants of the coordinate plane. When you
rearrange the equation into the slope-intercept form by isolating the y variable on the left
side, you get
y x23
. The slope-intercept form gives you the y-intercept and slope of the
line. The value of b is the y-intercept, and the value of m is the slope.
For this kind of question, you may want to draw on your noteboard a coordinate plane
graph and label the quadrants I, II, III, and IV.Nothing fancy, mind you, just enough to get
your bearings. Now, draw a point below the origin on the y-axis representing –3, the
y-intercept. Then draw a line that travels upward from left to right rising two units toward
the top of the paper for every one unit to the right. Your gure doesn’t have to be perfect.
From a rudimentary drawing, you can immediately see that the line passes through
Quadrants I, III, and IV.
So Choice (D) is your best choice. Choice (A) would be correct if you had a parallel line with
a positive y-intercept. Choice (B) is possible for a line parallel to the x-axis with a negative
y-intercept. Choice (E) would require a line with a negative slope passing through the
origin.
Any line must travel through at least two quadrants, unless the line runs directly on top of
either the x- or y-axis. A line that lies directly on top of an axis doesn’t go through any
quadrant. The lines that travel through only two quadrants are those that pass through the
origin or are parallel to either the x- or the y-axis. All other lines must eventually travel
through three quadrants.
Correct answer: Choice (D).
CHAPTER18 All Together Now: A Mini Practice Quantitative Section 267
IN THIS CHAPTER
» Honing your GMAT math skills
by working through practice
questions
» Taking a look at the answer
explanations to understand what
you did wrong— and right
All Together Now: A Mini
Practice Quantitative
Section
H
ere’s a chance to test your GMAT math skills before you embark on the real adventure of
taking the test. This chapter contains only the types of math questions you’ll see on the
GMAT, so it’s kind of like a mini practice test. To get a better idea of the time restrictions
you’ll face on test day, try to complete the questions in the following section in about 48 minutes.
If you want to avoid the time pressure for now, feel free to just focus on answering the questions.
You’ll have the opportunity to time yourself again when you take the full-length practice tests
included with this book.
Read through all the answer explanations (even the ones for the questions you answered correctly),
because you want to make sure you know why you got the answer you did and because you may
see something in the explanations that can help you with other questions.
Tackling GMAT Math Practice Questions
Here are 24 practice questions for the GMAT math section. Grab your pencil, set your timer for
48 minutes, and get started. (Try not to peek at the answers until you’ve come up with
yourown.)
Chapter18
268 PART 4 Conquering the Quantitative Section
1. If
3
250
y
y
and
y 5
, then y =
(A)
3
2
(B)
2
3
(C)
2
3
(D)
3
2
(E) 6
2. If Esperanza will be 35 years old in 6 years, how old was she x years ago?
(A) 41– x
(B) x– 41
(C) 35– x
(D) x– 29
(E) 29– x
3. What is the value of
x
y
33
?
(1)
xy
3
6
(2)
xy18
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
4. Sofa King is having “a sale on top of a sale!” The price of a certain couch, which already had been dis-
counted by
20%
, is further reduced by an additional
20%
. These successive discounts are equivalent to a
single discount of which of the following?
(A)
40%
(B)
38%
(C)
36%
(D)
30%
(E)
20%
CHAPTER 18 All Together Now: A Mini Practice Quantitative Section 269
5.
If x is a member of the set {44, 45, 47, 52, 55, 58}, what is the value of x?
(1) x is even.
(2) x is a multiple of 4.
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
6. In a given year, the United States census estimated that there were approximately 6.5 billion people in
the world and 300 million in the United States. Approximately what percentage of the world’s popula-
tion lived in the United States that year?
(A)
0 0046.%
(B)
0 046.%
(C)
0 46.%
(D)
4 6.%
(E)
46%
7. The symbol represents one of the following operations: addition, subtraction, multiplication, or divi-
sion. What is the value of
4 5
?
(1)
0 10
(2)
0 11
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
8. How many burritos did Dave’s Wraps sell today?
(1) A total of 350 burritos was sold at Dave’s Wraps yesterday, which is 100 fewer than twice the
number sold today.
(2) The number of burritos sold at Dave’s Wraps yesterday was 20 more than the number sold today.
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
270 PART 4 Conquering the Quantitative Section
9. To boost sales around the holidays, the government of the ctional country of Capitalitamia dictates
that a citizen may purchase goods up to a total value of $1,000 tax-free but must pay a 7% tax on the
portion of the total value in excess of $1,000. How much tax must be paid by a citizen who purchases
goods with a total value of $1,220?
(A) $14.00
(B) $15.40
(C) $54.60
(D) $70.00
(E) $87.40
10. In the preceding gure,
ab
b
5
2
, what does b equal?
(A) 108
(B) 99
(C) 81
(D) 72
(E) 63
11. Is the value of x closer to 75 than it is to 100?
(1)
100 75xx
(2)
x 85
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
12. How long did it take Ms. Nkalubo to drive her family nonstop from her home to Charlestown, West
Virginia?
(1) Ms. Nkalubo’s average speed for the trip was 45 miles per hour.
(2) If Ms. Nkalubo’s average speed for the trip had been
1
1
4
times faster, the trip would have taken
three hours.
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
CHAPTER 18 All Together Now: A Mini Practice Quantitative Section 271
13.
The arithmetic mean and standard deviation for a certain normal distribution are 9.5 and 1.5, respec-
tively. Which of these values is more than 2.5 standard deviations from the mean?
(A) 5.75
(B) 6
(C) 6.5
(D) 13.25
(E) 13.5
14. What is the measure of
ABX
in the preceding gure?
(1) BX bisects
ABY
and BZ bisects
YBC
.
(2) The measure of
YBZ
is 60 degrees.
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
15. On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she trav-
eled
1
3
of the total distance and again after she traveled
1
4
of the distance remaining between her rst
stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination.
What was the total distance in miles from Traci’s starting point to Seal Beach?
(A) 250
(B) 300
(C) 350
(D) 400
(E) 550
272 PART 4 Conquering the Quantitative Section
16. In the fraction
a
b
, where a and b are positive integers, what is the value of b?
(1) The lowest common denominator of
a
b
and
1
5
is 10.
(2) a = 3
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
17. If n is a positive integer and
x
n
34
, which of the following could not be a value of x?
(A) 1
(B) 13
(C) 45
(D) 61
(E) 253
18. What is the value of b?
(1)
31
2
4()b
(2)
39
42()()bc bc
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
19. This stem-and-leaf plot shows the number of automobiles sold by 22 sales associates of a Ace Auto Sales
during the month of January. Next month, management wants to increase its average number of auto-
mobiles sold per salesperson to 35. If the number of sales associates remains at 22, on average how many
additional automobiles will each salesperson need to sell next month for management to reach this goal?
(A) 3
(B) 5
(C) 32
(D) 35
(E) 110
CHAPTER 18 All Together Now: A Mini Practice Quantitative Section 273
20.
For all
a 0
and
b 0
,
()4
2
432
22
ab
ab
?
(A)
8
68
ab
(B)
8
64
ab
(C)
8
47
ab
(D)
2
68
ab
(E)
2
47
ab
21. What is the ratio of a to b?
(1) The ratio of 0.25a to 2b is 2 to 3.
(2) a is two more than four times b.
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
22. Akhil invests $1,200in a certicate of deposit (CD) that earns 1.05% in interest compounded biannually,
which means that he earns 1.05% of his existing money twice per year. The money he makes in inter-
est is added to his account balance and rounded to the nearest cent. After two years, the CD matures.
Akhil decides to use $400 of the funds to purchase a tablet and invest the remaining balance in another
CD.How much money did Akhil invest in this second CD?
(A) $800.00
(B) $850.40
(C) $851.20
(D) $1,250.40
(E) $1,251.20
23. What is the slope of a line on the (xy) coordinate plane with endpoints of (2, 5) and (10, 4)?
(A) –8
(B)
1
8
(C)
1
8
(D)
4
3
(E) 8
274 PART 4 Conquering the Quantitative Section
24. A downtown theater sells each of its oor seats for a certain price and each of its balcony seats for a
certain price. If Matthew, Linda, and Jake each buy tickets for a particular performance at this theater,
how much did Jake pay for one oor seat and one balcony seat?
(1) Matthew bought four oor seats and three balcony seats for $82.50.
(2) Linda bought eight oor seats and six balcony seats for $165.
(A) Statement (1) ALONE is sucient, but Statement (2) ALONE is NOT sucient to answer the ques-
tion asked.
(B) Statement (2) ALONE is sucient, but Statement (1) ALONE is NOT sucient to answer the ques-
tion asked.
(C) Both statements TOGETHER are sucient, but NEITHER statement ALONE is sucient to answer
the question asked.
(D) Each statement ALONE is sucient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sucient to answer the question asked.
Checking Out the Answer Explanations
1. A. The GMAT usually starts with a question of medium diculty, and this one is in that
range. If the product of two factors equals 0, then at least one of the factors must be 0
(because anything times 0 equals 0). Therefore, one of the factors in this equation must
equal 0. You know it isn’t the second one, because y doesn’t equal 5, and y would have to
equal 5 for the second term to result in 0.
Therefore, you need to create an equation that sets the rst factor equal to 0 and then solve
for y. Here’s what you get for the rst factor:
3
20
3
2
y
y
Cross-multiply (because 2
2
1
) and solve:
32
3
2
y
y
2. E. If Esperanza will be 35 years old in 6 years, she is 29 right now (
35 629
). Therefore, to
determine how old she was x years ago, simply subtract x from her current age of 29:
29– x.
3. D. This problem is simple when you recognize that because the two fractions have a
common denominator,
x
y
33
is the same thing as
xy
3
.
Statement (1) says that
xy
3
6
, and because
x
yxy
33 3
,
x
y
33
must also equal 6. So
you know that Statement (1) is sucient to answer the question and that the answer must
be either Choice (A) or Choice (D). To gure out which it is, consider Statement (2). If it’s
sucient, the answer is Choice (D). If not, the answer is Choice (A).
Because
x
yxy
33 3
, and Statement (2) tells you the value of x + y, you can substitute 18
for x + y in the expression and solve for a known value (
18 36
). So Statement (2) also
provides sucient information to answer the question.
CHAPTER 18 All Together Now: A Mini Practice Quantitative Section 275
4.
C. This is a percent decrease question. You can apply a formula to solve it, but a faster and
easier method is to apply actual numbers to the circumstances. To simplify your life, use a
nice, round gure like $100.
If the couch originally cost $100 but was discounted by 20 percent, you’d multiply $100
by20 percent (0.20) and subtract that from $100 to nd the price after the rst discount
(
100 02020.
, and
100 20 80
). After the rst round of discounts, the couch cost $80.
However, the couch was discounted an additional 20 percent. Now, you have to repeat the
process, this time using $80 as the original price (
80020 16.
, and
801664
). After both
discounts, the couch cost $64.
But you’re not nished yet. You need to calculate the total discount. The couch originally
cost $100 and later cost $64. The discount, in dollars, is 100– 64, which is $36. To nd the
percentage of the full discount, simply divide $36 by the original price of $100 (
36
100
03
6
.
or 36 percent).
5. E. Evaluate Statement (1). Knowing that x is even doesn’t help you much. Three numbers in
the set are even: 44, 52, and 58. So Statement (1) doesn’t allow you to narrow down the
value of x to one number. The answer can’t be Choice (A) or Choice (D).
Consider Statement (2). Two numbers in the set are multiples of 4: 44 and 52. So even
when you know that x is a multiple of 4, you can’t come up with a xed value for x.
Statement (2) by itself isn’t sucient, so the answer can be only Choice (C) or (E). You
still have one more evaluation: whether the two statements together provide sucient
information.
Multiples of 4 are always even, so the two statements together don’t point you to the value
of x. So the correct answer is Choice (E).
6. D. This question requires you to work with very large numbers, so you need to know what
large numbers look like.
One billion = 1,000,000,000, and 1 million = 1,000,000. In other words, 1 billion is
1,000million.
Now, look at the question at hand: 6.5 billion is written as 6,500,000,000. Writing out
6billion is obvious, and 0.5 billion is one-half of 1,000 million, which is 500 million, or
500,000,000. You write 300 million like 300,000,000. To solve for the percentage, simply
divide 300,000,000 by 6,500,000,000, using the fraction form:
300 000 000
6 500 000 000
,,
,,,
Simplify things by canceling out eight zeros on the top and bottom. (This step is legal
because you’re just reducing your fraction.) Then divide 3 by 65.
You don’t actually have to complete the mathematical calculation, because all the answer
choices are derivatives of 46. You do need to know, though, that when you divide 3 by 65,
your answer will have three places after the decimal. If you can’t gure this in your head,
quickly set up the division problem on your noteboard and mark where the decimal will be
in your answer.
So
3
65
0
046
. , but the question asks for a percentage. To convert the decimal to a percent-
age, move the decimal point two places to the right and add a percentage sign. The answer
is 4.6 percent.
You can also use estimation to narrow down the answers.
3
65
is about
3
60
, which reduces to
1
20
, or 0.05. The answer has to be slightly smaller than 0.05 because
3
65
is less than
3
60
, The
answer that is slightly less than 0.05 is 0.046 or
4 6.%
276 PART 4 Conquering the Quantitative Section
7. B. To determine the value of
4 5
, you have to gure out which of the four operations the
symbol represents. The way to do so is to plug each of the operations into the equations
oered by each of the two statements and see whether either of them allows you to narrow
the symbol down to just one operation.
Statement (1) gives you
0 10
. Plug in each operation to see whether any make the equa-
tion true. You know addition and subtraction don’t work because you can’t add or subtract 1
to or from a number and end up with the same number. Both multiplication and division
work:
0 10
, and
0 10
. So Statement (1) isn’t sucient because it doesn’t allow you to
narrow the symbol down to just one operation. The answer, then, can’t be Choice (A) or
Choice (D).
Statement (2) oers
0 11
. The only dierence between this equation and the one in
Statement (1) is the answer. You know that multiplication and division don’t work, because
they already produced an answer of 0. Subtraction results in –1, so the only operation that
works is addition (0 + 1 = 1). This means that Statement (2) alone gives you enough infor-
mation to determine which operation the symbol stands for, which allows you to gure out
the value of
4 5
.
Data suciency questions don’t ask for the actual numeric answer, so don’t take the time
to determine the actual value of the operation (not that it would take you long to do so for
this question).
8. A. Evaluate each statement to determine whether it allows you to gure out the exact
number of burrito sales for the day.
You can construct a mathematical equation from the language in Statement (1). The
unknown is the total number of today’s burrito sales. Let b = today’s burritos. Fewer means
subtraction, so yesterday’s sales equal 2b– 100. The equation then looks like this:
350 2 100b
This equation has only one variable, so you know you can easily solve this equation to nd
out how many burritos left the shop today. (Don’t take the time to actually gure it out,
though!) Statement (1) is sucient, and the answer is either Choice (A) or Choice (D). To
determine which it is, evaluate Statement (2).
Statement (2) tells you that the number of burritos sold at Dave’s Wraps yesterday was 20
more than the number sold today, but this statement gives you two variables. You don’t
know how many burritos were sold today, and you don’t know how many went out the door
yesterday. If y stands for yesterday’s burrito sales, the equation would look something like
this: y = 20 + b. You can’t denitively solve an equation with two variables without more
information, so Statement (2) isn’t sucient. The correct answer is Choice (A).
(Oh, and if you won’t be able to sleep unless we conrm for you the number of burritos
soldtoday, it’s 225: 450 = 2b, so 225 = b. Now be sure to get your sleep; you need it for
theGMAT!)
9. B. The rst thing that should jump out at you is that the rst $1,000 of purchases is
tax-free, so you don’t need to consider the rst $1,000. Subtract $1,000 from $1,220 to get
the value of purchases that will actually be taxed: $220.
To nd the amount of tax due, you multiply 220 by 7 percent (or 0.07), but you don’t have
to take the time to fully work out the calculation. To make things simple, you can estimate:
200 is close to 220, and
200 0071400..
, so the amount has to be just a little more than $14.
The only answer that’s just a little more than $14 is Choice (B). If you take the time to mul-
tiply 220 and 0.07, you’ll nd that it’s exactly $15.40. But because this is a test where
saving time is crucial, avoid making full calculations whenever possible.
CHAPTER 18 All Together Now: A Mini Practice Quantitative Section 277
10.
D. The key to solving this problem is to recognize that a and b are supplementary angles,
which means they add up to 180 degrees:
a b 180
. (Chapter14 has more information on
shapes and angles.)
Now all you have to do is substitute 180 for a + b in the original equation and solve:
ab
b
b
b
b
5
2
180 5
2
5
360
72
So the correct answer is Choice (D).
11. A. To solve this problem, recognize that the halfway point between 100 and 75 is 87.5, so if
x is greater than 87.5, it’s closer to 100. If it’s less than 87.5, it’s closer to 75. (If it equals
87.5, it’s the same distance from both.)
If the dierence between 100 and x (100– x) is greater than the dierence between x and
75 (x– 75), then x must be less than 87.5, because values greater than 87.5 would make
100– x less than x– 75. Therefore, you absolutely know from Statement (1) that x is closer
to 75. It’s sucient to answer the question, and the answer is either Choice (A) or Choice (D).
Now, look at Statement (2). Knowing that x > 85 doesn’t help, because values above 87.5
would make x closer to 100 and values between 85 and 87.5 would make it closer to 75.
Statement (2) isn’t sucient. For more about inequalities, consult Chapter13.
12. B. This is a distance problem, so to determine the time of Ms. Nkalubo’s trip, you have to
use the distance equation.
The formula for distance is
r td
, which stands for
Rate Time Distance
(see Chapter13
for details about this formula).
Statement (1) is pretty easy to evaluate. Knowing that her average speed was 45 miles per
hour gives you the rate value for the equation but nothing more, so you’re left with an
unknown distance and an unknown amount of time. You can’t solve an equation with two
variables without more information. Therefore, you can’t calculate her time. Statement (1)
isn’t sucient, so the answer can’t be Choice (A) or Choice (D).
Statement (2) takes a little more thought. At rst it may not appear to give you enough
information to gure out time. But if you look further, you’ll see that it enables you to set
up two simultaneous equations, and when you have two simultaneous equations with two
variables, you can nd the value of either variable. Here’s how: The rst equation is for
Ms. Nkalubo’s actual trip, which you can denote as Trip 1 (we’ve used a subscript 1 to show
the values for Trip 1). Use the standard formula for distance:
r td
11 1
That’s as much as you know about Trip 1 for now.
The second equation is for the theoretical trip proposed in the problem, which you can call
Trip 2 (which we’ve denoted with a subscript 2). Start with the standard distance formula:
r td
22 2
Take the equation further with the information provided by Statement (2). Begin with the
easy value. Trip 2 would take 3 hours, so
r d
22
3
. You also know that Ms. Nkalubo’s rate
for Trip 2 was
5
4
the rate of Trip 1. So
r
r
21
5
4
. Substitute this value for rate into the equation
for Trip 2:
5
4
3
12
rd
278 PART 4 Conquering the Quantitative Section
You should also recognize that d
1
and d
2
have the same value because the distances of the
two trips are the same (it’s the same trip!). Therefore, you can set the left side of the rst
equation equal to the left side of the second and divide the rate variable from both sides.
At this point, you have an equation with only one variable, so you know you can solve for
the exact length of Ms. Nkalubo’s trip. Statement (2)’s information is sucient to answer
the question, so the correct answer is Choice (B).
For those of you who hate to be left hanging and need to see how the equation turns out,
we’ll nish the calculations. Just remember, you shouldn’t do this part for the test; it’s a
waste of time. Here’s what the solution looks like:
r tr
t
t
t
11 1
1
1
1
5
4
3
5
4
3
15
4
3
3
4
The time is
3
3
4
hours, which is equal to 3 hours and 45 minutes. The family was probably
ready for some action after almost four hours in the car!
13. E. Don’t let the language of this problem scare you. You’re really just applying basic
operations.
The arithmetic mean is 9.5 and the standard deviation is 1.5, so you’ll use a deviation of 1.5
to nd values that stray from the mean. This means that the values that are 1 standard
deviation from the mean are 11 and 8, which is the mean (9.5) plus or minus the standard
deviation (1.5). The values that are 2 standard deviations from the mean are 12.5 and 6.5,
which you get from adding and subtracting 3 (
2 15.
) from the mean of 9.5. The values that
are 3 standard deviations from the mean are 14 and 5, which you derive by adding and sub-
tracting 4.5 (
315.
) from the mean.
So to solve this problem, you nd that the values that are 2.5 standard deviations from the
mean are 13.25 and 5.75, because
2 515375.. .
. Look for an answer choice that’s more than
13.25 or less than 5.75. The answer is 13.5, Choice (E).
14. C. The four angles lie along a straight line, so they add up to 180 degrees. (If you need a
refresher on the properties of angles, read Chapter14.)
Although it’s lovely to know that BX bisects (which means cuts exactly in half) the two
angles on the left side and that BZ bisects the two angles on the right side, without the
measure of at least one of the angles, you have no way of knowing the measurements of
any of the angles. So Statement (1) isn’t sucient, and the answer has to be Choice (B),
Choice (C), or Choice (E).
Statement (2) gives you only one of the angle measures, which by itself doesn’t clarify the
measure of
ABX
any better than Statement (1) does. Statement (2) isn’t sucient.
But remember that we said that for Statement (1) to work, you just need a value for at least
one of the angles. Well, Statement (2) provides that value. Taken together, the two state-
ments allow you to solve for the measure of
ABX
. You can stop right there. The correct
answer is Choice (C).
You don’t have to actually gure out the measurement of the angle, but because we’re so
thorough, we’re going to go through the calculations for you anyway. This step is unneces-
sary on test day. Knowing that BZ bisects
YBC
and that
YBZ
measures 60 degrees allows
CHAPTER 18 All Together Now: A Mini Practice Quantitative Section 279
you to deduce that
ZBC
is also 60 degrees. Additionally, you’ve now accounted for 120 of
the total 180 degrees allotted for the four angles, which leaves you 60 degrees to play with.
Finally, because BX bisects
ABY
, two equal angles remain. Two equal angles that together
equal 60 degrees must equal 30 degrees each, because
60
2
30
.
15. D. To nd the total distance of Traci’s trip, set up an equation that expresses the sum of the
three separate trip portions. Let x equal the total distance in miles. Traci stopped to rest
after she traveled
1
3
of the total distance, so the rst part of the trip is
1
3
x. She stopped
again after she traveled
1
4
of the distance remaining between her rst stop and her destina-
tion, which is the total distance she traveled minus the rst part of her trip. You can
represent the second part of the trip mathematically, like this:
1
4
1
3
xx
The third part of the trip is the remaining 200 miles. Add up the three parts of the trip to
set up the equation and solve for total distance:
xx
xx
xx
xx
xx
x
x
1
3
1
4
1
3
200
1
3
1
4
3
3
1
3
200
1
3
1
4
2
3
200
1
3
1
6
200xx
At this point, you can make it easier on yourself by multiplying each expression on both
sides by 6 to get rid of the fractions:
2 1 200 6
31200 6
1 200 3
400
xx x
xx
x
x
,
,
,
Traci traveled a total distance of 400 miles, so the correct answer is Choice (D).
16. E. This problem seems simple, but if you try to solve it too quickly, you may miss some-
thing. So consider all possibilities.
Evaluating Statement (1) can be tricky. Don’t jump to the conclusion that if the lowest
common denominator (LCD) of the two fractions is 10, then
a
b
must have a denominator of
10 and, therefore, b = 10.
The value of b could also equal 2, and the two fractions would still have an LCD of 10.
Because b has two possible values, Statement (1) is insucient. Therefore, the answer is
Choice (B), Choice (C), or Choice (E).
Statement (2) is easier to evaluate. The value of the numerator has no bearing on the value
of the denominator, so the fact that a = 3 is irrelevant to the value of b. Statement (2) is
also insucient, which means the answer is either Choice (C) or Choice (E).
Knowing that a = 3 tells you nothing about whether b is 10 or 2, which means that the two
statements together are still insucient to answer the question.
280 PART 4 Conquering the Quantitative Section
17. C. You could try to solve for n, but a faster and easier way to approach this problem is to
plug each of the answer choices into the given equation and pick the one that doesn’t make
the expression true:
•
Choice (A) gives you 1. Plug in 1 for x in the equation:
13 4
n
. Doing so makes n = 1, which
is a positive integer. Because 1 is a possible value for x, Choice (A) is wrong.
•
If you substitute 13 from Choice (B), you get
13 34
n
. And 13 + 3 is 16 and
4 16
2
. If n = 2,
it’s a positive integer, so eliminate Choice (B).
•
For Choice (C), you substitute 45 into the equation:
4534
n
. The equation comes out to
484
n
, and although it may seem like 4 could be a root of 48, it’s not. There’s no way n
could be a positive integer when x = 45. Choice (C) is the correct answer. You can choose
Choice (C) and go on, or you can check the last two answers just to be sure. Your decision
depends on how much time you have remaining.
•
If you plug in 61 from Choice (D) into the equation, you get
613 4
n
. And 61 + 3 = 64,
which is
4
3
. But 3 is a positive integer, so Choice (D) can’t be right.
•
Choice (E) is 253, and 253 + 3 = 256. And
256 4
4
, which would make n = 4, a positive
integer. Choice (E) makes the equation true, so it’s the wrong answer.
Be careful when you answer questions that ask you to nd the answer that can’t be true.
In these cases, if an answer choice works, you have to eliminate it rather than choose it.
Keep reminding yourself of your goal.
18. B. The rst statement provides an equation that contains b, but notice that b is squared, so
it’s likely the solution for b in this equation could be either positive or negative. You can
perform a quick check to be sure. The left side of the equation equals 1, so the exponent
must equal 0. Any value to the power of 0 is equal to 1. When you set the exponent equal
to 0 and solve, you get two possible values for b:
b
b
b
b
2
2
40
4
4
2
Statement (1) isn’t sucient, so eliminate Choices (A) and (D).
At rst glance, Statement (2) appears insucient as well because it contains more than one
variable, but check it to be sure. First, make the bases equal:
39
33
42
42 2
()()
()
()
bc bc
bc
bc
Then set the exponents equal to each other to discover whether you can solve for b:
b cbc
b
cbc
bb
b
42 2
42
22
42
4
()
The minute you realize that the c values cancel, you know that you can solve for b. The
answer must be Choice (B).
19. B. Apply the average formula to nd the current month’s average number of automobiles
sold. To nd the sum, you need to add all the values represented on the plot. This stem-
and-leaf plot presents a set of values in terms of their tens and ones digits. The left column
CHAPTER 18 All Together Now: A Mini Practice Quantitative Section 281
is the tens digit, and the right column is the ones digit for each of the numbers of
automobiles sold. Use data to nd the sum:
12 15 17 21822223 24 32532334
38 23950
() () () ()
() 52 61 660
Enter this data into the average formula:
A
A
A
sum of autos
# of autos
660
22
30
At this point, you may notice that to obtain an average of 35 autos, each sales associate
needs to sell 5 additional autos.
If this isn’t obvious at rst, you can apply the formula again to determine the total number
of additional autos the sales associates need to sell next month to achieve an average of
35autos sold per salesperson:
35
660
22
770
660
110
x
x
x
This number is the total number of additional autos the sales associates need to sell next
month to reach management’s goal, but the question asks for the average number each
sales associate needs to sell to achieve an average of 35 autos per salesperson. So divide
110 by 22:
110
22
5
On average, each sales associate needs to sell 5 additional automobiles to reach an average
of 35 autos per salesperson.
20. A. This question requires basic simplication. Begin by canceling terms. Because the whole
numerator is squared, you rst need to factor every term in the parentheses. Take them
one-by-one and apply process of elimination to the answer choices as you go.
4 16
2
Divide the coecients of 16 and 2 to get 8 and eliminate Choices (D) and (E) because they
don’t have a coecient of 8. Continue by squaring the variables in the numerator. When
you take an exponent to another power, you multiply the exponents:
( )aa
42 8
( )bb
32 6
The new expression is
8
86
22
ab
ab
.
Divide the variables by subtracting the exponents:
a
a
a
8
2
6
b
b
b
6
2
8
Combine the components to get a nal answer of
8
68
ab
.
282 PART 4 Conquering the Quantitative Section
If you picked Choice (B), you subtracted the 2 from 6 when you worked with the b expo-
nents. When you subtract a negative value, you actually add the value. If you picked
Choice(C), you added the exponents when you squared them instead of multiplying them.
21. A. Notice the rst statement gives you a ratio that contains both a and b. This looks
promising. Set up the ratio by translating English to math:
025
2
2
3
. a
b
. It should be clear that
you can solve this equation for
a
b
, but if you want to sure, here’s this solution:
025
2
2
3
0
75 4
0
75 4
4
075
.
.
.
.
a
b
ab
a
b
a
b
Statement (1) is sucient, so you eliminate Choices (B), (C), and (E) and move on to
Statement (2). When you translate Statement (2) into a math equation, you get
a b42
,
which you can solve for a or b, but not for
a
b
:
ab
ab
a
b
42
24
2
4
Statement (2) isn’t sucient, so Choice (D) is out, and Choice (A) is the answer.
22. C. Akhil begins with an initial CD investment of $1,200. Every six months he makes 1.05%
on his existing money. So after the rst six months, Akhil has 1.0105 times the $1,200
initial investment, or $1,212.60. But the balance doesn’t increase by $12.60 every six
months because Akhil makes 1.05% on the new existing balance, So after one year, he has
1.0105 times $1,212.60 instead of $1,200, which is a balance of $1,225.33. At a year and a
half, Akhil has 1.0105 times $1,225.33, or $1,238.20. Six months later the CD matures after
another 1.05% is added to Akhil’s balance.
$, .. $, .1 238 20 1 0105 1 251 20
.
The amount Akhil invests into a second CD is $1,251.20 less the $400 he uses to purchase
the tablet:
$, .$ $.1 251 20 400 851 20
. Pick Choice (C).
You can save some time by making a comparison between what Ahkil earns from com-
pounded interest to what he would earn from simple interest. The amount of compounded
interest earned in a certain time period should be greater than that earned from simple
interest. By multiplying $1,200 by 0.0105, you know he earns $12.60 each 6 months.
Multiplying $12.60 times 4 give you $50.40 earned from simple interest in 2 years, which
would make Ahkil’s balance $1,250.40. When you subtract $400 for the tablet, you learn
that Ahkil would have $850.40 to invest in the second CD if he had earned simple interest.
You can eliminate Choice (B) because he would have earned slightly more with compound
interest but not so much more that you can justify Choices (D) or (E). Choice (C) is the only
value that ts that description!
23. B. The equation to nd slope is
m
yy
xx
12
12
. Simply plug in values in this question. When
you plug the values into the slope equation and solve, you get this:
m
m
54
21
0
1
8
Pick Choice (B) and move on to the next question!
CHAPTER 18 All Together Now: A Mini Practice Quantitative Section 283
24.
E. This is the last question, and it happens to be one of the most dicult ones of the bunch.
At rst, you may think that you can solve this question with two simultaneous equations.
However, when you take a closer look, you see this isn’t the case. To get started, let f = the
cost of a oor seat and b = the cost of a balcony seat. Then evaluate the statements.
If you write out Matthew’s information in Statement (1) in mathematical terms, you get an
equation with two variables:
4 38250fb .
As we’ve said before, you can’t solve an equation with two variables without additional infor-
mation. This statement alone isn’t sucient, so the answer is either Choice (B), (C), or (E).
Likewise, Statement (2)’s information leads to an equation with two variables:
8 6 165fb
This equation alone isn’t enough to solve the problem, so the answer has to be Choice (C)
or Choice (E).
Here’s where you may have gotten prematurely excited. You may have thought that
Statements (1) and (2) provided simultaneous equations that could be manipulated to give
you the value of one of the variables. But if you look more closely, you’ll see that the equa-
tions are exactly the same. When you reduce the second equation or expand the rst, you
have identical equations. Look at the second equation:
8 6 165fb
Divide both sides by 2:
4 38250fb .
You don’t have simultaneous equations at all, and the two statements together won’t
enable you to solve the problem. Mark Choice (E).
Be aware of data-suciency questions that ask you to nd the sum (or dierence, product, or
quotient) of two variables rather than the individual value of one or both because the rule of
thumb that two equations are needed to solve for two unknowns may not apply in such a case. If
Matthew had purchased an equal number of oor seats and balcony seats, let’s say 4 of each, the
equation for his information would have looked like this:
4 48250fb .
. Since the questions asks
for the value of
fb
, the equation for Matthew’s information would be sucient by itself because
you could solve for
fb
by factoring 4 from both sides of the equation.
5
Excelling on
the Integrated-
Reasoning Section
IN THIS PART ...
Find out how to most eectively approach the four
integrated-reasoning question types (multi-source
reasoning, table analysis, graphics interpretation, and
two-part analysis).
Review crucial math, analytical, and data-interpretation
skills you need to successfully reason your way through
this section.
CHAPTER19 Best of Both Worlds: The Integrated-Reasoning Section 287
IN THIS CHAPTER
» Discovering what to expect from
the integrated-reasoning section
» Understanding how the
integrated-reasoning section is
scored
» Planning how to use your time
wisely to answer questions
» Working through the four
integrated-reasoning question
types
Best of Both Worlds: The
Integrated-Reasoning
Section
I
ntegrated-reasoning (IR) questions appear right after the analytical-writing section. The IR
section throws you something completely dierent from the ve-answer multiple-choice
questions you’re probably used to. The 12 questions in the integrated-reasoning section are
formatted in a variety of ways and include tables and graphs to test how well you apply reasoning
skills to dierent scenarios. A lot goes on at once in this section, and this chapter gives you the
information you need to manage it all successfully within the 30-minute time limit.
Understanding What the IR Section Is All About
True to its name, the integrated-reasoning section combines the critical-reasoning skills tested
in the verbal-reasoning section with some of the math skills you use to solve quantitative-
reasoning questions. Therefore, if you’re well prepared for the GMAT’s math and verbal sections,
you should do well in the IR section, too. We explain the details of the IR section and the purpose
behind it in the next two sections.
Chapter19
288 PART 5 Excelling on the Integrated-Reasoning Section
Skills tested
The most common math computations in the IR section involve these areas:
»
Basic statistics, such as average, median, mode, and range
»
Percentages
»
Rate and distance
»
Functions
»
Geometry formulas
You’ll need to apply these essentials of critical reasoning:
»
Basic elements of logical arguments: premises, conclusions, and assumptions
»
How to strengthen and weaken an argument
»
Argument types: cause and eect, analogy, and statistical
You can review the necessary math concepts in Chapters12,13, and14. Read more about evaluat-
ing logical arguments in Chapter6.
Question format
The IR section presents you with 12 questions, one question at a time, and you have 30 minutes
to answer them. Almost every question has multiple parts. To get credit for answering a question
correctly, you have to answer all its parts correctly. You don’t receive partial credit for getting one
part of the question correct. Unlike the verbal- and quantitative-reasoning sections, the IR sec-
tion isn’t computer adaptive. So the order in which you receive questions is preordained and not
based on your performance.
Your IR score is based on your answers to four types of questions. On average, you can expect to
come across about three of each question type on the GMAT, but the actual number of questions
of each type and the order in which they appear may vary. So count on seeing at least a couple of
each of these four question types crop up on your test:
»
Table analysis: This three-part IR question oers you a spreadsheet of values that you can
order in dierent ways by clicking the heading of each column. You use the data to make
judgments about three pieces of information; each of your judgments has to be correct to get
credit for the question.
»
Two-part analysis: Based on a short written explanation of a phenomenon, situation, or
mathematical problem, you come up with the proper assertions or mathematical expressions
that meet the two interrelated criteria presented in the question.
»
Graphics interpretation: A graph or chart gives you all the data you need to complete the
two missing pieces of information in one or two statements. You choose from a pull-down
menu of several answer options to record your answers.
»
Multi-source reasoning: These properly named questions present you with several sources
of information, such as short passages, graphs and charts, and business documents, from
which you draw logical conclusions to answer questions in either of two formats: standard
ve-answer multiple-choice questions and three-part questions that ask you to evaluate
statements.
CHAPTER 19 Best of Both Worlds: The Integrated-Reasoning Section 289
We cover the steps to answering each question type in the section “Approaching Each Question
Type,” later in this chapter.
To assist you with the mathematical computations you may need to make for some of the IR
questions, the GMAT software provides you with a simple calculator. Whenever you need it, you
click the box labeled Calculator and something that looks like Figure19-1 appears. You select its
functions by using your mouse. Don’t get too attached to it, though; the calculator is available
only for IR questions, so you won’t be able to use it in the quantitative-reasoning section. If you
want more information on the calculator’s features, see the nearby sidebar “Using the GMAT
calculator.”
USING THE GMAT CALCULATOR
The calculator in the GMAT IR section looks a lot like the calculator you can purchase at your local dollar
store or the one that appears when you access the Microsoft calculator accessory. It has minimal fea-
tures but everything you need to work out the calculations in the IR section. When you click on Calculator
at the top of your screen, the tool pops up. You can move it anywhere on the screen by dragging it with
your mouse. It stays open until you close it by clicking the X in the upper-right corner of the tool.
The number and operation keys work just like a regular calculator. You can clear a single entry with the
CE key or just the right digit with the
key. Start over again from scratch by clicking the C key, which
wipes out the entry and all its associated computations.
Unlike a scientific calculator, the GMAT calculator doesn’t follow the order of operations. So if you enter
4 510
, you get 90 instead of 54. To get the right value, you have to enter the values in the proper
order,
5104
.
The MS key stores a value to the memory. You can add values to the memory with the M+ key and
subtract them with the M- key. To access the value in the memory, click MR.To clear it, click MC.
The ± changes a positive value to negative and a negative value to positive. The / key means divide, and
the * key multiples. To find the square root of 34, you enter 34 and click on √. To find 35 percent of 70,
you enter
735
and hit the % key. Though we doubt you’ll use it much, the 1/x key finds the reciprocal
of any integer. To find the value of the reciprocal of 4, for example, you enter 4 and click the 1/x key—
voila!— 0.25 appears.
FIGURE19-1:
The GMAT
calculator.
© John Wiley & Sons, Inc.
290 PART 5 Excelling on the Integrated-Reasoning Section
Because using a computer calculator can be awkward, you’ll likely answer most IR questions
more quickly by using estimation or working out calculations by hand on your noteboard. Save
the calculator for only the most complex or precise computations.
Figuring Out How the IR Section Is Scored
Like the score you receive for the analytical-writing section, your integrated-reasoning score
has no inuence on your overall GMAT score, which consists of the combination of only your
quantitative-reasoning and verbal-reasoning scores. Based on your performance in the IR section,
your raw score is converted to a scaled score that ranges in whole numbers from 1 to 8 and is
recorded separately from all the other scores.
MBA programs decide how they use your IR score and may choose to disregard it altogether. So
your IR score is unlikely to make much of an impression unless it’s unusually low, in the 1 to
3 score range, or really high, such as the rare 7 or 8. A midrange score of 4, 5, or 6 likely won’t
signicantly hurt or help your chances of admission.
Making the Most of Your Time
If you’ve already calculated that answering 12 questions in 30 minutes gives you 2.5 minutes to
answer each question, you may be celebrating the fact that that gives you even more time per
question than you have for the quantitative- and verbal-reasoning sections. Don’t get too excited
just yet. Almost every IR question has multiple parts, and you have to answer all parts of the
question correctly to be credited with a correct answer. When you consider the average number of
sub-questions contained within each of those 12 questions, the actual number of IR answers you
have to come up with in 30 minutes may be as high as 30. Therefore, you have to use your time
wisely as you move through the section.
You’ll likely feel the time crunch more ercely in this section than the others. We provide some
coping skills to help you through it:
»
Conceal the timer. To maintain your sanity, refrain from constant clock-watching. Hide the
timer on the computer by clicking on it. After you answer about three questions, reveal the
timer by clicking on it again. It counts down from 30 minutes, so if you’re at 22 minutes, you’re
cruising comfortably. If you’re at 21 or fewer, you may need to make some more calculated
guesses to move through the section at a successful pace.
»
Know when to move on. Discipline yourself to submit your best stab at an answer if you nd
yourself spending more than several minutes on any one question. You don’t want to sacrice
getting to an easy, less-time-consuming question because you’ve worked too long on a harder
question. You can’t go back and revisit questions after you submitted your answers, so this
practice may be dicult for you, especially if you tenaciously seek perfection. Take a deep
breath, mark your best guess, and move on to what lies ahead.
»
Write stu down. Don’t be afraid to spend a little time upfront analyzing the loads of data in
some IR questions. Unless you’re someone who can juggle a lot of details in your head, you
should write on your noteboard as you think. A little note-taking may save you from reading
information over again, which is a real time-waster.
CHAPTER 19 Best of Both Worlds: The Integrated-Reasoning Section 291
»
Whisper to yourself. Studies show that processing information is easier if you speak out loud.
Don’t be afraid to whisper your way through some of the more complex problems the IR
section throws at you. You’ll likely take the test in a cubicle-like setting, so if you speak quietly,
you won’t disturb anyone.
Approaching Each Question Type
Each of the four IR question types tests your analytical ability in a slightly dierent way, so your
approach depends on the question format. This section outlines the important considerations for
handling each type.
Table analysis
Table-analysis questions present you with a table that contains several columns of data, similar
to the one in Figure19-2. As you can see, a little bit of explanatory material precedes the table,
but don’t waste too much time reading those words. Usually, everything you need to answer the
question appears in the data table.
The Sort By feature at the top of the table allows you to organize the information by column
heading, an element that comes in handy when you analyze the three statements that follow the
table. When you click on Sort By, a drop-down menu of all column headings appears. Clicking on
the column heading in the menu causes the table to rearrange its data by that category. So if you
were to click on Cuisine Type in the drop-down menu in Figure19-2, the table would rearrange the
order of the rows alphabetically so that all the American restaurants would be listed rst, followed
by the Asian, Italian, Latin, Mexican, Steakhouse, and Seafood restaurants, respectively.
Using the information in the table, you decide whether the proper response to each statement is
True or False, Inferable or Not Inferable, Yes or No, or some other similar either/or answer choice
dictated by the specications of the question. Then you indicate your choice by clicking on the
circle next to the appropriate answer.
These questions require you to manipulate data and make observations and calculations. Some of
the most common calculations are statistical ones, such as percentages, averages, medians, and
ratios, so table-analysis questions can be some of the easiest questions to answer in the IR sec-
tion. Here’s how to make sure you get them right:
»
Jump to the question immediately. Most of the information you need appears in the table,
so you rarely need to read the introductory paragraph that comes before the table. Glance at
the column headings to get an idea of the type of information the table provides, and then
move promptly to the question.
»
Read the question carefully. You’re most likely to get tripped up on these questions simply
because you haven’t read them carefully enough to gure out exactly what data they ask you
to evaluate.
»
Isolate the relevant column heading. Often, the key to answering a table-analysis question
is ordering the data properly. Quickly gure out which column provides you with the best way
to arrange the data and sort by that column. For example, if you were asked for the neighbor-
hood on the list with the most participating restaurants, you’d sort by Neighborhood.
292 PART 5 Excelling on the Integrated-Reasoning Section
»
Make accurate computations. Determine exactly what calculations the question requires
and perform them accurately, either in your head or on the calculator. Based on Figure19-2,
for example, you could easily gure the restaurant with the greatest average daily number of
meals sold by sorting by that column and glancing at the highest number. However, calculating
which participating restaurant in the Downtown neighborhood brought in the greatest
average daily gross revenue may require the calculator to multiply each restaurant’s price per
meal by its average daily number of meals sold.
»
Make use of your noteboard. Keep track of more complex calculations on your noteboard.
As you calculate each Downtown restaurant’s average daily gross revenue, for example, record
the results on your noteboard. Then you can easily compare the four values without having to
memorize them.
You can apply these strategies to a sample question.
For each of the following statements, select Yes if the statement is true based on the informa-
tion provided in Figure19-2. Otherwise, choose No.
FIGURE19-2:
Sample
table-
analysis
format.
© John Wiley & Sons, Inc.
CHAPTER 19 Best of Both Worlds: The Integrated-Reasoning Section 293
Statement (A) references two columns, Price Per Meal and Neighborhood. Sorting by Neighborhood
makes more sense because it lists all Downtown restaurants together so that you may better view
and compare each Downtown restaurant’s price per meal. After you’ve sorted by Neighborhood,
the table looks like this:
This arrangement allows you to see that two participating restaurants in the Downtown neigh-
borhood charged $20 per meal and two charged $40 per meal. The number of $20 meals sold by
both restaurants is 288, and the number of $40 meals sold at the two other restaurants is 314. To
nd the weighted average, multiply $20 by 288 and $40 by 314. Add the two products and divide
by the total number of meals sold (602):
A
A
A
()()
,,
.
20 288 40 314
602
5 760 12 560
602
30 43
Because $30.43 is approximately $30, you can say that the average price of a Downtown meal
was $30. The answer is Yes.
294 PART 5 Excelling on the Integrated-Reasoning Section
You’ve already gured out the second calculation for Statement (B). The average price per meal
at a Downtown restaurant is about $30. You can write
D 30
on your noteboard to remind you. All
the Uptown restaurants charged $40 per meal, so the average price per meal in Uptown is greater
than the average price in Downtown. Select No.
Statement (C) again focuses on one neighborhood, so you don’t have to resort to the table. The one
restaurant that included wine in the meal price sold 160 meals on average per day, which is more
than the 152 and 151 sold by the other two restaurants in the neighborhood. The answer is Yes.
Table-analysis questions may not require that you use all the data provided. For example, you
didn’t need to evaluate Cuisine Type for any of the question parts in the example question. Don’t
worry if you don’t use the data in some columns at all. Part of the task in answering table-
analysis questions is knowing what data is important and what’s irrelevant.
Two-part analysis
When you see a paragraph or two of information that sets you up to choose two pieces of infor-
mation from a table with three columns, you know you’re dealing with a two-part analysis ques-
tion. You select the answer for the rst part of the question in the rst column and the answer to
the second part in the second column. The third column provides the set of possible answer
choices for each part.
Reading the explanatory paragraph for these questions is absolutely essential. It provides the
conditions you need to consider and claries what each part of the question asks for. Read each
possibility in the third column carefully. Often, the dierences among the options are subtle.
The GMAT usually uses the two-part analysis question to test mathematical skills (such as gur-
ing functions and the properties of geometric shapes) and verbal logical reasoning abilities (such
as strengthening and weakening arguments). Often the best way to gure out the answer for the
math variety is to try each of the possible values to see which ones fulll the requirements. Usu-
ally, the best way to answer the verbal type is by process of elimination.
The following two sample questions give you an example of a math two-part analysis and a verbal
two-part analysis.
A set of expressions consists of a total of four expressions: these three expressions
28 46 2nn n,,
and one additional expression. From the following expressions, select the
one that could be the fourth expression in the set and the one that could be the resulting arith-
metic mean of the four expressions in the set. Make only one selection per column.
CHAPTER 19 Best of Both Worlds: The Integrated-Reasoning Section 295
Approach this question by trying out the possible answer choices as potential fourth expressions
to see which, when it’s included with other expressions in the set, results in an arithmetic mean
that’s another of the possible answer choices.
First, evaluate the three provided expressions. All contain one-digit values that are multiplied by
n and then have a one-digit value added or subtracted from that term. So evaluate similar expres-
sions, such as Choices (B), (C), and (F) before you consider less similar expressions, such as
Choices (A), (D), and (E).
If Choice (B),
32n
, were the fourth expression, the average mean of the set would be the result
of applying the average formula:
28 46232
4
12 12
4
33
nn nn
A
n
A
nA
Because
33n
isn’t one of the answer choices, you know that
32n
can’t be the fourth
expression.
Try Choice (C),
32n
. If you wrote your calculations for
32n
on your noteboard, you know that
the rst term of the average mean is the same because the 3n doesn’t change.
28 46232
4
12 8
4
3 2
nn nn
A
n
A
nA
This value is a possible option. When the fourth expression in the set is
32n
, the average mean
of the set is
32n
. Select Choice (C) for the rst column and Choice (B) for the second. Only one
possible set of answers exists, so if you’re condent about your calculations, you don’t have to
consider the other expressions. Submit your answer and move on.
Joseph: Health insurance premiums are growing at an alarming rate. This is, in part, because many
hospitals and clinics bill for unnecessary diagnostics and tests that inate the subsequent amount
that insurers pay out to them. These expenses are then passed on to consumers in the form of
increased insurance premiums. Therefore, reducing the number of unnecessary tests performed
by hospitals and clinics will eectively curb the rise in health insurance premiums.
Ronald: Often, the unnecessary diagnostics that you speak of are the result of decisions made by
doctors on behalf of their patients. Doctors usually choose the diagnostics that allow them to bill
insurers for more money but may not necessarily benet the patient in a meaningful way or
inuence the course of treatment chosen. As a result, in order to succeed in reducing the number
of unnecessary tests, patients should be allowed to decide which course of diagnostics they would
like to undergo.
In the following table, identify the unique assumption upon which each argument depends.
Make only one selection in each column: one in the rst column for the best representation of
Joseph’s assumption in his argument and one in the second column for the best representation
of Ronald’s.
296 PART 5 Excelling on the Integrated-Reasoning Section
Whereas the sample math two-part analysis question required you to gure out the answers to
both parts at the same time, this verbal-reasoning sample question is more easily handled one
column at a time. First, consider the assumption that’s most likely part of Joseph’s argument.
Then consider the one that pertains to Ronald’s.
The assumption is usually the statement that best links the premises of the argument to its con-
clusion. For details on evaluating arguments, see Chapter6.
Following are the premises of Joseph’s argument:
»
Hospitals and clinics are billing health insurance companies for unnecessary and expen-
sive tests.
»
This practice has caused health insurance companies to pay inated rates to hospitals and clinics.
»
The result is that health insurance companies are compensating by raising consumers’ health
insurance premiums.
Based on these premises, Joseph concludes that reducing unnecessary tests will signicantly
control the rise in health insurance premiums.
To nd the assumption that provides a link between the cessation of the unnecessary tests and
a signicant eect on increasing healthcare premiums, begin by narrowing your options. Joseph
doesn’t mention doctors in his argument, so you can eliminate Choices (A) and (D). Choice (E)
addresses healthcare premiums but not unnecessary tests, so it’s out. Choice (C) concerns other
insurance industries, so it has nothing to do with Joseph’s argument about healthcare premi-
ums. The best option for Joseph is the assumption that unnecessary tests make up a signicant
CHAPTER 19 Best of Both Worlds: The Integrated-Reasoning Section 297
portion of insurance billing. If they make up just a small portion, eliminating tests wouldn’t
have a signicant impact on the rising cost of healthcare premiums. Mark Choice (B) in the
column for Joseph.
Now evaluate Ronald’s argument. Here are his premises:
»
Doctors order unnecessary tests to increase their earnings.
»
Patients should be able to choose their tests.
»
Putting the decision regarding diagnostics and tests in the patients’ control would reduce the
number of unnecessary tests.
So you’re looking for the assumption that links patients’ decisions to fewer unnecessary tests.
Notice that Ronald doesn’t address healthcare premiums at all, so you can condently eliminate
Choice (E). Choice (B) is out because you’ve already attributed it to Joseph. Choice (C) doesn’t work
for the same reason that it doesn’t work for Joseph. Ronald’s argument concerns only healthcare.
Of the two remaining options (Choices [A] and [D]), only Choice (D) relates to patients’ decisions.
Only if patients make decisions dierently than doctors do would putting patients in control
lessen the number of unnecessary tests. So you mark Choice (D) in the column for Ronald.
Graphics interpretation
Not surprisingly, graphics interpretation questions require you to interpret graphs. You may see
line graphs, bar graphs, pie charts, Venn diagrams, and so on. Based on the information displayed
in the graph, you ll in two separate blanks by selecting the best option from a drop-down menu
for each blank. (In the example question later in this section, we include the answer options in
parentheses.) You have to complete both blanks correctly to get credit for one graphics interpre-
tation question.
The information you need to ll in the blanks comes primarily from the graph, so make sure you
know how to read charts and graphs. Chapter20 provides a review of the most common GMAT
charts and graphs to refresh your memory.
Here are some other tips to help you eciently move through graphics interpretation questions:
»
Analyze the graph or chart to determine exactly what information it provides and how.
Observe the labels and examine the numerical increments carefully.
»
Click on Select One to view all the answer options. To see the possible answers in the
drop-down menu for each blank, you have to click on the box that says Select One. Filling in
the blank is much easier when you’re limited to just the several available choices. Don’t
attempt to answer the question without seeing the answer choices rst.
»
Eliminate illogical answer choices. Approach the two parts of a graphics interpretation
question much like you would a standard multiple-choice question. Eliminate obviously incorrect
options and use your reasoning skills to select the best answer from the remaining choices.
»
Make estimations. The data in charts and graphs are rarely precise, so most of your calcula-
tions are estimates or approximations that you can work out on your noteboard or in your
head rather than on the calculator.
298 PART 5 Excelling on the Integrated-Reasoning Section
Here’s a sample graphics interpretation question to consider.
Scientists, health professionals, and life insurance agents are interested in examining the per-
centage of people in a population who will live to a certain age. One way to measure this infor-
mation is to look at the percentage of the population who has died after a certain number of
years. The following graph displays the results of such a study.
Approximately _____ (10, 40, 60, 80) percent of the population lives to at least 80 years of
age. A person who was a member of the study population would still have an 80 percent chance
of being alive at around a maximum age of _____ (15, 35, 55, 80) years.
Filling the rst blank in the question tests your graph-reading skills. Find 80 years of age on
the horizontal axis. Move your nger from the 80-year mark upward on the graph until you
reach the plotted curve. Move your nger to the left to see that at 80 years, about 60 percent of
people have died. Don’t stop there and choose 60 percent, however. The question asks for how
many are alive at the 80-year mark. Subtract 60 from 100 to get that approximately 40 percent
of the population lives to at least 80 years. The correct answer is 40 percent.
To complete the second blank, make sure you look at the answer choices rst. Because the state-
ment concerns the maximum value, consider higher ages rst. The oldest option is 80, but it’s
very unlikely that 80 percent of people are alive at age 80, so try the next highest age, 55. Move
along the graph until you reach 55 years. At 55 years of age, 20 percent have died, leaving a maxi-
mum of 80 percent alive. Ages above 55 can’t be right, so 55 is the correct answer.
If you start with the rst option of 15 years, you may be misled. Note that the graph shows you
that at about 15 years of age, less than 5 percent of people have died, which means that more than
95 percent of the population are still alive. That’s more than 80 percent, but the statement regards
the maximum age where 80 percent of the population is still kicking, so 15 can’t be correct.
Multi-source reasoning
The only IR question type with more than one question that pertains to a set of data is the multi-
source reasoning question. For this question type, the GMAT presents dierent kinds of informa-
tion in a series of two or three tabs. Each tab conveys a relevant aspect of a set of circumstances.
The topics of the scenarios vary greatly. You may have information concerning a certain scientic
CHAPTER 19 Best of Both Worlds: The Integrated-Reasoning Section 299
phenomenon, such as black holes or plant photosynthesis, or you may be asked to apply data that
relates to business situations, such as hiring decisions or event planning.
At least one of the tabs in the set contains several paragraphs of written information on a subject.
Others may contain additional paragraphs or data contained in tables, charts, or graphs. You use
the resources in all tabs to answer several questions, most of which have several parts. For exam-
ple, Figure19-3 shows you the rst tab for a sample multi-source reasoning scenario regarding
guest reservations for a hotel’s wedding block. The e-mail in this tab sets up the situation and
provides you with the guidelines for the reservation.
Figure19-4 shows what you nd when you click on the second tab: language from the contract
between the Pearson family and the resort.
When you click on the nal tab, you may see a table with relevant data, such as the one in
Figure19-5, which shows the wedding guest list and their reservation status.
FIGURE19-3:
Sample
multi-source
reasoning
format,
background
tab.
© John Wiley & Sons, Inc.
FIGURE19-4:
Sample
multi-source
reasoning
format,
contract tab.
© John Wiley & Sons, Inc.
300 PART 5 Excelling on the Integrated-Reasoning Section
The multi-source reasoning questions appear in one of two formats: three-part table (similar to
table-analysis questions) or standard ve-answer multiple-choice. Keep in mind that you have
to answer all three parts of the rst format to get credit for the one question. The multiple-choice
format may be one of the easiest questions to answer in the IR section. You can use the process of
elimination to narrow the answers, and you have to choose only one correct answer to get full
credit for the question.
The trickiest aspect of answering multi-source reasoning questions is sifting through the pleth-
ora of information to discover what’s relevant. Depending on the scenario, you may have to juggle
information in tables, diagrams, articles, and so on to come up with correct answers.
Here are some pointers to help you with the task:
»
Summarize each tab. As you read through the information in each tab for the rst time,
record pertinent points to help you remember which tab holds what type of data. That way
you don’t have to continually ip back and forth between screens as you answer questions. For
example, summarize the contract details in Figure19-4 on your noteboard with quick nota-
tions such as 9/7, 8, & 9 = $135/night; < 3 nights = $150/night; before/after 9/7 or 9/9 = $175/night.
»
Make connections. After you’ve seen the information in each tab, synthesize facts and gures
from one tab with correlative data from another. Keep track of your ndings on your note-
board. For example, you should notice as you read the information in Figures19-4 and19-5
that you can correlate the data in the table in the nal tab with the room-charge specications
in the second tab to gure out how much each guest will pay for resort rooms.
»
Rely on what the test gives you. Some of the topics in multi-source reasoning scenarios may
be familiar to you. Although familiarity may make the information more accessible to you, it
may also inuence you to answer questions based on what you know instead of what the
exam tells you. For example, you shouldn’t answer any questions about the Pearson wedding
sample scenario based on what you know about hotel booking from your own experience as a
front-desk manager.
Here’s another sample multi-source scenario with a couple of questions to help you get more
acquainted with the question type. This scenario has only two tabs, each conveying an opposing
opinion from two scientists on a specic scientic phenomenon.
FIGURE19-5:
Sample
multi-source
reasoning
format,
guest
list tab.
© John Wiley & Sons, Inc.
CHAPTER 19 Best of Both Worlds: The Integrated-Reasoning Section 301
Consider each of the following statements about atmospheric carbon-dioxide levels and deter-
mine whether Scientists 1 and 2 are both likely to agree by marking either Yes or No:
302 PART 5 Excelling on the Integrated-Reasoning Section
Statement (A) is a nice, noncontroversial statement with which both scientists would agree. Sci-
entist 1 stresses that rising carbon dioxide is linked to higher temperature (another factor), while
Scientist 2 discusses feedback factors, which are factors that respond to carbon-dioxide changes
and will, in turn, aect the carbon dioxide. Select Yes for Statement (A).
To answer Statement (B), notice that Scientist 2, who refers to improved energy technology,
clearly disagrees with the statement, but so does Scientist 1, who mentions the possibility that
carbon-dioxide levels will stabilize. Neither scientist would agree with Statement (B), so the
answer is No.
Scientist 2 disagrees with Statement (C) and actually discusses a slowing down in the rate of
carbon-dioxide-level increase. Because at least one of the scientists would disagree with the
statement, the answer to Statement (C) is No.
The next question is in multiple-choice format.
Which of the following statements does only Scientist 1 support?
(A) A change in atmospheric water vapor could signicantly aect global temperatures.
(B) The increase in atmospheric carbon-dioxide concentration from 280 parts per million to
360 parts per million that has occurred over the last 150 years is not expected to aect
climactic change negatively in the future.
(C) Recent increases in atmospheric carbon dioxide have surpassed those predicted by tem-
perature models dealing solely with carbon-dioxide models.
(D) Temperature uctuations will match carbon-dioxide changes when carbon-dioxide
changes are abrupt.
(E) Increases in carbon-dioxide concentration would lead to changes in feedback factors that
would compound any temperature increase associated with more carbon dioxide in the
atmosphere.
Focus on the information in the rst tab. Scientist 1 mentions a match between carbon dioxide
and temperature variations and then uses the recent large change in carbon-dioxide levels as
evidence that signicant changes in temperature will occur. Scientist 1 goes on to discuss how
continued sharp increases in atmospheric carbon dioxide will lead to similar dramatic tempera-
ture increases. Scientist 1 implies that the recent carbon-dioxide changes have been unprece-
dented. The data during the past 160,000 years show a correspondence between temperature and
carbon-dioxide uctuations, but this correspondence has occurred in the absence of the dramatic
changes the earth is now and soon will be experiencing. For Scientist 1 to use the uctuation cor-
respondence as evidence for what will soon happen, she must assume that the correspondence
will continue in light of current and near-future sharp changes. So Choice (D) is correct.
Choice (A) is supported by Scientist 2, and neither scientist would support Choices (B), (C), or (E).
In fact, Scientist 1 actually says that an increase in atmospheric carbon-dioxide concentration
from 280 parts per million to 360 parts per million can cause “signicant and detrimental cli-
mactic changes in the near future.”
CHAPTER20 Deciphering Data in Charts and Graphs 303
IN THIS CHAPTER
» Taking a ve-step approach to
integrated-reasoning questions
» Tackling tables to get the data you
need
» Getting a grasp on bar and line
graphs
» Circles and more circles: Pie charts
and Venn diagrams
Deciphering Data in Charts
and Graphs
N
ot every integrated-reasoning question relies on a chart or graph, but most do. This chapter
reviews the characteristics of the ways the GMAT represents data in the integrated-
reasoning section and explains how to read each type in the most ecient way.
The charts and graphs you’ll encounter on the GMAT integrated-reasoning section display data
in a variety of formats. You interpret the data provided in tables, bar graphs, line graphs, scatter
plots, pie charts, or Venn diagrams, and then you apply your analysis to draw conclusions about
a bunch of scenarios. You get to compare statistics, identify trends or lapses in trends, make pre-
dictions for the future, and so on.
Approaching Integrated-Reasoning
Data in Five Easy Steps
Most integrated-reasoning questions contain a chart or graph. You won’t have much time to
waste, so it’s a good idea to know how to extract data from the various types of charts and graphs
before you sit down in front of the computer on exam day. Regardless of the graph or chart you’re
working with, you’ll follow a similar, ve-step approach:
1. Identify the type of chart or graph.
Graphs display data in dierent ways, so start by recognizing which graph or chart type you’re
dealing with. To make this step easy, we provide detailed information on each of the most
common charts and graphs on the GMAT in this chapter.
2. Read the accompanying question and determine what it asks.
Before you attempt to read the chart or graph, examine the question to gure out exactly what
kind of information you need to answer it.
Chapter20
304 PART 5 Excelling on the Integrated-Reasoning Section
3. Isolate what you need to get out of the chart or graph to successfully answer the
question.
Refer to the chart or graph to discover where it conveys the specic data you need to answer
the question.
4. Read the chart or graph properly.
Examine the chart or graph carefully to spot trends and note where the quantities associated
with each variable appear and how the value of each increment is displayed.
5. Solve the problem.
Use the data you’ve carefully extracted from the chart or graph to come up with the correct
answer to the question.
The remaining sections in this chapter show you how to apply this approach to reading a variety
of charts and graphs.
Translating Information in Tables
Tables report, organize, and summarize data and allow you to view and analyze precise values. For
example, a table can be an eective way of presenting average daily high and low temperatures
in a given area, the number of male and female births that occur each year within a population,
or the ranking of a band’s top-ten hits.
The sample table in Figure20-1 records the four individual event and all-around scores for ve
gymnasts in a local meet. Its data is precise rather than approximated, which allows you to come
up with accurate analyses of the values. For example, you can see from the table that Kate just
barely edged out Jess on the balance beam by a 0.005 dierence in scores.
When you evaluate a table, pay particular attention to the column labels to determine exactly
what kind of information and values it displays. Read carefully to dierentiate values and deter-
mine, say, whether the numbers represent percentages or actual gures. For example, a few
seconds of careful consideration of the values in the sample table in Figure20-1 tells you that the
gymnasts’ all-around score is the sum of the other scores rather than their average. So if a ques-
tion asked you about a particular gymnast’s average score for all events, you’d know you’d have
to compute this calculation rather than report the provided all-around score.
FIGURE20-1:
You’re likely
to see a
table like
this one
as part of
a GMAT
integrated-
reasoning
question.
© John Wiley & Sons, Inc.
CHAPTER 20 Deciphering Data in Charts and Graphs 305
Not surprisingly, tables are the primary source of information in the integrated-reasoning table-
analysis question type. These questions use tables to display data, usually a lot of it. You may also
nd tables in multi-source reasoning and two-part analysis questions. (Chapter19 provides more
detail on how to answer all four integrated-reasoning question types.)
Making Comparisons with Bar Graphs
Bar graphs (also sometimes called bar charts) have a variety of uses. They’re especially good for
comparing data and approximating values. As the name suggests, they use rectangular bars to
represent dierent categories of data (either horizontally or vertically); the height or length of
each bar indicates the corresponding quantity for that category of data.
You see bar graphs most frequently on the GMAT in graphics interpretation questions, but they
may also appear in multi-source reasoning and two-part analysis questions. Simple bar graphs
present the relationship between two variables. More complex bar graphs show additional data by
displaying additional bars or by segmenting each individual bar. We show you how to read simple
and complex bar graphs in the following sections.
Simple bar graphs
Bar graphs provide an excellent way to visualize the similarities and dierences among several
categories of data. Even a simple bar graph, such as the one in Figure20-2, can convey a whole
bunch of information.
The chart heading in Figure20-2 denes the overall category of information: 2009 activity ticket
sales for Pleasantdale High School by group. You don’t need a title for the horizontal axis. It’s
obvious from the chart heading that each bar provides the data for each school group. From the
vertical axis title, you discover that the data represents number of tickets sold rather than the
total revenue from those tickets. In Thousands means that each major horizontal gridline repre-
sents 1,000 tickets. Each of the four minor gridlines between each major gridline represents
200tickets (the four lines divide the segments between the whole number into ve parts, and
1 000
5
200
,
). So the graph indicates that the number of drama club tickets sold was approximately
3,700 because the Drama Club bar ends between the third and fourth minor gridlines above the
3,000 mark. To nd the total number of drama club tickets sold, add 200 for each of the three
minor gridlines and half of that (100) as represented by the half space between the third and
fourth minor gridlines:
3 000 3 200 100 3 700,(),
.
Some GMAT bar graphs may display information for a range of values. An example appears in
Figure20-3. Based on this graph, you can gure that the minimum total number of tickets sold
by all groups in 2009 was the sum of the lowest number for each group (
4 000 5 000 6 000,,,
), or
15,000 tickets. The maximum possible total of tickets sold by the three groups combined was the
sum of the highest value for each category:
5 000 6 000 7 000,,,
, or 18,000.
Graphs with many bars
Altering the design of a bar graph allows you to convey even more information. Graphs with mul-
tiple bars reveal data for additional categories. For example, Figure 20-4 compares the ticket
sales totals for the three groups by year for three years.
306 PART 5 Excelling on the Integrated-Reasoning Section
The legend designates which group the bars stand for. This graph allows you to easily make com-
parisons over the years and among the three groups. For example, it’s easy to see that in 2009,
glee club ticket sales were not only greater than they had been in previous years but also exceeded
sales for either of the other two groups. Perhaps sales were inuenced by the launch of a popular
TV show featuring a high-school glee club!
Segmented bar graphs
Graphs with segmented bars display the characteristics of subcategories. Each bar is divided into
segments that represent dierent subgroups. The height of each segment within a bar represents
the value associated with that particular subgroup. For example, Pleasantdale High can provide
more specic comparisons of the ticket sales during dierent times of the year by using a seg-
mented bar graph, such as the one in Figure20-5.
FIGURE20-3:
Simple bar
graph show-
ing ranges
of values.
© John Wiley & Sons, Inc.
FIGURE20-2:
Simple bar
graph.
© John Wiley & Sons, Inc.
CHAPTER 20 Deciphering Data in Charts and Graphs 307
You apply subtraction to read a segmented graph. The top of each bar is the total from which you
subtract the designations for each subcategory. So for the Football Team bar in Figure20-5, the
total number of tickets sold in 2009 was 4,500. The number of tickets sold in the fall is repre-
sented by the lower segment, which climbs up to about the 4,000 mark. The number of tickets
sold in the spring is the dierence between the approximate total number of tickets (4,500) and
the approximate number of fall tickets (4,000), which is about 500. The graph also reveals that
activity sales for the glee club and drama club occur more consistently across both seasons than
for the football team, which sells many more tickets in the fall than it does in the spring.
Whenever you reference data from a bar graph, you speak in estimates. Bar graphs don’t pro-
vide exact values; that’s not their job. They allow you to make comparisons based on
approximations.
FIGURE20-4:
Bar graph
with
multiple
categories.
© John Wiley & Sons, Inc.
FIGURE20-5:
Segmented
bar graph
with sub-
categories.
© John Wiley & Sons, Inc.
308 PART 5 Excelling on the Integrated-Reasoning Section
Evaluating Line Graphs
Another graph that crops up frequently in GMAT graphics interpretation questions is the line
graph. Line graphs display information that occurs over time or across graduated measurements
and are particularly eective in highlighting trends, peaks, or lows. Typically (but not always),
the x-axis displays units of time or measurement (the independent variable), and the y-axis
presents the data that’s being measured (the dependent variable).
Basic line graphs
The line graph in Figure20-6 shows the garbage production for three cities for each of the four
quarters of 2011. You can tell from the graph that Plaineld produced more garbage in every quar-
ter than the other two cities did, and it’s evident that all three cities produced less garbage in
Quarter 3 than they did in the other quarters.
Scatter plots
Line graphs are extensions of scatter graphs, or scatter plots, which display the relationship between
two numerical variables. These graphs display a bunch of points that show the relationship
between two variables, one represented on the x-axis and the other on the y-axis. For example,
the scatter plot in Figure20-7 plots each city’s population on the x-axis and its garbage produc-
tion on the y-axis. Scatter plots show you trends and patterns. From Figure20-7, you can gure
out that, generally, a direct or positive relationship exists between a city’s population and the
amount of garbage it produces. The graph indicates that this is the case because the data points
tend to be higher on the y-axis as they move to the right (or increase) on the x-axis. You can also
surmise that of the 20 cities listed, more have fewer than 200,000 people than have greater than
200,000 people. That’s because the graph shows a greater number of points that fall to the left of
the 200,000 population line than to the right.
Scatter plots also convey trend and pattern deviations. The GMAT may provide a scatter plot with
or without a trend line. The trend line shows the overall pattern of the data plots and reveals
deviations. The scatter plot in Figure20-7 doesn’t display a trend line, so you have to imagine
FIGURE20-6:
Line graph.
© John Wiley & Sons, Inc.
CHAPTER 20 Deciphering Data in Charts and Graphs 309
one. You can lay your noteboard along the graph to help you envision the trend line if one isn’t
provided. Figure20-8 shows you the trend line for the garbage production graph. With the trend
line in place, you can more easily recognize that the largest city in the county deviates from
thetrend somewhat considerably. Its garbage production is less in proportion to its population
than that of most other cities in the county. You know that because its data point is considerably
below the trend line.
Complex scatter plots
Sometimes the GMAT crams even more information on a scatter plot by introducing another vari-
able associated with the data. The values for this variable appear on the y-axis on the right side
of the graph. This type of graph is just a way of combining information in one graph that could
appear on two separate graphs.
FIGURE20-8:
Scatter
plotwith
trend line.
© John Wiley & Sons, Inc.
FIGURE20-7:
Scatter plot
or scatter
graph.
© John Wiley & Sons, Inc.
310 PART 5 Excelling on the Integrated-Reasoning Section
Figure20-9 shows you an example of a complex scatter plot. It adds another variable (average
yearly income by population) to the mix. The average annual income for each city lies on the
y-axis. The points for one set of data have dierent symbols than those for the other so that you
can distinguish between the two sets. The legend at the right of the graph in Figure20-9 tells you
that garbage production is represented by diamonds, and the symbol for income is a square. The
trend line for the relationship between city population and average yearly income has a negative
slope, which shows you that the smaller the population, the greater the average yearly income.
This trend indicates an inverse relationship between city population and average yearly income.
The GMAT may ask you to identify the relationship between two variables as positive, negative,
or neutral. If the trend line has a positive slope, the relationship is positive; if it has a negative
slope, the relationship is negative. If the trend line is horizontal or the points are scattered with-
out any recognizable pattern, the relationship is neutral, meaning that no correlation exists
between the variables.
When you encounter scatter plots and line graphs with more than two variables, make sure you
keep your variables straight. So if you’re asked a question about garbage production, using
Figure 20-9, you have to use the data represented by the left vertical axis and the diamond
symbol rather than the right axis and the squares.
Like bar graphs, line graphs display approximate values. Use the technique explained in the ear-
lier section “Simple bar graphs” to help you estimate the values associated with each data point
from the axes labels and grid marks on these graphs.
Clarifying Circle Graphs (Also Known
as Pie Charts)
Circle graphs, also known as pie charts, show values that are part of a larger whole, such as percent-
ages. The graphs contain divisions called sectors, which divide the circle into portions that are
proportional to the quantity each represents as part of the whole 360-degree circle. Each sector
FIGURE20-9:
Scatter
plot with
multiple
variables.
© John Wiley & Sons, Inc.
CHAPTER 20 Deciphering Data in Charts and Graphs 311
becomes a piece of the pie; you get information and compare values by examining the pieces in
relation to each other and to the whole pie.
When a graphics-interpretation question provides you with a circle graph and designates the
percentage values of each of its sectors, you can use it to gure out actual quantities. The circle
graph in Figure20-10 tells you that Plaineld has more Republican aliates than Democrat and
that Democrats constitute just over twice as many Plaineld residents as Independents do.
When you know one of the quantities in a circle graph, you can nd the value of other quantities.
For example, if a multi-source reasoning question in the integrated reasoning section provides
you with both the scatter plot in Figure20-7 and the circle graph in Figure20-10 and tells you
that the city of Plaineld was the city in Figure20-7 with the highest population, you can use
information from both graphs to discover the approximate number of Plaineld residents who
are registered Democrats. The city with the largest population in Figure20-7 has around 500,000
residents. Figure20-10 tells you that 32 percent of Plaineld residents are Democrats. So just
about 160,000 (
500 000 032,.
) Democrats reside in Plaineld.
Extracting Data from Venn Diagrams
Venn diagrams, such as the one in Figure20-11, are made of interconnected circles— usually two
or three— and are a great way to show relationships that exist between sets of data. Each data
set is represented by a circle; the interaction of the circles shows how the data relates.
You see Venn diagrams most often in graphics-interpretation questions. For example, the GMAT
could tell you that the Venn diagram in Figure20-11 represents the results of a survey of 100 cat
and dog owners. You know from the diagram that 29 of those surveyed own cats, but no value
appears for the number of dog owners. The shaded portion represents the intersection: the four
members of the survey who own both cats and dogs. If you need to nd the number of those sur-
veyed who own dogs, you can’t simply subtract 29 from 100 because that doesn’t take into con-
sideration the four people who own both types of pets. The total number of people in the survey
who own dogs is actually (100– 29) + 4, or 75.
FIGURE20-10:
Circle graph
or pie chart.
© John Wiley & Sons, Inc.
312 PART 5 Excelling on the Integrated-Reasoning Section
Your calculations can get a little more complicated when not all the members of the general set
are represented by the circles in the Venn diagram. For example, say the survey represented in
Figure20-11 was modied a bit to represent 100 pet owners instead of 100 cat and dog owners.
The 100 members of the survey could own cats, dogs, or other pets. The results of this survey
appear in Figure20-12.
Based on this diagram, the GMAT could pose questions that ask for the number of people who
own only cats but not dogs, the number of people who own at least one cat or one dog, or the
number of those surveyed who own neither a cat nor a dog. Here’s how you’d solve for these three
cases:
»
The number of people who own cats but not dogs is simply the dierence between the
quantity in the cat-owner circle and the quantity of members who own both cats and dogs:
29425
. Of the 100 people surveyed, 25 own cats but don’t own dogs.
FIGURE20-11:
Venn
diagram of
100 cat and
dog owners.
© John Wiley & Sons, Inc.
FIGURE20-12:
Venn
diagram
of 100 pet
owners.
© John Wiley & Sons, Inc.
CHAPTER 20 Deciphering Data in Charts and Graphs 313
»
To nd how many of the surveyed pet owners own at least a cat or a dog, you just need to add
the values in each circle and subtract the quantity in the shaded intersection:
( )29 65 490
.
Of the 100 people surveyed, 90 owned at least one cat or one dog.
»
Figuring the number of pet owners who own neither a cat nor a dog means that you’re looking
for the quantity that exists outside of the two circles. The number of people represented inside
the circles plus the number of people outside of the circles is equal to 100, the total number of
people surveyed. You know the number of people represented by the space inside the circle;
it’s the same number as those who own at least a cat or a dog (90). If x represents the number
of pet owners who don’t have a cat or a dog, the equation would be
90 100x
. When you
solve for x, you gure out that 10 people in the survey owned some pet other than a dog or cat.
So to evaluate Venn diagrams correctly, keep track of the total members in the set and what they
represent. Information in the question will allow you to assess whether the circles represent the
total number of members or whether a subset of members resides outside of the circle, so reading
carefully will allow you to accurately interpret the Venn diagram. When you’ve successfully
gured out the general set and the subsets, extracting information from Venn diagrams is easy.
6
Practice Makes
Perfect
IN THIS PART ...
Bring all your new skills to the table and take a
complete GMAT practice test.
Go over the answers and explanations to nd out how
you did and where you need to improve. Understand
why the right answers were right and the wrong
answers were wrong so that you can answer more
GMAT questions with condence.
Remember: When you’re ready for more, be sure to
take the other online practice tests available with this
book. You can nd instructions for accessing these
tests in the Introduction.
CHAPTER 21 GMAT Practice Test 317
GMAT Practice Test
T
he more practice you get answering GMAT questions before you take the test, the better
you’ll do on exam day. Increase your chances for a top score with the following practice
exam, consisting of three sections of multiple-choice questions and an analytical-writing
prompt. You have to write an essay in 30 minutes, nish 12 integrated-reasoning questions
(located only on the online version of this test) in 30 minutes, complete 37 math questions in 75
minutes, and answer 41 verbal questions in 75 minutes.
To make the most of this practice exam, take the test under conditions similar to those you’ll face
on test day:
»
Find a place where you won’t be distracted (preferably as far from your refrigerator as possible).
»
If possible, take the practice test at approximately the same time of day as when you’ll be
taking the actual GMAT.
»
Use a timer to keep track of the time limits for each section.
»
Take no more than two eight-minute breaks.
»
Mark your answers by circling the appropriate letters in the text. (On the actual GMAT, you’ll
mark your answer by clicking the oval next to the correct answer.)
»
Use a blank piece of paper to simulate the noteboard for keeping notes and making calculations.
»
If possible, complete your essay on a computer with the grammar and spelling correction
functions turned o.
»
When your time is up for each section, put down your pencil and stop working.
After you nish, turn to Chapter22 to check your answers with the answer key and read through
the answer explanations— even the ones for the questions you got right. The explanations may
present a way of approaching a problem that you haven’t considered.
If you want to practice taking the test electronically, go to
www.dummies.com and use your pin
code to activate the online access that accompanies the purchase of this book. (Instructions are in
the Introduction.) You’ll nd this test, along with ve others for even more practice. You can
answer the questions digitally, and the software tabulates correct and incorrect responses. This
summary provides you with a snapshot of which areas you excel in and which areas you may need
to review again.
Chapter21
CHAPTER 21 GMAT Practice Test 319
Answer Sheet
The test is divided into four sections, though only three of the sections appear here in the book.
(You can nd the Integrated Reasoning section in the online version of this practice test.). Sec-
tion1 requires you to write an essay within 30 minutes. Sections3 and4 ask you to select the best
answer among answer choices.
Section1: Analytical Writing Assessment
320 PART 6 Practice Makes Perfect
CHAPTER 21 GMAT Practice Test 321
Section3: Quantitative
Section4: Verbal
322 PART 6 Practice Makes Perfect
Section1: Analytical Writing Assessment
TIME: 30 minutes for one essay
DIRECTIONS: In this section, you’re asked to write a critique of the argument presented. The prompt requests
only your critique and does not ask you for your opinions on the matter.
Think for a few minutes about the argument and organize your response before you start writing. Leave time
for revisions when you’re nished.
You’ll be scored based on your ability to accomplish these tasks:
•
Organize, develop, and express your thoughts about the given argument.
•
Provide pertinent supporting ideas with examples.
•
Apply the rules of standard written English.
DO NOT TURN THE PAGE UNTIL TOLD TO DO SO DO NOT RETURN TO A PREVIOUS TEST
STOP
1. Essay Topic: “Charter schools, which are
learning institutions that are publicly funded
but privately operated, were devised to oer
new opportunities for teachers and to give
students and families alternatives to tra-
ditional, public school settings. They are
supposed to be locally managed to ensure the
same level of accountability to which pub-
lic schools are held. Increasingly, however,
America’s charter schools are being run by
private companies without local interests, and
accountability at the local level is suering as
a result. Statistics also indicate that nearly half
of all new charter school teachers leave within
one year of hiring, so charter schools have
simply not lived up to all they promised.”
Examine this argument and present your
judgment on how well reasoned it is. In your
discussion, analyze the author’s position and
how well the author uses evidence to support
the argument. For example, you may ques-
tion the author’s underlying assumptions or
consider alternative explanations that may
weaken the conclusion. You can also provide
additional support for or arguments against
the author’s position, describe how stating
the argument dierently may make it more
reasonable, and discuss what provisions may
better equip you to evaluate its thesis.
CHAPTER 21 GMAT Practice Test 323
Section2: Integrated Reasoning
TIME: 30 minutes for 12 questions
DIRECTIONS: Follow these directions for each of the four question types:
1. For graphics interpretation questions, examine the graph or chart and select the answer from the list that
most accurately completes the statement.
2. The two-part analysis questions have two solutions. Select one choice from the list in the rst column and
one choice from the list in the second column to provide a complete answer for the question.
3. Analyze the data in the table analysis problems to determine which of the two opposing answer choices
most clearly denes the accuracy of the statements.
4. The multi-source reasoning questions present you with several sets of dierent data. Read through the
data and select the information you need to answer the questions.
NOTE: To simulate the look and feel of the integrated reasoning section on the actual GMAT, we include these
questions in the online practice exams only.
DO NOT TURN THE PAGE UNTIL TOLD TO DO SO DO NOT RETURN TO A PREVIOUS TEST
STOP
324 PART 6 Practice Makes Perfect
Section3: Quantitative
TIME: 75 minutes for 37 questions
DIRECTIONS: Choose the best answer from the ve choices provided.
1. If a doughnut-making machine is operated
for three hours, how many cases of doughnuts
will the machine be able to produce?
1. The machine produces doughnuts at a
rate of ve doughnuts per minute.
2. The doughnut company sells cases of
doughnuts in two sizes: cases of 80
doughnuts, and cases of 240 doughnuts.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
2. The gure depicts a rectangle and a circle.
Point A is the corner of the rectangle and the
center of the circle. Point B, where the shapes
intersect, bisects the length of the rectangle.
What is the area of the circle?
1.
y 6
2. The area of the rectangle is 18.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
CHAPTER 21 GMAT Practice Test 325
3.
10 15
23
31
xy x
y
y
If
x 4
and
y 15.
, what is the value of y?
(A)
19
3
(B)
3
19
(C)
3
19
(D)
1
3
(E)
19
3
4. A stand at a farmer’s market is selling peaches
individually and in cartons. An individual
peach costs $1. When bought in a carton of
30, the price of each peach is discounted by 10
percent. Since it is the end of the growing sea-
son, there is a sale going on where the price is
further discounted by 60 percent. What is the
price of two cartons of peaches?
(A) $9.00
(B) $10.80
(C) $18.00
(D) $21.60
(E) $32.40
5. If
y 4
, what is the value of
2 7xy
?
1.
xy32
2.
2 50xy
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
6. The table shows the peak price each year for stocks from ve dierent companies. Which stock had the
greatest increase in peak price from Year 1 to Year 3?
(A) OMK
(B) RRW
(C) LKP
(D) AWL
(E) TCK
326 PART 6 Practice Makes Perfect
7. How many kilometers does a bullet train travel
to get from Tokyo to Kyoto?
1. It takes the bullet train two hours to get
from Tokyo to Kyoto.
2. The bullet train travels at an average
speed of 250 kilometers per hour from
Tokyo to Kyoto.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
8. If
y 1
, what is the value of the following
expression:
4 16 4
yz z
?
(A) 4
(B) 16
(C) 64
(D) 128
(E) 256
9. When
x 0
,
21
32x
x
can be simplied to
which of the following?
(A)
1
6
x
(B)
32
3
x
(C)
1
6
x
(D)
1
3
(E)
3
26
x
x
10. Sophia is buying a smartphone and a phone
charger at an electronics store for a total price
of $630. This price reects a discount from the
original prices of both devices due to a sale the
store is oering. Assuming no taxes or other
fees are involved, what was the original price
of the phone charger alone?
1. The sale that the store is oering is 15
percent o a total purchase of $500 or
more or 20 percent o a total purchase
of $800 or more.
2. The original price of the smartphone
alone was $720.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
11. A line passes through the points (–2, 2) and
(–1, –3). At what point does this line intersect
the line with the equation
y x 8
?
(A) (–5, 3)
(B) (0, –8)
(C) (–3, 5)
(D)
3
5
14
3
,
(E)
8
3
16
3
,
12. If
y
x
2
and
x 0
, which of the following is
equal to
y
x
x
24
?
(A)
4
4
2
xx
(B)
x 1
4
(C)
x
x
4
2
(D)
x
2
1
(E)
1
4
CHAPTER 21 GMAT Practice Test 327
13.
In a survey of 20 families living on Oak Street,
17 said they had previously shopped at Fresh
Food Mart, and 12 said they had previously
shopped at Sally’s Market. How many families
said they had shopped at both stores?
1. Fifteen percent of the families surveyed
said they had not shopped at either store.
2. All of the families that said they had
shopped at Sally’s Market also said they
had shopped at Fresh Food Mart.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
14. Anthony runs a business manufacturing
machine parts. If Anthony’s business manu-
factured 80,000 machine parts last year and
88,000 machine parts this year, how many
parts will the business need to produce next
year to maintain the same percent growth
from year to year?
(A) 88,000
(B) 88,800
(C) 96,000
(D) 96,800
(E) 100,000
15. What is the surface area of a right circular cyl-
inder with a height of 3 and a diameter of 1?
(A)
35.
(B)
375.
(C)
7
(D)
8
(E)
12 25.
16. If x and y are positive integers, is
x
y
1
?
1.
xy3
2.
x
y
5
1
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
17. Patrick and Mel are each selling shirts at a
rock concert to promote their favorite bands.
It costs each of them the same amount to
produce each shirt. Mel is selling her shirts
for $60. If Patrick is making 20 percent more
prot than Mel, and his prot is $24 per shirt,
how much is Patrick charging for his shirts?
(A) $48.00
(B) $62.00
(C) $64.00
(D) $68.80
(E) $72.00
18. If
7
25
3
xx
, what is the value of x?
(A)
3
49
(B)
30
49
(C) 1.5
(D)
15
7
(E)
49
3
328 PART 6 Practice Makes Perfect
19.
fx
yx
xy
,
3
3 . If
y 1
, what is the value
of
fxy,
?
1.
y
1
2
2
2
2.
xy45
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
20. In the triangle in the gure, what is the length
of side m?
1.
p 4
2.
A 90
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
21. Given
35
2
4
2
3
xx
, which of the following
describes the possible values for x?
(A)
x
29
17
(B)
x
3
14
(C)
x
29
17
(D)
x
29
17
(E)
x
1
6
22. Roland and Felicia are testing circuit boards
for wiring errors. Working together, they can
test a circuit board in eight minutes. How
many circuit boards can Felicia test in an hour
on her own?
1. Felicia can test circuit boards twice as
fast as Roland.
2. If Roland and Felicia get their friend
Cory to help them, they can all work
together to test a circuit board in seven
minutes.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
23. A parking lot contains ten cars. The average
age of the cars is seven years. If the average
age of nine of the cars is six years, what is the
age of the remaining car in years?
(A) 3
(B) 7
(C) 10
(D) 16
(E) 20
CHAPTER 21 GMAT Practice Test 329
24.
If Cindy ran at 7.5 miles per hour for 16 min-
utes, and then ran at 6 miles per hour for 10
minutes, how far in miles did she run total?
(A) 2.5
(B) 2.8
(C) 3
(D) 3.5
(E) 5
25. If
a b0013510
2
..
, what is the value of a?
1.
300 3105ab .
2.
100 10 58 5ab .
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
26. What is the perimeter of the shape in the
gure?
1. All angles in the gure are right angles.
2.
t 2
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
27. Jerry is moving from his current apartment
into a house. He is spending a total of $2,000
on moving expenses. These expenses are
distributed between buying moving supplies,
hiring labor for moving his items, and renting
a truck. Ten percent of his moving expenses
were spent on supplies, and the truck rental
cost ve times as much as hiring labor. How
much did Jerry spend on his truck rental?
(A) $300
(B) $500
(C) $1,200
(D) $1,500
(E) $1,800
28. The gure shows a right triangle with base x
and height y. If y is doubled, by what percent
does x need to be increased to triple the area of
the triangle?
(A) 20 percent
(B) 50 percent
(C) 100 percent
(D) 150 percent
(E) 200 percent
330 PART 6 Practice Makes Perfect
29. At Bailey’s bike shop, 75 percent of the bikes
sold are mountain bikes, and the rest are road
bikes. What percentage of the bikes sold are
mountain bikes for kids?
1. Twenty percent of the bikes sold are for
kids and 80 percent are for adults.
2. Twenty percent of the bikes sold are road
bikes for adults.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
30. Using the expression
4 38xyz
, what is
the value of x?
1.
xyz
2.
zy43
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
31. George’s Gas Station gets fuel from two dier-
ent fuel suppliers: Dyon and Brian’s Biofuels.
Each supplier provides fuel with a dierent
percentage of ethanol, and George mixes them
together in his supply tank. If George currently
has 1,000 gallons of fuel at 11 percent ethanol
in his supply tank, how much fuel from Bri-
an’s Biofuels would he need to add to achieve a
nal mixture that is 12 percent ethanol?
1. Brian’s Biofuels provides fuel with 80
percent ethanol.
2. The mixture currently in George’s supply
tank has 10 gallons of fuel from Brian’s
Biofuels and 990 gallons of fuel from
Dyon.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
32. If the hypotenuse of the triangle in the gure
has a length of 9, what is x?
(A) 4.5
(B) 6
(C)
40 5.
(D)
45
(E)
162
CHAPTER 21 GMAT Practice Test 331
33.
Taco Fusion restaurant served a total of 60
guests for lunch today. Twenty of the guests
ordered sushi, and 45 of the guests ordered
tacos. If ve of the guests didn’t order tacos or
sushi, how many of the guests ordered both?
(A) 0
(B) 5
(C) 10
(D) 15
(E) 20
34. The population of Greenvale increases by 10
percent each year. Assuming constant growth,
how many people will be living in Greenvale at
the end of this year?
1. Over a two-year period, the population
growth in Greenvale is 21 percent.
2. At the beginning of last year, there were
10,000 people living in Greenvale.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
35. The gure depicts a triangle with a base of x
and a height of y. What is the value of the area
of the triangle?
1.
xy 100
2.
y 10
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
332 PART 6 Practice Makes Perfect
36. A company is selling liquid nitrogen at a price
of $2.00 per gallon. If they want to make a
prot of 25 percent of their cost of production,
how much can they spend on production of
each gallon of liquid nitrogen?
(A) $1.25
(B) $1.50
(C) $1.60
(D) $1.75
(E) $1.80
37. Jack’s morning routine includes three activi-
ties: taking a shower, drinking coee, and
walking to work. He does each activity in
sequential order without overlapping. Assum-
ing no gaps between each activity, it takes him
45 minutes to complete his routine. How long
does it take him to drink coee?
1. It takes him four times as long to walk to
work as it takes him to drink coee.
2. Showering and drinking coee take him
a total of 25 minutes.
(A) Statement (1) alone is sucient, but
Statement (2) alone is not sucient to
answer the question asked.
(B) Statement (2) alone is sucient, but
Statement (1) alone is not sucient to
answer the question asked.
(C) Both statements together are sucient,
but neither statement alone is sucient
to answer the question asked.
(D) Each statement alone is sucient to
answer the question asked.
(E) Statements (1) and (2) together are not
sucient to answer the question asked.
DO NOT TURN THE PAGE UNTIL TOLD TO DO SO DO NOT RETURN TO A PREVIOUS TEST
STOP
CHAPTER 21 GMAT Practice Test 333
Section4: Verbal
TIME: 75 minutes for 41 questions
DIRECTIONS: Follow these directions for each of the three question types:
•
Sentence-correction questions: Choose the answer choice that best phrases the underlined words
according to the rules of standard English. The rst answer choice duplicates the phrasing of the under-
lined portion; the other four choices provide alternative phrasings. Choose the one that rephrases the
sentence in the clearest, most grammatically correct manner.
•
Reading-comprehension questions: Choose the best answer to every question based on what the
passage states directly or indirectly.
•
Critical-reasoning questions: Pick the answer choice that best answers the question about the argument
provided.
Questions 1–6 refer to the following passage, which
is excerpted from Playing against Nature: Integrating
Science and Economics to Mitigate Natural Hazards in
an Uncertain World, by Seth Stein and Jerome Stein
(Wiley2014).
Natural hazards are the price we pay for living
on an active planet. The tectonic plate subduction
producing Japan’s rugged Tohoku coast gives rise
to earthquakes and tsunamis. Florida’s warm
sunny weather results from the processes in the
ocean and atmosphere that cause hurricanes. The
volcanoes that produced Hawaii’s spectacular
islands sometimes threaten people. Rivers that
provide the water for the farms that feed us
sometimes ood.
Humans have to live with natural hazards. We
describe this challenge in terms of hazards, the
natural occurrence of earthquakes or other phe-
nomena, and the risks, or dangers they pose to
lives and property. In this formulation, the risk is
the product of hazard and vulnerability. We want
to assess the hazards— estimate how signicant
they are— and develop methods to mitigate or
reduce the resulting losses.
Hazards are geological facts that are not under
human control. All we can do is try to assess them
as best we can. In contrast, risks are aected by
human actions that increase or decrease vulnerabil-
ity, such as where people live and how they build.
We increase vulnerability by building in hazardous
areas, and decrease it by making buildings more
hazard resistant. Areas with high hazard can have
low risk because few people live there. Areas of
modest hazard can have high risk due to large
population and poor construction. A disaster occurs
when— owing to high vulnerability— a natural
event has major consequences for society.
The harm from natural disasters is enormous.
On average, about 100,000 people per year are
killed by natural disasters, with some disasters—
such as the 2004 Indian Ocean tsunami— causing
many more deaths. Although the actual numbers of
deaths in many events, such as the 2010 Haiti
earthquake, are poorly known, they are very large.
Economic impacts are even harder to quantify,
and various measures are used to try to do so.
Disasters cause losses, which are the total negative
economic impact. These include direct losses due
to destruction of physical assets such as buildings,
farmland, forests, etc., and indirect losses that
result from the direct losses. Because losses are
hard to determine, what is reported is often the
cost, which refers to payouts by insurers (called
insured losses) or governments to reimburse some
of the losses. Thus, the reported cost does not
reect the losses to people who do not receive such
payments.
334 PART 6 Practice Makes Perfect
1. The main idea of the rst paragraph is best
expressed as
(A) The factors that make an area desirable
are also those that can pose the most risk.
(B) The Hawaiian Islands would not exist
if not for powerful and explosive
volcanoes.
(C) Floods, volcanoes, and earthquakes pose
threats to the natural environment.
(D) Humans must learn to live with natural
hazards such as volcanoes and tsunamis.
(E) Natural hazards are most prevalent in
areas that are sunny and warm.
2. Which of the following might the author of the
passage consider an “indirect loss” associated
with a disaster?
(A) Desecration of a library due to vandalism
(B) Damage to a school building in a re
(C) Loss of retail clothing sales due to a mall
ood
(D) Death of a ranch’s livestock due to vol-
canic eruption
(E) Destruction of a pavilion due to a
hurricane
3. According to the passage, an important
distinction between hazards and risks is
(A) risks occur naturally, while hazards arise
because of human actions
(B) hazards result from risks, and risks
result from vulnerability
(C) hazards can lead to disasters, while risks
cannot
(D) hazards are not under human control,
while risks usually are
(E) risks are harder to quantify than hazards
4. The passage is primarily concerned with
(A) describing the causes and impacts of
natural disasters
(B) assessing the impact that disasters
render on the global economy
(C) depicting the various ways human
beings may endanger themselves
(D) raising awareness of the loss of human
lives due to the severity and unpredict-
ability of natural disasters
(E) explaining that natural disasters are not
under human control
5. Which of the following best describes the pur-
pose of the fourth paragraph in relation to the
passage as a whole?
(A) It uses numerical data and metrics to
describe the economic impacts of natural
disasters.
(B) It emphasizes how little is actually
known about how many lives are lost in
natural disasters.
(C) It outlines the dierences between
hazards and risks to set up information
detailed in the remainder of the passage.
(D) It provides sensory details about spe-
cic recent natural disasters that may be
familiar to readers to evoke an emotional
response.
(E) It applies statistical data to emphasize
the magnitude of damage created by
natural disasters.
6. Which of the following logically follows the
information given in the passage?
(A) The number of unreported deaths in the
2010 Haitian earthquake exceeded the
number of unreported deaths in the 2004
Indian Ocean tsunami.
(B) In the years 2010 and 2004, there were
more deaths due to natural disasters
than average.
(C) The number of deaths due to natural
disasters along Japan’s tectonic plate is
greater on average than those experi-
enced on islands such as Hawaii or Haiti.
(D) Economic costs are more frequently
unreported than numbers of deaths in
any given natural disaster.
(E) Areas of high hazard, such as Japan’s
Tohoku coast, may have a lower risk of
natural disaster costs than areas where
hazard incidents are lower.
CHAPTER 21 GMAT Practice Test 335
7. Before the primary school can open to the
public in time for the fall semester, the crew in
charge of the project must nish construction,
cleaning, and safety-proong it’s interior.
(A) must nish construction, cleaning, and
safety-proong it’s interior
(B) must nish construction of, cleaning,
and safety-proof its interior
(C) must nish constructing, cleaning and
safety-proong it’s interior
(D) must nish constructing, cleaning, and
safety-proong its interior
(E) must nish construction, cleaning and
safety-proong the interior
8. So many accounts of this continents’ past
begin with Europeans striding ashore, claim-
ing this “newfound land” and its human
inhabitants for its respective empires.
(A) continents’ past begin with Europeans
striding ashore, claiming this “newfound
land” and its human inhabitants for its
respective empires
(B) continent’s past begin with Europeans
striding ashore, claiming this “newfound
land” and its human inhabitants for
their respective empires
(C) continents’ past begin with Europeans
striding ashore, claiming this “newfound
land” and its human inhabitants for
their respective empires
(D) continent’s past begins with Europeans
striding ashore, claiming this “newfound
land” and its human inhabitants for its
respective empires
(E) continent’s past begins with Europeans
striding ashore, claiming this “newfound
land” and its human inhabitants for
their respective empires
9. Injera, an East African atbread, has been a
main component of Ethiopian dishes for gen-
erations and are still used by many Ethiopians
today, who use it to feed themselves in the
same manner Americans use atware.
(A) are still used by many Ethiopians today,
who use it to feed themselves
(B) are still used by many Ethiopians today,
who feed themselves with it
(C) it is still used today by many Ethiopians,
who use it to feed themselves
(D) is still used today by many Ethiopians to
feed themselves
(E) is still used by many Ethiopians today,
who use it to feed themselves
10. The size of oceanic waves is a function of the
velocity of the wind and of fetch, the length
of the surface of the water subject to those
winds. The impact of waves against a coastline
is a function of the size of the waves and the
shape of the sea bottom. The degree of erosion
to which a coastline is subject is a function of
the average impact of waves and the geologic
composition of the coastline.
If these statements are true, which one of the
following must also be true?
(A) The degree of erosion to which a coast-
line is subject is related to the shape of
the sea bottom.
(B) The size of oceanic waves will not uc-
tuate far from an average for any given
stretch of ocean.
(C) The fetch of winds is related to the shape
of the sea bottom.
(D) The size of oceanic waves is related to
the shape of the sea bottom.
(E) The average velocity of the wind in an
area plays no role in the degree of ero-
sion to which a coastline is subject.
336 PART 6 Practice Makes Perfect
11. Health insurers are largely immune to the
factors that are limiting prot in many sec-
tors of the healthcare economy. Consumers
have shown a willingness to pay almost any
price for health insurance premiums. Capital
demands, which are the responsibility of doc-
tors and hospitals, are increasing dramatically,
even as cost-containment measures, largely
encouraged by the insurers and their friends
in government, have forced new levels of scal
discipline upon hospitals and doctors. Patients
still need MRIs and buildings to put them in,
but hospitals are limited in how much they can
charge patients for the use of these facilities.
Which one of the following most accurately
describes the role that the statement “patients
still need MRIs and buildings to put them in”
plays in the argument?
(A) It is a specic example of a general
condition described in the course of the
argument.
(B) It is used to counter a consideration
that may be taken to undermine the
argument.
(C) It is used to indirectly support the claim
made by the argument.
(D) It describes a social side eect of the
benet with which the argument is
concerned.
(E) It introduces the conclusion that the
argument intends to support.
12. The softball team tried to raise enough money
to purchase new uniforms for the upcoming
season, but between them, the 20 players were
only able to raise about 70 percent of the cost.
(A) between them, the 20 players were only
able to raise about 70 percent of the cost
(B) between them, the 20 players were only
able to have raised about 70 percent of
the cost
(C) among them, the 20 players were only
able to raise about 70 percent of the cost
(D) among them, the 20 players were only
able to have raised about 70 percent of
the cost
(E) among them, only about 70 percent of
the cost was raised by 20 players
13. Forcing businesses to furnish employees
with paid leave for family concerns, such as
paternity leave or leave to care for a sick child,
is a terrible idea. If a business allows employ-
ees to take this time o, the workers will take
advantage of the privilege and come to work as
little as possible. This will destroy productivity
and workplace morale.
Which one of the following, if true, most seri-
ously weakens the argument?
(A) European countries guarantee employees
generous family leave and paid vaca-
tion time, but the European standard of
living is slightly below that of the United
States.
(B) Most male workers refuse to take
paternity leave even though it is allowed
under federal law and their employers
encourage it; they fear they may anger
co-workers and harm their chances for
promotion if they take time o for what
is still seen as a frivolous reason.
(C) The FMLA requires employers to grant
employees 12 weeks a year of unpaid
leave for family purposes; although
employers save money because the leave
is unpaid, they often must spend money
to nd a replacement for the employee
who takes time o.
(D) In some workplaces, the loss of a single
employee at a busy time of year can be
devastating, even if that employee plans
to return after a few weeks; allowing
family leave can overwhelm the employ-
ees who stay on the job.
(E) Allowing employees to take leave for
family matters reduces absentee-
ism, improves morale, and surpris-
ingly increases productivity because the
employees who are granted leave tend to
work much harder and more eciently
when they come back to work.
CHAPTER 21 GMAT Practice Test 337
14. Not all of the players was on board with the
new uniforms for the girls’ basketball team,
but the team made their choices.
(A) was on board with the new uniforms for
the girls’ basketball team, but the team
made their choices
(B) was on board with the new uniforms for
the girls’ basketball team, but the team
had made its choices
(C) were on board with the new uniforms for
the girls’ basketball team, but the team
made their choice
(D) were on board with the new uniforms for
the girls’ basketball team, but the team
had made its choice
(E) were on board with the new uniforms for
the girls’ basketball team, but the team
has made its choice
15. The nation’s increasing reliance on automa-
tion is reducing the number of jobs available to
hardworking people, forcing many families to
make the unfortunate choice between having a
roof over their heads or receiving healthcare.
(A) forcing many families to make the
unfortunate choice between having
a roof over their heads or receiving
healthcare
(B) forcing many families to make the
unfortunate choice between having
a roof over their heads and receiving
healthcare
(C) forcing many families to make the
unfortunate choice between having a
roof over their heads or healthcare
(D) forcing many families with making the
unfortunate choice between having a
roof over their heads and healthcare
(E) forcing many families to make the
unfortunate choice among having a roof
over their heads and healthcare
16. Software engineers know that a poorly written
application can consume more memory than
it should and that running out of memory can
cause an application to crash. However, if a
crashing application causes the whole oper-
ating system to crash, the fault lies with the
operating system.
Which one of the following, if true, is least
helpful in establishing that this conclusion is
properly drawn?
(A) Operating systems with generous
amounts of memory are less susceptible
to crashing, even when applications are
poorly written.
(B) Operating systems can isolate the mem-
ory used by individual applications, even
when an application uses a large amount
of memory.
(C) An operating system can monitor an
application’s consumption of memory
and take action when that gets too high.
(D) Techniques for programming operating
systems to catch and handle memory
errors are well-dened and well-known
among programmers.
(E) Because many applications can run
simultaneously under a single operat-
ing system, the operating system should
have a well-dened method of managing
memory consumption.
338 PART 6 Practice Makes Perfect
17. This museum does not grant people the
right to use images of items in its collection
in online publications. We are obliged to do
everything in our power to ensure the contin-
ued appeal of visiting our collection in person.
The conclusion above depends on assuming
which one of the following?
(A) Taking photographs of art objects,
especially using a ash, can damage
the objects by accelerating the fading of
paint.
(B) The museum sells pictures of its collec-
tion in its gift shop, which is an impor-
tant source of income for the museum.
(C) Images placed online are easily copied
and reused by other people.
(D) The quality of most electronic images,
especially those online, falls short of the
professional standards of the museum.
(E) If people see online images of items in
the museum’s collection, they will no
longer be interested in seeing the collec-
tion with their own eyes.
18. The town’s legislators heard arguments from
the crowd about how town facilities and parks
no longer properly accommodate the towns-
people now that the number of residents have
increased so considerably.
(A) the number of residents have increased
so considerably
(B) the numbers of residents have so con-
siderably increased
(C) the number of residents has increased so
considerably
(D) the numbers of residents have so con-
siderably increased
(E) the number of residents has been
increasing considerably so
19. Risks are eected by human actions that
increase or decrease vulnerability, like where
people live and how they build.
(A) Risks are eected by human actions that
increase or decrease vulnerability, like
where people live and how they build.
(B) Risks are aected by human actions that
increase or decrease vulnerability, like
where people live and how they build.
(C) Risks are eected by human actions that
increase or decrease vulnerability, such
as where people live and how they build.
(D) Risks are aected by human actions that
increase or decrease vulnerability, such
as where people live and how they build.
(E) Risks are aected by human actions
which increase or decrease vulnerability,
such as where people live and how they
build.
Questions 20–23 refer to the following passage,
which is excerpted from Handbook of Early
Childhood Development Programs, Practices, and
Policies by Elizabeth Votruba-Drzal (Editor) and Eric
Dearing (Editor) (Wiley 2017).
Researchers, educators, and policymakers
generally agree that school readiness is a multidi-
mensional concept that includes cognitive, execu-
tive functioning, language, socioemotional,
behavioral, and health characteristics that contrib-
ute to children’s ability to adapt and thrive in
school settings. These performance domains are
correlated but typically are assessed and studied as
independent indicators of school readiness and
predictors of later achievement. Importantly, the
guiding denitions of school readiness typically
include skills and behaviors that are related to
learning processes as well as learning outcomes, as
opposed to the K–12 system, which often only
emphasizes student outcomes based on children’s
performance on academic achievement tests.
CHAPTER 21 GMAT Practice Test 339
In the area of cognition, school readiness
includes both acquired knowledge or skills in
particular content area (such as knowing a certain
number of letters) as well as learning/
processing skills or how fast children acquire
knowledge. In particular, there has been a growing
emphasis on executive functioning skills and how
these skills interact with other domains to promote
learning in preschool classrooms. Executive
functioning typically is dened as the set of skills
and behaviors required to attain a goal, including
working memory, attention control, attention
shifting, and response inhibition. For young
children, this means being able to resist distrac-
tions (e.g., pay attention to a teacher rather than
talk with peers), inhibit dominant responses in
emotional contexts (e.g., raise hand instead of
talking while the teacher is reading a book), and
prioritize and sequence information and hold onto
it in memory (e.g., plan and carry out the series of
steps required to line up for lunch).
In addition, school readiness includes chil-
dren’s language skills, including their receptive
language (i.e., the ability to listen and understand
language) and expressive language (i.e., the ability
to communicate with others using verbal lan-
guage). Children’s socioemotional skills are also an
important component of school readiness and
include behaviors such as cooperation with
teachers and peers and developing social relation-
ships, as well as behavior problems, including
aggression or poor regulation. There are also a set
of skills referred to as approaches to learning,
which reect children’s curiosity, exibility,
attention, persistence, and engagement. The
physical health domain includes motor develop-
ment, such as development of ne and gross motor
skills, and healthy behavior practices. Collectively,
all of these skills are theorized to aect children’s
learning opportunities and their acquisition of new
skills and behaviors in the classroom setting.
20. According to the passage, being able to resist
distractions is a form of
(A) socioemotional growth
(B) executive functioning
(C) behavioral growth
(D) motor development
(E) cognitive growth
21. The author of the passage makes the distinc-
tion between the guiding principles of school
readiness and those observed by the K–12
system to
(A) emphasize that school readiness regards
the process as much as the results
(B) demonstrate the failings of the K–12
system
(C) explain why the guiding principles of
school readiness are superior to those
used at K–12 settings
(D) emphasize the author’s personal opin-
ion about the importance of student
outcomes
(E) explain how cognition factors into a
child’s degree of success in a school
setting
22. The passage indicates that attention to which
of the following school readiness skills has
likely increased in recent years?
(A) responding accurately on standardized
achievement tests
(B) using verbal language to communicate
ideas to others
(C) cooperating with peers and managing
aggressive behaviors
(D) paying attention to the teacher
(E) ensuring that students consume a
healthy breakfast
23. It can be inferred from the passage that
children who interact successfully with their
teachers and other students have strong
(A) motor skills
(B) receptive language skills
(C) expressive language skills
(D) executive functioning skills
(E) socioemotional skills
340 PART 6 Practice Makes Perfect
24. Career counselor: Many large international
companies have changed their practices
regarding international assignments. They
are placing much more emphasis on help-
ing spouses of expatriate employees to adjust
to the foreign environment. This has reduced
premature returns by 67 percent.
Which one of the following is an assumption
upon which the career counselor’s argument
depends?
(A) Spousal and marital diculties were
formerly responsible for many prema-
ture returns from foreign assignments.
(B) When an employee is placed in a for-
eign assignment for a year or less, his
or her family sees the assignment as an
adventure.
(C) Expatriate employees work long hours
and travel a great deal, and their chil-
dren make new friends at school, but
spouses often have no friends and no
work to support them while they’re
abroad.
(D) The majority of international assign-
ments today last for less than a year, but
ten years ago, 70 percent of them lasted
much longer than one year.
(E) Many companies now oer expatriate
spouses language training, career guid-
ance, and assistance in nding homes
and schools.
25. One work of art is not more important because
it was made after another nor does it make its
predecessor obsolete.
(A) after another nor does it make its
predecessor obsolete
(B) after another, it neither makes its
predecessor obsolete
(C) after another; nor does it make its
predecessor obsolete
(D) after another neither does it make its
predecessor obsolete
(E) after another, nor does it make its
predecessor obsolete
26. A most unsociable dog he proved to be, resent-
ing all their advances, refusing to let them
lay hands on him, menacing them with bared
fangs and bristling hair.
(A) resenting all their advances, refusing to
let them lay hands on him, menacing
them with bared fangs and bristling hair
(B) resenting all advances, refusing to let
them lay hands on him, menacing them
with bared fangs, and bristling hair
(C) resenting all the advances that they
made, refusing to let them lay hands on
him, menaced them with bared fangs
and bristling hair
(D) resenting all their advances, refusing
to let them lay hands on him, menaced
them with bared fangs and bristling hair
(E) resenting all the advances that they
made, refusing to let them lay hands
on him, and menacing them with bared
fangs and bristling hair
27. Scientists have discovered a gene that controls
whether an individual is monogamous. They
took a gene from the monogamous prairie vole
and implanted it into its more promiscuous rel-
ative, the meadow vole. Thereafter, the meadow
voles with the new gene became monogamous.
Which one of the following, if true, would
provide the most support for the argument’s
conclusion?
(A) Studies on humans and other mammals
have shown that receptors for the hor-
mone vasopressin play a role in autism,
drug addiction, and the formation of
romantic attachments.
(B) Prairie voles typically form lifelong part-
nerships, which scientists have linked to
an increased number of receptors for the
hormone vasopressin.
(C) Meadow voles live in a harsher envi-
ronment than prairie voles and cannot
aord to pass up opportunities to mate
as often as possible.
(D) The scientists used a harmless virus to
capture the gene and transfer it into the
meadow voles.
(E) The meadow voles that had the prai-
rie vole gene implanted in them were
released into and observed in the same
habitat in which they had previously lived.
CHAPTER 21 GMAT Practice Test 341
28. Physician: Scottish researchers have developed
a test that allows them to predict at what age
a woman will experience menopause. The sci-
entists use a model that compares a woman’s
ovaries to “average” ovaries to see whether
her ovaries are aging faster or more slowly
than average. They have discovered that the
size of ovaries is directly related to the number
of eggs they contain, which in turn is directly
related to fertility. This discovery will signi-
cantly inuence women’s decisions on when
to have children.
The physician’s conclusion follows logically if
which one of the following is assumed?
(A) Women with smaller ovaries tend to
have less success with assisted repro-
duction techniques, such as invitro
fertilization.
(B) Most women experience menopause
around the age of 50, but their fertility
starts to decline at the age of 37.
(C) Women who want to have children
increasingly seek to delay doing so for
many varied reasons.
(D) The test cannot tell women how likely
they are to conceive in the years just
prior to menopause.
(E) Every woman is born with several mil-
lion eggs in her ovaries, which formed
while she was a fetus; the number of
eggs dwindles over her lifetime, until at
menopause she has 1,000 or fewer.
29. The top two students, Arthur and Abraham,
excelled not only academically but in
athletics too.
(A) excelled not only academically but in
athletics too
(B) excelled not only academically and also
athletically
(C) engaged in excellence not only academi-
cally but athletically
(D) excelled not only academically but also
in athletics
(E) excelled not only academically but also
athletically
30. To earn a graduate equivalency diploma, a
student must pass tests on subjects taught
in high schools, proving that he or she has
mastered them to the degree assumed of a
high-school graduate. It makes sense for a
student to drop out of high school and earn a
GED.A GED takes much less time to earn than
a high-school diploma and provides evidence
that the student has learned everything he or
she would have learned in high school.
Which one of the following, if true, most seri-
ously weakens the argument?
(A) Some GED-prep programs incorporate
enrichment activities into their test
preparation, such as taking students to
art exhibits and theatrical performances.
(B) Most colleges and universities consider a
GED equivalent to a high-school degree
for admission purposes.
(C) Many successful businesspeople dropped
out of high school and earned a GED.
(D) Employers assume that high-school
graduates generally have a much higher
level of mastery of academic subjects
than those who earn GEDs.
(E) Many GED students are slightly older
than high-school students, and they
often hold jobs in addition to studying to
pass the GED tests.
Questions 31–35 refer to the following passage,
which is excerpted from Beyond Cybersecurity:
Protecting Your Digital Business, by James
M.Kaplan, Tucker Bailey, Derek O’Halloran, Alan
Marcus, and Chris Rezek (Wiley 2015).
All business investments require trade-os
between risk and reward. Does the interest rate on
a new bond issue adequately compensate for the
risk of default? Are the potential revenues from
entering a new emerging market greater than the
risk that the investments will be conscated by a
new regime? Does the value of oil extracted via
deep-water, oshore drilling outweigh the chance
of a catastrophic accident? Tough questions must
be answered by weighing up the business impera-
tives against a calculation of the risk— and the
greater the risk, the harder it is to make the case
for investment.
342 PART 6 Practice Makes Perfect
Technology investments are no dierent.
They, too, have always been a trade-o between
risk and return. However, for enterprise technol-
ogy, increased global connectivity is raising the
stakes on both sides of the equation. The commer-
cial rewards from tapping into this connectivity are
enormous, but the more tightly we are connected,
the more vulnerabilities exist that attackers can
exploit and the more damage they can do once
inside. Therefore, when a manufacturer invests in
a new product life-cycle management system, it is
making a bet that the system will not enable the
theft of valuable intellectual property. When a
retailer invests in mobile commerce, it is betting
that cyber-fraud won’t critically damage prot-
ability. When a bank invests in customer analytics,
it is betting that the sensitive data it analyzes
won’t be stolen by cyber-criminals. The odds on all
those bets appear to be shifting away from the
institutions and toward cyber-attackers. They
could swing decisively their way in the near future
given most companies’ siloed and reactive
approach to cybersecurity.
Our interviews with business leaders, chief
information ocers (CIOs), chief technology
ocers (CTOs), and chief information security
ocers (CISOs) indicate that concerns about
cyber-attacks are already aecting large institu-
tions’ interest in and ability to create value from
technology investment and innovation. Potential
losses, both direct and indirect, reduce the
expected economic benets of technology invest-
ments, as do the high cost and lengthy time frame
required to build the defense mechanisms that can
protect the organization against a growing range
of attackers. In short, the models companies use to
protect themselves from cyber-attack are limiting
their ability to extract additional value from
technology.
Concern about cyber-attacks is already having
a noticeable impact on business along three
dimensions: lower frontline productivity, fewer
resources for information technology (IT) initia-
tives that create value, and— critically— the
slower implementation of technological
innovations.
31. The primary purpose of this passage is to
(A) identify gaps in the business world that
lead to cybersecurity breaches
(B) refute the notion that companies are
failing to thwart hackers
(C) discuss how the modern business mar-
ketplace is all about risk and reward
(D) explain how attention to cybersecu-
rity impacts companies’ technological
innovation
(E) demonstrate how today’s hack-
ers are winning the ght against big
corporations
32. According to the passage, all of the following
decrease the economic benets of technologi-
cal investment EXCEPT:
(A) experiencing stolen intellectual property
(B) realizing indirect losses
(C) weighing business outcomes and risks
(D) investing in cyber-security protection
technology
(E) reacting to cyber-threats only when
necessary
33. When the author asserts that companies take a
“siloed and reactive” approach to cybersecu-
rity, he is implying that companies
(A) perform thorough research before
implementing programs meant to
improve cybersecurity
(B) combat problems after they have
occurred
(C) have made strides against hackers in the
ultimate battle of cybersecurity
(D) invest too much in cybersecurity
(E) take unnecessarily large investment
risks and disregard the importance of
cybersecurity
CHAPTER 21 GMAT Practice Test 343
34.
Which of the following is most likely an
example of intellectual property as mentioned
in the second paragraph?
(A) works of art posted to social media
(B) personal information, such as Social
Security numbers or banking information
(C) computers and related technological
devices
(D) customer and client lists and related
contact information
(E) an outline of a streamlined manufactur-
ing process
35. It can be inferred from the passage that the
author considers which of the following to be
true regarding increased global connectivity?
(A) Increased global communications mean
more risk for security breaches.
(B) Global connectivity is a primary reason
for the increasingly delayed progress of
modern technology.
(C) Global connections are largely detrimen-
tal to humankind.
(D) The commercial rewards associated with
global connectivity are minimal.
(E) The more tightly companies are con-
nected, the more power they have
against hackers.
36. I bought a pair of glasses from an optometrist.
One of the lenses regularly pops out of the
frame. Therefore, this optometrist doesn’t
know how to make a good pair of glasses.
The reasoning in the argument is most vul-
nerable to criticism on the grounds that the
argument
(A) does not allow the optometrist a chance
to defend himself
(B) does not consider the possibility that
other optometrists also make defective
frames
(C) criticizes the optometrist’s use of a par-
ticular technique when making glasses
(D) jumps to the conclusion that the defect
in the glasses must be due to the optom-
etrist’s lack of skill
(E) accuses the optometrist of deliberately
sabotaging the glasses
37. A new kind of primate, the fat-tailed lemur,
has been discovered in Madagascar. These
lemurs hibernate, sleeping in holes in trees
for up to seven months out of the year. Winter
temperatures in Madagascar rarely drop below
86 degrees, so these lemurs do not hibernate
to escape the cold but perhaps to conserve
energy during the dry season, when food is
scarce. This is the rst time anyone has found
an animal that hibernates during hot weather,
disproving the common belief that only ani-
mals in cold climates hibernate.
Which one of the following most accurately
describes the role played in the argument by
the assertion that this is the rst time anyone
has found an animal that hibernates during
hot weather?
(A) The statement challenges the long-held
belief that primates never hibernate.
(B) The statement accuses scientists who
have studied hibernation in the past of
wrongfully assuming that hibernation
only occurs in cold weather.
(C) The statement highlights the importance
of this discovery because it disproves a
long-held theory about hibernation.
(D) The statement calls into question the
assumption that this behavior is true
hibernation and suggests that it may be
something else.
(E) The statement sets up a rival theory so
that the primatologist can disprove it.
344 PART 6 Practice Makes Perfect
38. When we think about peoples of the past, we
intuitively try to imagine what he or she would
have looked like in real life and to visual-
ize their physical features, dress, and general
appearance.
(A) we intuitively try to imagine what he or
she would have looked like in real life
and to visualize their physical features
(B) we intuitively try to imagine what they
would have looked like in real life and to
visualize their physical features
(C) we intuitively try to imagine what he or
she would have looked like in real life
and visualize his or her physical features
(D) we intuitively try to imagine what they
would have looked like in real life and
to visualize what their physical features
were like
(E) we intuitively try to imagine what they
would look like in real life and visualize
their physical features
39. Motorcyclists are told to always wear helmets
when they ride their motorcycles. But helmets
only protect riders when they have wrecks,
and wrecks occur only once out of every 1,000
rides. Therefore, a motorcyclist would be per-
fectly safe if he wore his helmet only once out
of every 1,000 rides.
Which one of the following employs a awed
argumentative strategy that is most closely
parallel to the awed argumentative strategy
in this statement?
(A) My European client calls once a week,
always in the evening, after everyone
has left the oce. I’ll be sure to get his
messages if I turn on my telephone’s
answering machine once a week.
(B) This sunscreen allows me to stay in the
sun 15 times longer than I could without
sunscreen. If I apply two coats of it, it
will allow me to stay in the sun 30 times
longer.
(C) The odds are 1,000 to 1 against winning
the big jackpot on this slot machine. If
I play the slot machine 1,000 times, I’m
sure to win the big jackpot.
(D) Seat belts protect passengers in auto-
mobile accidents, but accidents only
occur in one out of every 2,000 car trips.
Because drivers are in the car the most,
they should wear their seat belts most
often.
(E) Top business schools accept one out of
every 20 MBA applicants. Therefore,
someone who wants to get into a top
business school should apply to 20 of
them.
CHAPTER 21 GMAT Practice Test 345
40. Even though Carter had fewer quarters in his
piggybank than did his brother Clark, Clark
had less money overall.
(A) Even though Carter had fewer quarters in
his piggybank than did his brother Clark,
Clark had less money overall.
(B) Even though Carter had fewer quarters
than his brother, Clark, in his piggybank,
Clark had fewer money overall.
(C) Even though Carter had less quarters
than his brother, Clark, in his piggybank,
Clark had less money overall.
(D) Even though Carter had less quarters in
his piggybank than did his brother Clark,
Clark had less money overall.
(E) Even though Carter had fewer quarters
than his brother, Clark, in his piggybank,
Clark had less money overall.
41. Rugby is somewhat like American football in
that both involve downs, tackles, and touch-
downs, but it also combines elements from
other sports, like soccer and hurling.
(A) Rugby is somewhat like American
football in that both involve downs,
tackles, and touchdowns, but it also
combines elements from other sports,
like soccer and hurling.
(B) Rugby is somewhat like American foot-
ball in that all involve downs, tackles,
and touchdowns but it also combines
elements from other sports, like soccer
and hurling.
(C) Rugby is somewhat like American
football in that both involve downs,
tackles, and touchdowns, but it also
combines elements from other sports,
such as soccer and hurling.
(D) Rugby is somewhat like American
football in that all involve downs,
tackles, and touchdowns, but it also
combines elements from other sports,
such as soccer and hurling.
(E) Rugby is somewhat like American
football in that both involves downs,
tackles, and touchdowns, but it also
combines elements from other sports,
such as soccer and hurling.
DO NOT TURN THE PAGE UNTIL TOLD TO DO SO DO NOT RETURN TO A PREVIOUS TEST
STOP
CHAPTER 22 Practice Test Answers andExplanations 347
Practice Test Answers
andExplanations
Y
ou’ve nished the test, but you’re not done yet. Reading through the following explana-
tions may be the most important part of taking the practice exam. Examine the informa-
tion for the questions you missed as well as those you answered correctly. You may nd
tips and techniques you haven’t thought of before in one of the answer explanations. If you’re
short on time or just want to quickly check your answers, head to the end of this chapter for an
abbreviated answer key.
Section1: Analytical Writing Assessment
Scoring the practice analytical writing task is a little dierent than scoring the other sections.
Your job is to honestly analyze the essay you’ve written and assign yourself a score. You can also
ask a friend or composition teacher to look over your essay and give you an opinion. Refer to the
scoring considerations in Chapters7 and9 for guidance on what readers are looking for. To help
you determine your score for this section, we’ve included a sample essay and an explanation of
its strengths and weaknesses. Use these tools to identify your own essay’s strengths and weak-
nesses and improve your essay response before you take the actual test.
Here’s a sample response to the essay prompt:
The author of the prompt is making the argument that American charter schools have failed to “live
up to the hype,” so to speak, and he or she makes some sound arguments in doing so. The
argument is well-organized in that the author rst discusses what charter schools are supposed to
accomplish (more options as far as school choice and more opportunities for teachers) before
discussing some of the ways in which they have failed to accomplish what was intended, such as
the fact that many teachers leave within the rst year.
While the argument is well-organized, the author falters somewhat in his or her explanation of why
charter schools are failing. In addition to the goal of increasing opportunities for teachers, the
author notes that charter schools seek to give students and families alternatives to traditional,
public schools. While the author provides an explanation for why these schools aren’t achieving
Chapter22
348 PART 6 Practice Makes Perfect
their goals as far as teachers (again, teachers are leaving), he or she does not address how they fail
in terms of giving students and families more options as far as school choice, and the overall
strength of the argument suers because of this obvious omission.
It might make for a stronger argument if, instead of referencing school choice in the beginning, the
author just cut straight to the chase and referenced teachers and accountability. He or she does
discuss how charter schools are failing in terms of accountability later in the argument (when he or
she notes that many are getting taken over by private companies without local interests), so it might
strengthen the argument to only call out points that can be successfully refuted later on.
It also seems a little odd that the entire argument focuses on how charter schools are failing, but
yet it fails to address— at all— the academic performance of charter school students. One could
argue that academic performance should be the single-biggest indicator of whether a school is
succeeding, and the author’s failure to even touch upon that diminishes the strength of the points
he or she does make.
Here is a quick analysis of the sample essay:
The essay author carefully considered the strengths and weaknesses of the arguments made
about charter schools before crafting the response. The essay also identies two clear omissions
that probably should have made it into the original argument— the prompt author’s failure to
address how charter schools are “failing” in how they oer alternative environments to tradi-
tional public school settings, and the fact that she never touched upon the academic performance
of students in charter schools when arguing against them.
While the argument would benet from these additions, it might also benet from more clarity
about the areas in which the essay author thought the original argument was strong. While the
essay notes that the author of the prompt made “sound arguments” for why charter schools have
failed to live up to the hype while using the plural form “arguments,” the only sound argument
actually referenced is the fact that many teachers leave within the rst year. The essay in its
entirety may have proved more convincing if its author had called out other sound arguments.
Nonetheless, the author did provide a thoughtful analysis of the argument made in the prompt,
and she was largely articulate and grammatically correct in doing so. The essay is also free from
spelling errors and ows well. Because the author carefully considered the subject matter and
poked some valid holes in the initial argument, and because she wrote a clear, concise response
that was virtually free from spelling or grammar issues, it is unlikely this essay would score below
a 4. However, the author’s failure to clarify her comments about sound arguments might keep it
from scoring higher.
Section2: Integrated Reasoning
Refer to “Section2: Integrated Reasoning” of Practice Exam 1 online to check your answers for
the 12 questions in this section. (Note: You can nd instructions for accessing the online practice
in the Introduction.)
CHAPTER 22 Practice Test Answers andExplanations 349
Section3: Quantitative
1. E. Statements (1) and (2) together are not sucient to answer the question asked.
Look at the information the question provides, and evaluate whether more is needed for a
solution.
1. Find out what to solve for.
This question is asking you how many cases of doughnuts a machine will be able to produce
in a three-hour period of time. You could nd the answer to the question if you knew the
number of doughnuts the machine produces per hour and the number of doughnuts in a
case. Rewrite the question as an equation where the solution (x) is the number of cases
produced in three hours.
x
doughnuts produced per hour
doughnuts per case
ho
3u
ur
s
At this point, you have two unknowns on the right side of your equation. You don’t know
how many doughnuts the machine can produce in each hour, and you don’t know how
many doughnuts are needed to ll a case.
2. Examine Statement (1).
Statement (1) tells you that the machine produces 5 doughnuts per minute (which is 300 per
hour). This eliminates one of the unknowns in your equation, but still doesn’t give you
enough information to solve the question. Write down
1 no
. You can eliminate Choices
(A) and (D).
3. Evaluate Statement (2).
Statement (2) says that the company sells cases of doughnuts in two sizes: 80 doughnuts
and 240 doughnuts. This statement doesn’t provide you with the information needed to
solve the problem. Write down
2 no
and eliminate Choice (B).
4. Check out what you’ve written.
You have double nos, so look at all of the information provided by both statements.
5. Evaluate the two statements together.
Statement (2) told you that the doughnuts may be packaged in cases of either 80 or 240
doughnuts. While this may seem to be helpful in solving the question, it actually means that
you need more information to solve the problem. You would need to know which size of
case is being lled. Because this information isn’t provided in either statement, you won’t be
able to solve this question.
2. D. Each statement alone is sucient to answer the question asked.
Analyze all of the information given in the problem before looking at each statement.
1. Find out what to solve for.
The problem provides you with a gure showing an overlapping rectangle and circle and
asks you for the area of the circle. You can convert the question into an equation, solving for
the circle’s area (A). Using the standard formula, the area is equal to
multiplied by the
circle’s radius (r) squared. So
Ar
2
.
350 PART 6 Practice Makes Perfect
From the information the question provides, you know that you need to gure out either the
value of x or the value of y to solve the problem. Looking rst at x, you know one gure is a
rectangle, so the height on both sides is the same. This means the height on both sides
equals x. From the information provided in the problem, you also know the center of the
circle is at the same point as the corner of the rectangle. So, you can solve the problem if you
can solve for x. In terms of x, then, the area of the circle is
Ax
2
.
From the information in the question, you can also write your equation in terms of y. The
question tells you that Point B bisects the length of the rectangle, so
r
y
2
, and
therefore
A
y
2
2
.
2. Examine Statement (1).
Statement (1) tells you that
y 6
. You can use this value for y to solve the above equation for
the area of the circle,
A
y
2
2
. Statement (1) is sucient. Write yes next to (1) on your
noteboard and eliminate Choices (B), (C), and (E).
3. Evaluate Statement (2).
Statement (2) tells you that the area of the rectangle is 18. This gives you
xy18
. You
previously determined from the problem statement that the radius of the circle is equal to x,
and also equal to half of y. So knowing
r x
and
r
y
2
, you can substitute in values for x and
y in terms of r:
r r218
, so
2 18
2
r
, and therefore
r
2
9
. This allows you to solve for the
area of the circle. Statement (2) is also sucient. Write yes next to (2) and pick Choice (D).
3. A.
19
3
This question gives you an equation with variables of x and y, and asks you to solve for the
value of y. It gives you a value of x, and says that
y 15.
. Looking at the rst part of the
expression, you may notice that you are able to factor the numerator. Factor out the common
factor of 5x:
52 3
23
31
xy
y
y
Since you know that
y 15.
, you know that the denominator is not equal to 0, so you are
able to cancel out the common factor of
23y
. Now you have
531xy
.
Rearranging the equation to solve for y:
y
x15
3
When you insert 4 for x, you arrive at the conclusion that
y
19
3
.
4. D. $21.60
In this price discount problem, you will need to apply multiple price discounts to the original
price of the peaches in order to calculate the nal price. The problem tells you that each
peach costs $1, so a carton of 30 peaches would therefore cost $30. But the problem says that
the price is discounted by 10 percent when the peaches are bought in a carton of 30. If the
discount is 10 percent, then the price of the peaches will be
110%
, which is 90 percent. So,
two cartons of peaches would be 60 peaches, and the price would be
$%$60 90 54
.
The problem tells you that there is an additional discount of 60 percent. To apply the addi-
tional discount, simply multiply $54 by 40 percent, and you get $21.60.
CHAPTER 22 Practice Test Answers andExplanations 351
5.
D. Each statement alone is sucient to answer the question asked.
Be sure to evaluate each statement individually.
1. Find out what to solve for.
The question is asking for the value of
2 7xy
. So, it’s asking you to solve the equation
zxy27
. But, the question already provides you with the value of y. So you just need to
gure out the value of x.
2. Examine Statement (1).
Statement (1) tells you that
xy32
. Since you already know
y 4
, you can use this
equation to solve for x. Going back to the question, you can plug in your values for x and y
and determine the solution. Statement (1) is sucient. Write yes next to (1) on your note-
board. You can eliminate Choices (B), (C), and (E).
3. Evaluate Statement (2).
Statement (2) tells you that
2 50xy
. Again, since you know the value of
y 4
from the
question, you can use this equation to solve for x. Then you can insert your values for x and y
and come up with the solution. Statement (2) is also sucient. Write yes next to (2), and pick
Choice (D).
6. D.AWL
This data-interpretation question presents you with a table showing peak prices of various
stocks over the course of ve years. The question is asking you to nd which stock had the
greatest increase in peak price from Year 1 to Year 3. Looking at the peak prices for OMK, you
can see that they were $5.12in Year 1 and $9.12in Year 3. This is an increase of $4. Use esti-
mation to evaluate the rest of the table.
Continuing down the table, you can see that the peak price of RRW increased by about
$. $. $.45 00 30 00 15 00
, and the peak price of LKP increased by about
$. $. $.30 00 15 00 15 00
.
If you don’t nd an answer with a greater increase, you’ll have to evaluate these two options
more carefully later. But there are still two more stocks to evaluate. Looking at AWL, its peak
price increased by about
$. $. $.155 00 130 00 25 00
. AWL is now the highest increase in peak
price you’ve seen and is denitely higher than TCK, which increased from around $62.00 to
$74.00, an increase of only about $12.00.
Of all the stocks, the peak price of AWL, Choice (D), increased the most from Year 1 to Year 3.
7. C.Both statements together are sucient, but neither statement alone is sucient to answer
the question asked.
Be sure to separate out the facts of each statements:
1. Find out what to solve for.
The question is asking for the distance that a bullet train will travel to get from Tokyo to
Kyoto. This is a rate question. So, to nd the distance travelled (d), you will need to multiply
the rate of travel (r) by the time spent travelling (t). In other words, you need to solve
d rt
.
2. Examine Statement (1).
Statement (1) provides the time required for the bullet train to get from Tokyo to Kyoto. This
gives you
t 2 hours
. While this gets you one step closer to a solution, you still don’t know
the rate at which the train travels. Statement (1) isn’t sucient. Write down
1 no
. Eliminate
Choices (A) and (D).
352 PART 6 Practice Makes Perfect
3. Evaluate Statement (2).
Statement (2) says that the bullet train travels at a speed of 250 kilometers per hour from
Tokyo to Kyoto. This gives you the rate of travel of the train. But, as it turns out, knowing the
rate of travel alone is not enough to solve for the distance travelled. Statement (2) alone isn’t
sucient. Write down
2 no
. Eliminate Choice (B).
4. Check out what you’ve written.
You have two nos. Since each statement alone is insucient, you need to consider both
statements together.
5. Evaluate the two statements together.
Statement (1) gives you the time travelled
t 2 hours
, and Statement (2) tells you that the
rate of travel is
r 250 kilometers/hour
. Because you have the necessary pieces of the
equation, you’re able to solve for the distance that the bullet train travels. The two state-
ments together provide you with enough information to solve the question.
8. C. 64
This question concerns exponents. You are given an expression and asked for the value of the
expression if
y 1
. Look for a way to make the bases of the terms the same. Because
16 4
2
,
you can rewrite the expression as:
4 44
2yz z
Since exponents with the same base can be added together, you can simplify the expression to:
4
2yz z
The z terms cancel out and you are left with
4
2y
. You know that
y 1
, so the expression
becomes
4
3
, or 64. The answer is Choice (C).
9. A.
1
6
x
The rst fraction involves addition, so you’ll need to nd a common denominator. The easi-
est common denominator to nd for 3 and x would be 3x. So, multiply the rst fraction by
3
3
and the second fraction by
x
x
to create the common denominator. Then add:
21
3
6
33
6
3xx
x
x
x
x
Multiply this new fraction by
x
2
:
6
32
6
6
2
x
x
xxx
x
Simplify:
6
6
6
66
1
6
22
xx
x
x
x
x
x
x
And you’re done!
10. C. Both statements together are sucient, but neither statement alone is sucient to answer
the question asked.
Don’t get too concerned about performing calculations or attempting to completely solve the
problem. Just focus on whether the statements provide enough information to reach a solution.
CHAPTER 22 Practice Test Answers andExplanations 353
1. Find out what to solve for.
The question is asking for the original price of a phone charger. The statement tells you that
the total discounted price (t) is $630. You don’t know enough about the details of the
discount yet to start solving the problem, so it’s time to look at each statement.
2. Examine Statement (1).
Statement (1) gives you the details of the sale that the store is oering. Since you know that
the discount is going to be applied to the total purchase price, you can write an equation to
help determine the original price of the phone charger alone. Use d to represent the
discount percentage. The discounted price will be the original price multiplied by
1 d
.
The total discounted price (t) is equal to
1 d
multiplied by the sum of the original prices of
the smartphone (s) and the phone charger (c). So
tdsc1
. You know that
t $630
,
and you can gure out whether d is 15 percent or 20 percent, but you don’t know the original
prices for the smartphone or the phone charger. Therefore, you still have two unknowns in
your equation: s and c.
With a single equation and two unknowns, you don’t have enough information to solve the
problem. Statement (1) is insucient. Write down
1 no
. You can eliminate Choices
(A) and (D).
3. Evaluate Statement (2).
Statement (2) tells you that the original price of the smartphone alone was $720. Since this
doesn’t give you any information about the details of the sale that the store is oering,
Statement (2) is not sucient. Write down
2 no
and eliminate Choice (B).
4. Check out what you’ve written.
You have nos for each statement, so now you need to look at both of them together.
5. Evaluate the two statements together.
Using Statement (1), you know that the total purchase must have been at least $500 to end
up with a nal price of $630, so you know there is a discount of at least 15 percent. To gure
out if the customer is receiving a discount of 20 percent, multiply $800 by 0.8, which equals
$640. Since the nal price is less than $640, you know that the total price was not high
enough to get the 20 percent discount. So, the discount was 15 percent, and
d 015.
.
You can substitute in values for t and d:
630 1015. sc
Statement (2) provided you with the nal piece of information that you were missing after
evaluating Statement (1). Now that you have this, you can plug in $720 for s in your equation
and solve for the original price of the phone charger. The combination of the two statements
provides enough information to answer the question.
11. B.
( ,)08
This is a coordinate geometry question, so you’ll need to work with equations of lines and
slope to determine where the lines intersect.
While drawing out a sketch of the points and lines will help to visualize the problem, you
shouldn’t rely on your artistic skills to nd the correct answer; some of the points may be
close together, and graphing by hand isn’t 100 percent accurate.
354 PART 6 Practice Makes Perfect
You know that the rst line passes through the points (–2, 2) and (–1, –3). To nd the equa-
tion of this line, rst you’ll need to nd the slope, m. To nd m, gure out rise over run by
dividing the dierence in y values by the dierence in x values:
m
y
x
23
21
5
1
5
Once you know the slope is –5, you can substitute the value for m in the equation of the line:
y xb5
.
You know the point (–2, 2) is on the line, so substitute these coordinates for x and y to nd
the value for b:
yxb
b
b
b
5
252
210
8
Now you know the equation for the rst line:
y x58
.
The equation for the second line is
y x 8
. To nd where the two lines intersect, set them
equal to each other and solve for x:
xx
x
x
858
60
0
When you know that
x 0
, you can tell the correct answer is Choice (B); it’s the only answer
with an x value of 0.You don’t have to solve for y to solve this problem, but you can if you
want by substituting x into either equation:
y
y
08
8
12. B.
x 1
4
This problem deals you an algebraic expression with two unknowns: x and y. The problem
tells you that
y
x
2
, so you can insert that value for y in the equation to get the expression
solely in terms of x. Solve by performing division in the rst fraction:
x
x
x
x2
1
24
, which
simplies to
1
4
when you cancel x from the numerator and denominator.
Then add to nd the correct answer:
1
44
1
4
xx
.
13. D. Each statement alone is sucient to answer the question asked.
For this problem, drawing a Venn diagram may help you visualize the relationships in
thedata.
CHAPTER 22 Practice Test Answers andExplanations 355
1. Find out what to solve for.
The question is asking you to determine how many families have shopped at both Fresh
Food Mart as well as Sally’s Market.
You are determining the number of families that have shopped at both stores (b). Based on
the diagram, you know that
nf bs20
. The problem statement tells you that 17 of the
families have shopped at Fresh Food Mart, so
fb17
. It also tells you that 12 of the
families have shopped at Sally’s Market, so
b s 12
. At this point, you have three equations
with four unknowns. Statements that supply a value for at least one of the unknowns will
allow you to solve for any of the others.
2. Examine Statement (1).
Statement (1) tells you that 15 percent of the families haven’t shopped at either store.
Therefore,
n 01520.
, so
n 3
. You can substitute n into your rst equation to give you
320fbs
. You now have three equations with three unknowns, so you can solve for
each of the variables.
You could stop here, but if you want to be completely sure of your answer, you can solve for
b: Substituting
fb17
into your rst equation, you get
31720s
. This gives you
s 0
.
When you substitute s into your nal equation, you get
b 012
, therefore
b 12
. Statement
(1) is sucient. Write
1 yes
on your noteboard. You’ve eliminated Choices (B), (C), and (E).
3. Evaluate Statement (2).
Statement (2) says that all the families who have shopped at Sally’s Market have also
shopped at Fresh Food Mart. This tells you that no families have shopped at only Sally’s
Market, so
s 0
, and therefore
b 12
. Statement (2) is also sucient. Write
2 yes
. Both
statements are sucient.
14. D. 96,800
This is a percent change problem dealing with the number of parts produced in dierent
years. Knowing that Anthony’s business made 80,000 parts last year and 88,000 parts this
year, you can calculate the percent growth using the percent change formula, which is the
dierence between the two values divided by the original value:
parts produced this year parts produced last year
parts prooduced last year
x
x
x
10
88 000 80 000
80 000 100
8 000
80 000
,,
,
,
,
1100
1
10 100
10
x
x%
To maintain 10 percent growth next year, the business will need to produce the same number
of parts as last year + 10 percent more, which you can express as 110 percent or 1.1 of 88,000:
88 000 11 96 800,.,
, which is Choice (D).
Make sure you use the new year’s value when calculating the percentage increase for the
upcoming year. Choice (C) reects an increase of 8,000 parts, but that amount is 10 percent
of the parts made last year and only about 9.1 percent of the parts made this year. To main-
tain 10 percent growth, the number of additional parts made next year must be greater than
this year’s.
356 PART 6 Practice Makes Perfect
15. A.
35.
To nd the surface area of a cylinder, you need to add up the areas of each of its components.
The area of each circular base is
r
2
. Multiply this formula by 2 to account for both circular
ends of the cylinder:
2
2
r
.
You have the formula for the area of both ends, but you still have to consider the area of the
curved side of the cylinder. That dimension is the circumference of the circular base
2 r
multiplied by the height (h) of the cylinder:
2 rh
.
Find the total surface area by adding the two dimensions:
2 2
2
rrh
.
Now plug in the values. The diameter of the cylinder is 1, and the radius is half the diameter,
or 0.5. The height of the cylinder is 3. Insert 0.5 for r and 3 for h, and nd the sum:
22
2
05 2053
2025 215
05
2
2
rh rh SA
SA
SA
..
..
. 3
35
SA
SA.
16. A.Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the
question asked.
Be careful not to jump ahead, even if you are able to gure out the solution with the rst
statement.
1. Find out what to solve for.
The question is asking whether
x
y
1
. Since y is a positive integer, you can multiply both
sides of the equation by y. So now you just need to gure out whether
xy
.
2. Examine Statement (1).
Statement (1) says that
xy3
, so
xy3
. Clearly,
xy
. Therefore, x is not greater than
y, and the inequality given in the question is false. Statement (1) is sucient. Write down
1 yes
and eliminate Choices (B), (C), and (E).
3. Evaluate Statement (2).
Statement (2) tells you that
xy
y
1
.
Multiply both sides of the equation by y to get
xy5
, which you can also present as
xy5
. While you can come up with some values for x and y that would satisfy both this
equation and the equation given in the problem statement, Statement (2) really doesn’t give
you enough information to determine whether the statement
x
y
1
is true or false in every
case. Statement (2) is not sucient. Write down
2 no
on your noteboard. The answer must
be Choice (A).
17. C. $64.00
This a prot question dealing with two dierent merchants each selling the same product.
You can eliminate Choice (A) right away. If Patrick makes more prot than Mel, he must be
charging more than $60, the price Mel charges for her shirts.
A general equation for the prot of each merchant is that prot (p) is equal to selling price
(s) minus cost (c). So,
psc
. You can write a prot equation for each merchant to make
solving the question easier. For Mel (M),
psc
MMM
. Because Mel is selling her shirts for
$60,
s
M
60
and
pc
MM
60
.
For Patrick (P),
psc
ppp
. You know that Patrick’s prot is $24, so
24 sc
pp
.
CHAPTER 22 Practice Test Answers andExplanations 357
If Patrick makes 20 percent more prot than Mel, then
pp
pM
120%
. Find Mel’s prot by
substituting $24 for
p
p
in the equation:
24 12
24
12
20
.
.
p
p
p
M
M
M
Once you know Mel’s prot is $20 per shirt, you can nd the cost of her shirt:
pc
c
c
c
Mm
m
m
m
60
20 60
40
40
Because you know Patrick and Mel have the same shirt cost, you can now nd out how much
Patrick sells his shirt for:
psc
s
s
ppp
p
p
24
40
64
Patrick sells his shirt for $64.00, Choice (C).
18. B.
30
49
To solve this algebra question with one unknown, begin by dividing both sides by 7:
7
25
3
25
3
7
xx
xx
Next, determine a common denominator for the fractions on the left side and nd their sum:
xx xxx
25
5
10
2
10
7
10
Set that sum equal to
3
7
and solve for x:
7
10
3
7
493
0
30
49
x
x
x
19. B.Statement (2) alone is sucient, but Statement (1) alone is not sucient to answer the
question asked.
You may be tempted to start this problem by solving for variables, but wait until you’re sure
this activity actually helps you answer the question:
1. Find out what to solve for.
The question is asking for the value of a function of x and y. The problem statement tells you
that y is 1, so you just need the value of x to determine the value of the function.
2. Examine Statement (1).
Statement (1) gives you the equation
y
1
2
2
2
. You already know the value of y, so solving
this equation isn’t going to get you any closer to the solution. Statement (1) is not sucient.
Write no next to (1) on your noteboard and eliminate Choices (A) and (D).
358 PART 6 Practice Makes Perfect
3. Evaluate Statement (2).
Statement (2) tells you that
xy45
. Substituting in
y 1
, you can solve for x and deter-
mine that x is also equal to 1. Going back to the function, you can plug in values of 1 for x and
y and determine the value of the function. Statement (2) is sucient. Write yes next to (2) and
pick Choice (B).
20. E.Statements (1) and (2) together are not sucient to answer the question asked.
As you answer the questions, rely only on the given information and not assumptions about
the properties of geometric gures.
1. Find out what to solve for.
The question is asking for the length of side m of a triangle. The gure alone doesn’t really
give you many clues about the angles or lengths of any of the sides of the triangle, so there’s
not much you can gure out up front.
2. Examine Statement (1).
Statement (1) tells you that side p has a length of 4. This alone really isn’t useful. Since you
don’t know the angles, you can’t gure anything else out. Although it may be tempting to
assume that sides p and n are the same length since they look similar, resist the urge!
Statement (1) is not sucient. Write
1 no
on your noteboard and eliminate Choices
(A) and (D).
3. Evaluate Statement (2).
Statement (2) tells you that angle A is 90 degrees, meaning that this is a right triangle. This
also means that m is the hypotenuse of the triangle and can be solved for using the equation
pnm
22 2
. However, you still don’t know what the lengths of sides n and p are, so you
can’t yet solve the problem. Statement (2) is also not sucient. Write
2 no
. You’ve elimi-
nated Choice (B).
4. Check out what you’ve written.
You have two nos, so you need to look at the information in both statements together.
5. Evaluate the two statements together.
Using the length of p from Statement (1) and the fact that the triangle is a right triangle from
Statement (2), you can write the equation
4
2
22
nm
. While each statement provides some
information about the properties of the triangle, you are still missing the length of side n, so
you can’t quite solve for the length of side m. Even with the information from both state-
ments combined, there is not enough to solve the problem.
21. D.
x
29
17
This question presents you with an inequality and asks for the possible values of x to solve
the inequality. The fastest way to solve this problem is to get x by itself on one side of the
inequality. An easy way of getting rid of the denominators is by multiplying the entire
inequality by 6.
6
35
2
64 6
2
3
33 5242 2
xx
xx
CHAPTER 22 Practice Test Answers andExplanations 359
Then, you can more simply solve the inequality for x:
33 5242 2
915242 4
15 33
24
17 29
29
17
xx
xx
xx
x
x
Remember, when dividing an inequality by a negative number, the inequality sign ips from
greater than to less than or vice versa.
22. A.Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the
question asked.
Rewriting the word problems as equations can help you determine whether you have enough
information to solve the problem.
1. Find out what to solve for.
This is a work-rate problem dealing with the rates at which Roland and Felicia can perform
testing of circuit boards. The question is asking how many circuit boards Felicia can test in an
hour. Let f be the number of minutes it takes for Felicia to test a circuit board alone. To nd
the number of circuit boards Felicia can test in an hour, you divide 60 minutes by f.
The problem statement tells you that Roland and Felicia together can test a circuit board in
eight minutes. This can be rewritten as an equation, with r being the number of minutes it
takes for Roland to test a circuit board on his own:
111
8fr
.
2. Examine Statement (1).
Statement (1) tells you that Felicia can test circuit boards twice as fast as Roland. This means
Felicia can test a circuit board in half the time that it takes Roland. From this you can write
the equation
f
r
2
. Using this equation in combination with the equation you wrote above,
you have two equations with two variables, and can solve for f. This will allow you to nd the
number of circuit boards Felicia can test in an hour. Statement (1) is sucient, so write
1 yes
on your noteboard. You’ve eliminated Choices (B), (C), and (E).
3. Evaluate Statement (2).
Statement (2) throws an extra person into the mix, and tells you that with their friend Cory
helping them, the three can test a circuit board in seven minutes. From this, you can write
the equation
1111
7frc
. Looking at the equation and the one you developed from the
problem statement, you can see that you have two equations with three unknowns. You
won’t be able to solve the question with just this information. Statement (2) on its own is not
sucient, so write
2 no
.
23. D. 16
This question deals with the average age of cars in a parking lot. It tells you that the average
age of the ten cars is seven years. The equation for averages can help for this problem:
Average
Sum
Quantity
.
You know that the average age is seven years, and the quantity of cars is ten, so the sum of
the ages is 70 years:
7
10
70
Sum
Sum
.
360 PART 6 Practice Makes Perfect
The problem then tells you that the average age of nine of the cars is six years. Using the same
average equation, you can nd that the sum of the ages of those cars is 54 years:
6
9
54
Sum
Sum
.
The dierence in the sums is the age of the remaining car:
70 54 16
. The age of the tenth
car is 16 years.
24. C. 3
This is a rate problem dealing with the speed and distance of a runner, Cindy. In rate prob-
lems, rate multiplied by time equals distance.
First, Cindy runs for 16 minutes at 7.5 miles per hour. Multiplying the rate by the time will
get you the distance traveled. However, you need to convert the units so that you’re only
dealing with minutes.
75 1
60
16 2
. miles
hour
hour
minutes
minutes miles
So, for the rst portion of her run, Cindy traveled a distance of two miles. For the second
portion, Cindy runs at six miles per hour for ten minutes.
61
60
10 1
miles
hour
hour
minutes
minutes
mile
Therefore, Cindy ran for two miles at 7.5 miles per hour and then for one mile at 6 miles per
hour, which results in a total of three miles.
25. B.Statement (2) alone is sucient, but Statement (1) alone is not sucient to answer the
question asked.
Don’t get tripped up dealing with decimals!
1. Find out what to solve for.
The question is asking for the value of a. Since you are given an equation with two variables,
a and b, you know you need to nd b to solve for a. Rewriting the equation to not use
scientic notation may also make it easier to handle:
a b0010035..
.
2. Examine Statement (1).
Statement (1) gives you an additional equation, also with unknown variables of a and b. At
rst glance, it seems like you should be able to use this equation to solve the problem, since
you have two equations and two unknowns. Solving this new equation for b gives you
b a100 35.
.
Substituting this expression back into the original equation gives you
a a001 100 35 0 035...
. When you simplify, you get
a a 0 035 0 035..
. Trying to solve
for a, you realize that the equation given to you in Statement (1) is just the same equation
given in the problem statement, and it doesn’t help you to nd the value of a. Statement (1)
is not sucient, so write
1 no
on your noteboard. You can eliminate Choices (A) and (D).
3. Evaluate Statement (2).
Statement (2) also provides you an additional equation with unknown variables a and b.
Using the same process as before, you can rearrange the equation in terms of b to get
b a58510.
. Substituting this expression back into the original equation, you get
a a001585 10 0 035.. .
. At this point, it’s obvious you can solve for a, so Statement (2) is
sucient. Write yes next to (2) on your noteboard. The correct answer is Choice (B).
CHAPTER 22 Practice Test Answers andExplanations 361
26.
E.Statements (1) and (2) together are not sucient to answer the question asked.
Use only the information the problem gives you.
1. Find out what to solve for.
The question is asking you for the value of the perimeter of a four-sided shape. Since the
problem statement doesn’t say anything about the lengths of the sides or the angles, don’t
assume the shape is a square or a rectangle even if it appears so. At this point, you know
that you need to add up
tuvw
to calculate the perimeter.
2. Examine Statement (1).
Statement (1) says that all the angles in the gure are right angles. This tells you that the
shape is a rectangle. This doesn’t really get you any closer to solving the problem, because
you’re still stuck at
tuvwperimeter
. Statement (1) is not sucient, so write
1 no
on
your noteboard. You can eliminate Choices (A) and (D).
3. Evaluate Statement (2).
Statement (2) gives you a value of 2 for t. If you knew that the shape was a square, that
would be enough to calculate the perimeter. But the problem statement doesn’t tell you
that, so Statement (2) is also not sucient. Write
2 no
and eliminate Choice (B).
4. Check out what you’ve written.
You have two nos on your noteboard, so you need to see if you can solve the problem with
both statements together.
5. Evaluate the two statements together.
Using both statements together, you know that the shape is a rectangle where one side has
a length of 2. Since it’s a rectangle, you know that the opposite side has the same value, so v
is also 2. However, you don’t have enough information to gure out the length of u and w, so
you can’t solve the problem. The statements together are insucient.
27. D. $1,500
This problem can be translated to math equations to help visualize the information in the
problem. The total amount spent is equal to the sum of buying supplies (s) plus hiring labor
(l) plus truck rental (t). The equation is
2 000, slt
.
You know that Jerry spent 10 percent on supplies:
2 000 10 200,%
.
So,
s 200
.
You also know that the truck rental cost ve times as much as hiring labor:
tl5
.
Substitute the values for s and t into your rst equation:
2 000 200 5
1
800 6
300
,
,
ll
l
l
When you know Jerry spent $300 on hiring labor, you know that he spent ve times as
much, or $1,500, on his truck rental.
28. B. 50 percent
This geometry problem deals with a right triangle. The question asks you to nd what x
would have to be if the area of the triangle were tripled and if y were doubled. Problems that
concern primarily variables may be easier to solve when you give those variables simple
values. For example, you could treat the triangle in the gure as a 3:4:5 right triangle.
Itsbase and height would therefore be 3 and 4, so the area would be
1
2
34
, which is 6.
362 PART 6 Practice Makes Perfect
Ifyoutriple the area to 18 and double y to 8, the resulting value for x in the larger triangle
would be
4
1
2
:
1
2
818
4
18
18
4
4
1
2
x
x
x
x
Because
4
1
2
is 50 percent greater than 3, the answer is Choice (B).
You can also solve by creating equations for the area of each triangle. You can use subscripts
of 1 to denote the original triangle and 2 to denote the new, larger triangle:
Ax
y
Ax
y
11
1
222
1
2
1
2
Based on information in the question, you also know that
AA
21
3
and
y y
21
2
.
Plug the value into the area expression for the larger triangle:
Axy
Axy
xy
xy
xy xy
22
2
12
1
11
21
11 21
1
2
3
1
2
2
3
1
2
1
2
2
3
2
Simplify the equation by dividing
y
1
from both sides of the equation:
3
2
15
12
12
xx
xx
.
This tells you that the larger triangle has a side length x that is 1.5 times the length of the
original side x. This is an increase of 50 percent.
29. C. Both statements together are sucient, but neither statement alone is sucient to answer
the question asked.
Using a chart can help you get the question information organized.
1. Find out what to solve for.
The question provides some information about the types of bikes sold at a bike shop. You
can tell that the shop sells mountain bikes and road bikes. The question is asking you what
percentage of bikes sold are mountain bikes for kids. Since you don’t have any information
yet about what percentage of bikes are for kids, you need more information.
2. Examine Statement (1).
Statement (1) tells you that 20 percent of the bikes sold are for kids and 80 percent are for
adults. This is a key piece of information missing from the problem statement. With this new
data, you can draw a table to organize the information:
CHAPTER 22 Practice Test Answers andExplanations 363
At this point, still too many dierent possibilities exist for how the types of bikes could be
distributed. You need more information to determine what percent of bikes sold are
mountain bikes for kids. Statement (1) is not sucient, so write
1 no
on your noteboard.
You can eliminate Choices (A) and (D).
3. Evaluate Statement (2).
Statement (2) tells you that 20 percent of the bikes sold are road bikes for adults. You can
create another table, this time lling it in with the information from the question and
Statement (2):
You can determine that 5 percent of the bikes sold are road bikes for kids because you know
that 25 percent of all bikes sold are road bikes and 20 percent are road bikes for adults. But
once again, you don’t have enough information to solve the problem. Statement (2) is not
sucient. Write
2 no
on your noteboard and eliminate Choice (B).
4. Check out what you’ve written.
You’ve found that each statement on its own isn’t sucient, so now it’s time to evaluate
whether they give you enough information combined.
5. Evaluate the two statements together.
You can nally ll in the table using all the information provided in both statements:
Both statements combined give you what you need to determine the percentage of bikes
sold that are mountain bikes for kids.
30. D. Each statement alone is sucient to answer the question asked.
Don’t underestimate simple-looking questions. Be diligent and work through the steps.
1. Find out what to solve for.
The question is asking for the value of x, and gives you the expression
4 38xyz
. At this
point, all you can do is rearrange the equation to put x on one side:
4 38
43 8
38
4
xyz
xyz
x
yz
This information doesn’t get you any closer to solving for x.
364 PART 6 Practice Makes Perfect
2. Examine Statement (1).
Statement (1) tells you that x, y, and z are all equal. Substitute x for y and z in the expression,
and you get
4 38xxx
, which you can surely solve for x. Statement (1) is sucient.
Write
1 yes
on your noteboard. You can eliminate Choices (B), (C), and (E).
3. Evaluate Statement (2).
Statement (2) gives you the equation
zy43
. At rst glance, this may not seem too
helpful, since you only have two equations and three unknowns. But when you substitute
the equation into the original expression in place of z, you get
4 3438xy y
. The y
terms end up cancelling each other, so you’re left with
4 48x
, which you can also clearly
solve for x. Solution (2) is also sucient.
31. A.Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the
question asked.
Converting word problems into equations may help you solve them.
1. Find out what to solve for.
This is a mixture problem, so you know you’ll need to use a mixture equation. You only know
that George has 1,000 gallons of fuel in his supply tank at 11 percent ethanol, but you don’t
know the percentages of ethanol in the suppliers’ fuel. Write the problem in equation form:
%%
ethanol in Supply Tank gallons in Supply Tank ethannol in Brian’s
gallons of Brian’s addedfinal % ethan
ool final # of gallons
With b designating the percent of ethanol in Brian’s Biofuels and g the number of gallons of
Brian’s Biofuel needed to add, substitute the information you know already into the
equation:
11 1 000 12 1 000%, %,bg g
You need to determine g, so you can see that what you really need is the percent of ethanol
in Brian’s Biofuels, or b.
2. Examine Statement (1).
Statement (1) tells you that Brian’s Biofuels provides fuel with 80 percent ethanol. This is the
value for b you were previously missing. All you have to do is plug in 80 percent for b in the
equation you wrote above, and solve for g. Statement (1) is sucient. Write
1 yes
on your
noteboard and eliminate Choices (B), (C), and (E).
3. Evaluate Statement (2).
Statement (2) gives you information about the mixture currently in George’s supply tank. It
has 10 gallons of fuel from Brian’s Biofuels and 990 gallons of fuel from Dyon. Writing this as
an equation where d is the percent of ethanol in Dyon fuel,
you have
11 1 000 10 990%, bd
.
Using this equation along with the one you developed form the problem statement, you
have two equations with three unknowns, so you aren’t able to reach a solution. Statement
(2) is not sucient. Write
2 no
on your noteboard and pick Choice (A).
32. C.
40 5.
This problem shows you an isosceles right triangle and tells you that the hypotenuse has a
length of 9. For a right triangle, apply the Pythagorean theorem: the sum of the legs squared
equals the hypotenuse squared.
CHAPTER 22 Practice Test Answers andExplanations 365
xx
x
x
x
222
22
2
9
2
9
40 5
40 5
.
.
You can also solve this problem by observing the side ratios of isosceles right triangles:
11 2::
. Because the hypotenuse is 9, the side length of each leg is
4 52.
.
92
9
2
9
2
2
2
92
2
45 2
x
x
x
x
x.
But that answer isn’t available. Clearly, though, Choices (A) and (B) are wrong. To convert
your answer to one that expresses the entire value as a square root, square 4.5 to get 20.25.
Then take 20.25 times the 2 under the root sign to get 40.5. The answer that is the same as
4 52.
is Choice (C).
33. C. 10
This problem is asking how many of the 60 guests at Taco Fusion restaurant ordered both
tacos and sushi for lunch. You may nd it helpful to draw a diagram:
In the diagram, t is the number of guests that ordered only tacos, s is the number that
ordered only sushi, b is the number that ordered both, and n is the number that ordered
neither.
The problem tells you that there were 60 guests, so
ntbs60
.
You know 20 guests ordered sushi, so
b s 20
. In terms of b,
sb20
.
You also know 45 of the guests ordered tacos, so
tb45
. In terms of b,
tb45
.
Finally, ve of the guests ordered neither item, so
n 5
.
When you substitute these expressions for s, t, and n into your rst equation, you get this:
5452060
70 60
10
10
bb b
b
b
b
34. B.Statement (2) alone is sucient, but Statement (1) alone is not sucient to answer the
question asked.
Even if a piece of information seems helpful, don’t count it as sucient if it isn’t necessary.
366 PART 6 Practice Makes Perfect
1. Find out what to solve for.
The question is asking for the population of Greenvale at the end of this year. The problem
statement tells you that the population grows by 10 percent each year, but doesn’t give you
any idea what the population is. To solve the question, you need to know the population of
Greenvale.
2. Examine Statement (1).
Statement (1) tells you that the population of Greenvale grows by 21 percent over a two-year
period. While this tidbit may seem useful at rst, it’s really just a restatement of information
you already have. You know that the population grows by 10 percent each year, so this
statement just tells you that over a two-year period
110110 121%%%
.
Statement (1) is not sucient. Write
1 no
on your noteboard and eliminate Choices
(A) and (D).
3. Evaluate Statement (2).
Statement (2) says that there were 10,000 people living in Greenvale at the beginning of last
year. This data gives you a starting point to calculate the population at the end of this year. If
the population grew by 10 percent last year, then the population at the end of last year was
10 000 11011 000,%,
. So the population at the end of this year will be
11 000 11012 100,%,
. Statement (2) is sucient. Write
2 yes
on your noteboard, and
pick Choice (B).
35. A.Statement (1) alone is sucient, but Statement (2) alone is not sucient to answer the
question asked.
Make sure you know your basic geometric formulas for area.
1. Find out what to solve for.
The question is asking for the area of the triangle. You know the formula for the area of a
triangle is one-half the base times the height. In this case, the base of the triangle is x, and
the height of the triangle is y, so
A
xy
2
.
2. Examine Statement (1).
Statement (1) tells you that
xy 100
. This is very helpful for nding the area, because you
can plug it directly into your area formula. Substituting in 100 for xy, you know you can solve
for A:
A
100
2
. Statement (1) is sucient. Write
1 yes
on your noteboard and eliminate
Choices (B), (C), and (D).
3. Evaluate Statement (2).
Statement (2) says that
y 10
. You can substitute this data into your area formula to get
A
x
10
2
, but you still need to know the value of x to solve the problem, so Statement (2) is
insucient. Write
2 no
on your noteboard, and pick Choice (A).
36. C. $1.60
This question asks you to gure out the cost of production when given a prot percentage.
Be sure to set up your prot equation correctly. You can’t just multiply $2.00 by 75 percent
to gure out the cost. In this case, the prot percentage is based on the cost, not on the price
the company charges.
Write an equation using p as the price the company is selling each gallon of liquid nitrogen
for and c as the cost of production of one gallon of liquid nitrogen when it wants a prot to
be 25 percent of its cost:
pc c025.
.
CHAPTER 22 Practice Test Answers andExplanations 367
So
pc125.
. Because you know the price is $2.00, you can solve for the cost:
2125
16
.
.
c
c
The cost of production is $1.60.
37. C.Both statements together are sucient, but neither statement alone is sucient to answer
the question asked.
Apply the steps:
1. Find out what to solve for.
The question tells you that Jack has three activities that make up his morning routine. Assign
a variable to each one to represent the amount of time it takes him to complete that activity.
That way, you can rewrite the problem as an equation. The total time taken, 45 minutes, is
equal to the time spent taking a shower (s) plus the time spent drinking coee (c) plus the
time spent walking to work (w). So, your equation is
45 scw
. The question is asking you
how long it takes for Jack to drink coee, so you’re solving for c.
2. Examine Statement (1).
Statement (1) says that it takes Jack four times as long to walk to work as it takes him to drink
coee. In equation form, this is
wc4
. Substitute this value for w in the equation:
454sc c
. You still have two unknown variables; you would need to know how long it
takes Jack to take a shower to solve the question. Statement (1) is not sucient. Write
1 no
on your noteboard and eliminate Choices (A) and (D).
3. Evaluate Statement (2).
Statement (2) tells you that showering and drinking coee take Jack a total of 25 minutes.
You can write this out in equation form:
sc25
. You can then substitute this value into the
original equation:
4525 w
. You know
w 20
, but you can’t solve for c. Statement (2) is
also not sucient. Write
2 no
on your noteboard. You’ve eliminated Choice (B).
4. Check out what you’ve written.
You have doubles nos, so you need to look at both statements together.
5. Evaluate the two statements together.
When you combine the equation from Statement (1),
454sc c
, with the knowledge
from the second statement that
sc25
, you know
45254c
, which clearly allows you to
solve for c. The two statements together provide enough information to solve the problem.
Section4: Verbal
1. A.The factors that make an area desirable are also those that can pose the most risk.
The substantiating details in the paragraph describe situations where those factors that
create desirable areas such as the Toboku coast, Florida, Hawaii, and productive farmlands
are the same factors that create great destruction, so Choice (A) is the best answer. Choice (B)
is too specic. Choice (C) mentions the destructive forces in the paragraph but not the con-
comitant desirability of the environments they also cause. Choice (D) requires too much
speculation. The paragraph states that humans pay a price for living on Earth, but it doesn’t
state the requirement that they learn to live with the risks. The paragraph is less about
humans and more about the kinds of natural risks on Earth. Choice (E) doesn’t address all of
the risks provided in the paragraph and is therefore too specic to be its main idea.
368 PART 6 Practice Makes Perfect
2. C.Loss of retail clothing sales due to a mall ood
In the nal paragraph of the passage, the author discusses what he calls direct and indirect
losses. Direct losses, he notes, are those that involve the destruction of physical assets; indi-
rect losses are those that arise as a result of the direct ones. Choices (A), (B), (D) and (E) all
involve the actual destruction of physical assets: a library, school building, livestock, and a
pavilion, respectively. Choice (C), on the other hand, reports the loss of income due to a
direct loss— a mall ood. Thus, only Choice (C) denotes an indirect loss because loss in
sales isn’t tangible and therefore isn’t a physical asset.
3. D. hazards are not under human control, while risks usually are
Skim the answer choices to determine whether any of them can be easily eliminated. Choice (B)
isn’t a true statement according to the information contained in the passage. The passage
notes that “... risk is the product of hazard,” which is the opposite of stating that hazards
result from risks. You can also eliminate Choice (A) because it claims that risks occur natu-
rally while hazards result from human interaction; the passage states that the opposite is
true. So, you’ve narrowed options down to Choices (C), (D), or (E). Choice (C) makes another
false statement— nowhere in the passage does the author report that hazards, and not
risks, can lead to disasters. Rather, he implies that the two together increase the risk of a
disaster. Choice (D) sounds like a serious contender, and the rst two lines of the third para-
graph back it up. Just to be sure, however, take a look at Choice (E). The words “harder to
quantify” may jump out at you because you nd them in the nal paragraph, but upon more
scrutiny, you can determine that the author claims that “economic impacts,” not risks, are
hard to quantify. Choice (D) is the best answer.
4. A. describing the causes and impacts of natural disasters
Eliminate answers that contain information that appears in just a part of the passage rather
than the whole. The author doesn’t discuss economic impacts until the nal paragraph, so
Choice (B) isn’t a strong contender for the passage’s primary concern. The role of human
beings in risk is covered early in the passage, but the passage also discusses that some haz-
ards are simply beyond human control, so Choice (C) isn’t the best expression of the primary
purpose. Choice (D), too, only tells part of the story; in addition to loss of human life, the
passage discusses nancial costs. Choice (E) is also inaccurate; the author notes that hazards
aren’t under human control, but risks, at least to some degree, are. By process of elimina-
tion, Choice (A) is the best answer. This general summary statement incorporates informa-
tion discussed in the entire passage.
5. E.It applies statistical data to emphasize the magnitude of damage created by natural
disasters.
Choice (A) is incorrect because the numerical information in the fourth paragraph relates to
human lives lost rather than economic impacts. Choice (B) mentions a specic detail in the
fourth paragraph, but the detail provides supporting evidence rather than the primary pur-
pose of the paragraph. Choice (C) provides a better description of the function of the third
paragraph than the fourth. And you can eliminate Choice (D) because its statement isn’t true;
the paragraph gives numerical data about one event rather than sensory detail about several.
Only Choice (E) oers a plausible explanation for the function of the fourth paragraph in rela-
tion to the rest of the passage. The paragraph provides statistics regarding a specic event
that provides an example of the colossal destruction a natural disaster can cause.
6. E.Areas of high hazard, such as Japan’s Tohoku coast, may have a lower risk of natural
disaster costs than areas where hazard incidents are lower.
The third paragraph claries that the highest cost risk isn’t always associated with the
greatest hazard. Places with less hazard risk may experience greater costs because the
CHAPTER 22 Practice Test Answers andExplanations 369
hazard aects more people or the area is less prepared to withstand damage. Therefore,
Choice (E) is correct.
The passage doesn’t provide clear data regarding the number of reported and unreported
deaths in the tsunami and earthquake disaster, so you can’t denitively compare number of
deaths in Choice (A). The passage says that the tsunami in 2004 caused many more deaths
than average, but it doesn’t say the same for the 2010 Haiti disaster, so Choice (B) is wrong.
Because you don’t have actual data for deaths due to natural disaster in Japan, Hawaii, and
Haiti, you also can’t pick Choice (C). The passage suggests that both economic costs and
death totals are unreported for natural disasters, but it doesn’t compare the two, so you
can’t justify Choice (D).
7. D. must nish constructing, cleaning, and safety-proong its interior
Two primary problems exist in this sentence. The easiest to spot is likely the use of it’s (the
contraction of it is) instead of the possessive form its. Eliminate Choices (A) and (C). Then
check parallel structure in the underlined list. All projects must share the same grammatical
form. Choices (B) and (E) improperly mix the noun construction with the gerund forms of
cleaning and safety-proong, and Choice (E) improperly denes construction as cleaning and
safety-proong the interior. The only answer choice that corrects both issues is Choice (D).
8. B. continent’s past begin with Europeans striding ashore, claiming this “newfound land”
and its human inhabitants for their respective empires
As you compare answer choices, note that some present the plural form continents’ and
others make it singular. Because it’s preceded by the singular this instead of the plural these,
you know there is just one continent and Choices (A) and (C) are out of contention. Another
discrepancy is whether the verb should be the plural begin or the singular begins. The subject
is plural— accounts— so the answer needs to contain the plural form begin to agree with the
subject. Choices (D) and (E) are wrong. Yet another issue is whether the last pronoun should
be the plural their or the singular its. The respective empires belong to the Europeans, which
is plural, so their is proper, verifying that Choice (B) is correct.
9. D. is still used today by many Ethiopians to feed themselves
Because the subject of the sentence (injera) is singular, the proper verb is the singular is
rather than are. Eliminate Choices (A) and (B). Choice (C) introduces an unnecessary pro-
noun, it, that also causes the sentence to be improperly punctuated. The addition of it creates
another independent clause, and independent clauses linked by a conjunction such as and
must also be separated by a comma. Between Choice (D) and Choice (E), (D) is the better-
constructed option. The adverb today describes when the bread is used and therefore should
occupy a position close to the verb used, as presented in Choice (D). Choice (D) also elimi-
nates the redundant inclusion of a second use. You already know that Ethiopians use the
bread; you don’t need to state the action again. Choice (D) is the properly worded answer.
10. A.The degree of erosion to which a coastline is subject is related to the shape of the
sea bottom.
Choice (A) makes sense because the impact of waves is related to the shape of the sea
bottom, and the coast’s erosion is related to the impact of waves. Choice (B) is wrong
because the statements only state the factors (wind velocity and fetch) that inuence wave
size; there’s nothing to suggest that wave size stays close to an average. Choice (C) doesn’t
work; if fetch is the length of the surface of the water, it shouldn’t be related to the shape of
the sea bottom. Choice (D) is wrong because the size of waves comes from wind and fetch,
not the shape of the bottom. Choice (E) looks wrong, too. Wind velocity creates size of waves,
size of waves aects impact, and impact aects erosion, so average velocity of wind playing
no role in erosion doesn’t make sense. Choice (A) is the best answer.
370 PART 6 Practice Makes Perfect
11. A.It is a specic example of a general condition described in the course of the argument.
The argument is that because patients need medical care and hospitals, regardless of
whatthose services cost, hospitals and doctors rather than insurers bear the brunt of
cost- containment measures; the MRI statement provides an example. Choice (A) is a good
answer; the statement is a specic example of capital demands (MRIs and buildings) of the
general condition of scal discipline described in the argument. Choice (B) doesn’t work
because the MRI statement doesn’t counter an attack. Choice (C) isn’t as good an answer as
Choice (A). The author’s claim or conclusion is that health insurers are still proting from
healthcare while doctors, hospitals, and patients are being increasingly squeezed, but the
MRI statement doesn’t indirectly support that claim. Choice (D) doesn’t work. Patients’
needing treatment isn’t a social side eect but a normal event that remains consistent,
regardless of changing circumstances. Choice (E) is wrong; the MRI statement doesn’t intro-
duce the conclusion about the immunity of health insurers. Choice (A) is correct.
12. C. among them, the 20 players were only able to raise about 70 percent of the cost
Use between when discussing two entities, and use among when referring to groups of more
than two. Therefore, you can easily eliminate Choices (A) and (B). Choice (D) has a verb tense
problem; the present perfect tense have raised suggests that fundraising eorts are ongoing.
Choice (E) changes to the passive voice “cost was raised by 20 players” for no apparent
reason. Active voice is generally a better construction than passive voice. Choice (C) correctly
changes between to among without creating new errors.
13. E.Allowing employees to take leave for family matters reduces absenteeism, improves
morale, and surprisingly increases productivity because the employees who are granted
leave tend to work much harder and more eciently when they come back to work.
To weaken the argument, look for an answer showing that allowing family leave doesn’t hurt
productivity or perhaps even helps it. Choice (A) doesn’t aect the argument because stan-
dard of living isn’t an issue, and it doesn’t mention workplace productivity. Choice (B) could
arguably weaken the argument because it provides evidence that workers may not abuse the
privilege of leave— fathers aren’t taking family leave at all, which weakens the conclusion
that workers would work less if they had leave. On the other hand, if taking paternity leave
angers co-workers, that strengthens the conclusion that family leave hurts workplace
morale, so this isn’t the best answer. Choice (C) strengthens the argument by showing that
FMLA leave costs the employer money. Choice (D) also strengthens the argument by illus-
trating the destruction caused by one employee leaving for a while. Choice (E) weakens the
argument. If employers are worried about productivity and morale, this choice says that
allowing leave actually increases productivity and morale. Choice (E) is the right answer.
14. D. were on board with the new uniforms for the girls’ basketball team, but the team had
made its choice
First, eliminate Choices (A) and (B) because they pair the singular verb was with the plural
subject all. Then eliminate Choice (C) because it uses the plural pronoun their to refer to the
singular noun team. Between Choices (D) and (E), (D) is the better option. Choice (E) con-
tains the present perfect tense “has made,” but the events take place in the past as indicated
by the initial past-tense verb. Choice (D) is the winner.
15. B. forcing many families to make the unfortunate choice between having a roof over their
heads and receiving healthcare
The proper conjunction is and for linking two elements one is choosing between. So Choices
(A) and (C) are wrong because they include the conjunction or. Making a choice between one
element or the other is incorrect. Choice (D) replaces “to make” with “with making,” but the
proper preposition to pair with force is to; one is forced to take action rather than forced with
CHAPTER 22 Practice Test Answers andExplanations 371
taking action. Choice (E) incorrectly swaps between for among, which doesn’t work for a two-
item choice.
16. A.Operating systems with generous amounts of memory are less susceptible to crashing,
even when applications are poorly written.
Okay, you want to nd the four answers indicating that operating systems are responsible
for the smooth functioning of applications and are able to somehow manage their memory
problems. The best way to do this is by process of elimination. If you can nd four answers
that show the operating system handling applications’ memory issues, then the answer
that’s left over should be correct. Choice (B) helps the conclusion because it shows that oper-
ating systems are responsible for handling the memory used by individual applications.
Choice (C) helps because it shows that operating systems can spot overuse of memory and
stop it. Choice (D) helps because it tells you that programmers should know how to program
an operating system that can prevent memory errors, which means all operating systems
should be able to do this. Choice (E) helps the conclusion because it describes what an e-
cient operating system should be able to do. Choice (A) is the only answer that doesn’t put
responsibility for memory management on the operating system; adding memory to the
computer evidently can let the operating system o the hook. Choice (A) is the right answer.
17. E.If people see online images of items in the museum’s collection, they will no longer be
interested in seeing the collection with their own eyes.
The argument seems to assume that if people see the images online, they won’t have any
interest in visiting in person. Choice (A) isn’t the point because the author of the argument
isn’t worried about damaging the images. Choice (B) doesn’t work because the author
doesn’t mention a concern for decreased revenue. Choice (C) likely isn’t the author’s con-
cern. He isn’t specically worried about the extent of online distribution but rather its eect.
Check the remaining answers to see whether you have a better option. Choice (D) isn’t his
concern, either, because he doesn’t mention quality issues. Choice (E) is the best answer. The
author is worried that online publication of the images will remove the incentive to visit the
actual museum in person.
18. C. the number of residents has increased so considerably
Eliminate Choices (B) and (D) because they pluralize numbers. There is a number of residents
rather than numbers of them. Choice (A) has the singular form number, but incorrectly pairs
it with the plural verb have. That leaves you with Choices (C) and (E), and Choice (E) unnec-
essarily adds been to the verb and creates an awkward construction by moving so after con-
siderably. Choice (C) is the best answer.
19. D.Risks are aected by human actions that increase or decrease vulnerability, such as
where people live and how they build.
This sentence requires you to choose between aect and eect. The sentence uses the word as
a verb, so you need to pick an option with aect rather than eect. Choices (A) and (C) can’t
be right. You can also eliminate Choice (B) because it uses like to mean “for example.” The
better option is “such as,” which leaves you with Choices (D) and (E). Choice (E) switches
that to which, but which introduces nonessential clauses and therefore should be preceded by
a comma. The descriptive clause is essential, so that is the proper pronoun and Choice (D) is
the answer.
20. B. executive functioning
Answering this question is pretty cut and dried. The second paragraph indicates that learn-
ing how to resist distraction is part of what it takes for a child to recognize and work toward
a goal, which is dened as— you guessed it— executive functioning. Choices (A), (C), (D),
372 PART 6 Practice Makes Perfect
and (E) are all touched upon to some extent in the passage, but the denitive answer is
Choice (B).
21. A. emphasize that school readiness regards the process as much as the results
The author’s key point is that school readiness is about assessing a child’s ability to learn
rather than relying on test results and the like to determine knowledge. When they’re in a
K–12 school setting, kids have to demonstrate “school readiness” through the results of aca-
demic testing and grades. Choice (A) expresses this point best. Choice (B) is wrong because
although the author notes the dierence between the guiding principles of school readiness
and those used by K–12 school systems, nothing in the passage suggests that she considers
those of the latter “failings.” Choice (C) essentially makes the same argument as Choice (B),
so you can knock that option from contention, too. Eliminate Choice (D); no evidence exists
that this passage is about the author’s opinion. Choice (E) is out, too. Although the author
deals with cognition in the second paragraph, this factor isn’t the primary reason for making
the more general distinction between school readiness and K–12 guidelines. Stick with
Choice (A).
22. D. paying attention to the teacher
In the second paragraph, the author mentions a growing emphasis on executive functioning
skills in the concept of school readiness. She then denes executive functions as those per-
taining to working memory, attention control, attention shifting, and response inhibition.
She gives the example of paying attention to the teacher as an indication of ability to resist
distractions. Because paying attention to the teacher is an indication of executive function-
ing, this skill has likely been one of those on which there has been a “growing emphasis,”
and Choice (D) is best.
Choice (A) is easy to eliminate; performance on achievement tests is associated with the
K–12 system. The other answers relate to school readiness factors mentioned in the last
paragraph and aren’t included as part of executive functioning. Choice (B) is associated with
language skills, Choice (C) is dened as a socioemotional skill, and Choice (E) is part of the
physical health domain.
23. E. socioemotional skills
In the nal paragraph of the passage, the author mentions cooperation with teachers and
peers and developing social relationships as examples of socioemotional skills, which is
Choice (E). Motor skills pertain to the physical health domain. As for Choices (B) and (C), the
author places them into the language skills category. Strong executive functioning skills are
discussed in detail in the second paragraph, where the author notes that these skills help
kids work toward achieving specic goals. Choice (E) is the best bet.
24. A.Spousal and marital diculties were formerly responsible for many premature returns
from foreign assignments.
If helping spouses has improved expatriate retention by such a huge amount, then unhappy
spouses must have previously been responsible for lots of premature returns. Choice (A)
looks like a good answer. If unhappy spouses contributed to employees’ leaving international
assignments, helping spouses adjust would improve the situation. Choice (B) is wrong. If
spouses are already thrilled with the international experience, their dissatisfaction is
unlikely to contribute to employees’ leaving their overseas posts. Choice (C) would support
the argument, but it’s too specic to be a necessary assumption on which the conclusion
depends (there could well be other reasons why spouses are dissatised). Choice (D) doesn’t
explain why helping spouses has improved retention. Choice (E) provides an example of
what companies are doing to help spouses but isn’t the assumption that links the argu-
ment’s premises to the conclusion. Choice (A) is the best answer.
CHAPTER 22 Practice Test Answers andExplanations 373
25.
E. after another, nor does it make its predecessor obsolete
The conjunction nor should be preceded by a comma when it joins two independent clauses,
so Choices (A) and (C) improperly punctuate independent clauses joined by a conjunction.
Choice (B) doesn’t help; it changes the last part of the sentence to an independent clause and
therefore creates a comma splice. It also uses neither incorrectly. The conjunction neither has
to be followed by its partner nor. Choice (D) creates the same conjunction error, and it also
has a punctuation problem. Joining independent clauses in the same sentence with no
punctuation creates a fused sentence. Choice (E) is the only answer that uses conjunctions
properly.
26. A. resenting all their advances, refusing to let them lay hands on him, menacing them with
bared fangs and bristling hair
Check the answers for parallel structure. The list of the dog’s unsociable traits is presented
in –ing form, so eliminate Choices (C) and (D) because they break the structure with the
past-tense form menaced. Pay attention as you examine Choice (B); it can’t be correct.
Bristling is used as an adjective to describe the dog’s hair rather than a noun to end the list of
traits. So the comma before the and is incorrect. The options are down to Choices (A) and (E).
Choice (E) contains unnecessary words. The use of their advances is more succinct than the
advances that they made, so Choice (A) is a better answer. Don’t get caught up with the lack of
a comma and conjunction before the last element of the list. The sentence takes a bit of
poetic license with standard list form, and no option exists to change the format.
27. E.The meadow voles that had the prairie vole gene implanted in them were released into
and observed in the same habitat in which they had previously lived.
Look for information that supports the assumption that the meadow voles’ change in behav-
ior was caused by the implanted gene. Choice (A) is wrong. The choice doesn’t relate the
eects of the hormone to the gene that makes meadow voles monogamous. Choice (B)
explains what’s up with prairie voles but not with meadow voles, and neither’s genes are
mentioned. Choice (C) explains why meadow voles are typically promiscuous but says noth-
ing about whether a gene plays a part in that. Choice (D) says nothing about whether the
transferred gene is the cause of the monogamous behavior. Choice (E) provides the most
support for the assertion that the scientists’ work with genes was the factor that turned the
formerly promiscuous meadow voles into models of monogamy because it rules out a possi-
ble other important factor that may have explained the change (dierent surroundings).
Choice (E) is the correct answer.
28. C.Women who want to have children increasingly seek to delay doing so for many varied
reasons.
The conclusion is that predicting when menopause will occur will make a dierence to
women planning when to have children, which must mean that not knowing when meno-
pause will occur makes it dicult to plan. Choice (A) is wrong because it doesn’t explain why
predicting menopause will help anyone. Choice (B) just provides general information about
menopause. Choice (C) may be right— it provides a reason that women would benet from
knowing when they will experience menopause (they’re delaying longer, so they need to
know how long is too long to delay). Choice (D) isn’t relevant because the argument is about
how accurately predicting the onset of menopause aects childbearing decisions, not how
likely a woman is to conceive in the years immediately prior to menopause. Choice (E) is just
information about ovaries, not an explanation of how this test will help make family plan-
ning decisions. Choice (C) is the best answer.
374 PART 6 Practice Makes Perfect
29. E. excelled not only academically but also athletically
To maintain parallel structure, the two elements joined by the conjunction but must share
the same grammatical form. So athletically is a better choice to pair with academically than is
“in athletics.” Eliminate Choices (A) and (D). The conjunction not only must be paired with
either but also or but, so Choice (B) is out. Choice (C) contains the awkward phrasing
“engaged in excellence,” which is less precise than simply excelled. Choice (E) is the best
answer.
30. D.Employers assume that high-school graduates generally have a much higher level of
mastery of academic subjects than those who earn GEDs.
The argument suggests that a GED is just as good as a high-school education; look for an
answer that contradicts that. Choice (A) doesn’t work. You don’t want evidence showing the
benets of earning GEDs. Choice (B) doesn’t pose a problem. If universities accept GEDs,
that’s more evidence that they’re as good as diplomas. Choice (C) actually strengthens the
argument. Choice (D) does weaken it. If a GED might put one at a disadvantage in the job
market, that’s a reason to stay in school. Choice (E) doesn’t strengthen or weaken the argu-
ment. Choice (D) is correct.
31. D. explain how attention to cybersecurity impacts companies’ technological innovation
Perform a quick scan through the answer choices and see if any catch your eye. Of those
available, only Choice (D) specically references the relationship between cyber-attacks and
technological innovation, which was a major part of the subject matter. Choices (A), (B), and
(E) similarly suggest that the main idea regards the hackers’ success, but the passage is less
about hackers and more about how companies react to hacking. And Choice (E) even suggests
that hacking is heroic. Choice (C) presents the primary purpose of the rst paragraph but not
the entire passage. Choice (D) is the only option that incorporates ideas that appear through-
out the passage.
32. C. weighing business outcomes and risks
The third paragraph clearly states that indirect losses and the cost of defending against
cyber-threats reduce the benets of technology investments, so you can eliminate Choices
(B) and (D). Likewise, in the second paragraph, you nd evidence to support that theft of
intellectual property is a risk of increased global connectivity created by technology invest-
ment, so Choice (A) is out. The last sentence of the second paragraph also suggests that the
way that companies approach cyber-threats— reacting to them only when they occur— is
costly and will likely result in more cyber-attacks. Therefore, Choice (E) likely decreases the
benet of investing in technology. The passage doesn’t indicate that the mere act of weigh-
ing risk and reward in itself incurs cost, so Choice (C) is the answer that has the least chance
of decreasing the potential gains of investing in technology.
33. B. combat problems after they have occurred
When the author references companies’ “siloed and reactive approach” to cybersecurity, he
does so after his discussion about how investing in technology comes with inherent cyberse-
curity risks. The implication is that companies take on these risks without a clear plan for
protecting against them, and therefore, the hackers seem to be winning the battle against
business security systems. Choice (A) incorrectly asserts that companies are performing their
due diligence when it comes to trying to prevent cybersecurity, so you can likely count this
one out. Choice (C) mistakenly gives the credit to companies, so you can eliminate that one
for the same reason you knocked out Choice (A). The passage doesn’t quantify what consti-
tutes “too much” investment, and regardless of whether Choice (D) is true, the passage
infers that this “siloed and reactive approach” is not so much about spending money but
about waiting for issues to develop rather than attempting to prepare for them. Finally,
CHAPTER 22 Practice Test Answers andExplanations 375
Choice (E) suggests that companies are moving full speed ahead with unnecessary techno-
logical innovations and advancements, which is contradictory to the information in the rest
of the passage that suggests companies are becoming slower to innovate because of cyberse-
curity concerns. Choice (B) correctly indicates that companies’ reactive approach waits for
problems to happen before considering the potential risks of technological investment. It’s
the best answer.
34. E. an outline of a streamlined manufacturing process
The second paragraph specically links intellectual property to a new product life-cycle
management system. The answer that relates most directly to proprietary product informa-
tion is Choice (E), information regarding a proprietary product producing process. Choice (A)
describes intellectual property but not that which would likely be leaked in a new product
life-cycle management system. The other choices aren’t examples of intellectual property.
35. A.Increased global communications mean more risk for security breaches.
The passage reveals that increased global connectivity created rewards as well as risks;
Choice (C) overstates its risks and Choice (D) understates the rewards, so eliminate Choices
(C) and (D). Choice (B) is incorrect. According to the passage, global connectivity makes
companies more vulnerable to hackers, but dealing with the attacks is the primary reason for
delayed technological innovation, not general connectivity. The second paragraph links tight
connections to greater vulnerability rather than to greater power over hackers, so Choice (E)
is wrong. The best answer is Choice (A). The author mentions global connectivity to set up
the paragraph about the risks associated with increased access.
36. D. jumps to the conclusion that the defect in the glasses must be due to the optometrist’s
lack of skill
The conclusion is that the optometrist is incompetent; the evidence is that one lens pops out
regularly. But there’s no evidence that that’s because of the optometrist’s lack of skill.
Choice (A) is wrong. Although giving the optometrist a chance to defend himself would be
nice, it’s not a fault of the argument that the speaker doesn’t provide one. Choice (B) is
wrong because other potentially unskilled optometrists have no bearing on the skills of the
one in question here. Choice (C) doesn’t work. The author doesn’t mention any particular
techniques. Choice (D) may be the answer. The author does jump to a conclusion here with-
out making a connection between the glasses and the optometrist’s skill. Choice (E) is wrong
because the author doesn’t suggest that sabotage played a role in the bad glasses. Choice (D)
is the best answer.
37. C.The statement highlights the importance of this discovery because it disproves a long-
held theory about hibernation.
This discovery of an animal that hibernates in hot weather may be groundbreaking, espe-
cially if previous scientic wisdom held that hibernation only happens in cold weather.
Choice (A) is wrong because the belief being challenged isn’t that primates never hibernate
but that animals never hibernate in the heat. Choice (B) isn’t right because the assertion
isn’t an accusation of any kind. Choice (C) makes the most sense because it’s an important
discovery. Choice (D) is wrong. The argument never disputes the conclusion that the behav-
ior is in fact hibernation. Choice (E) doesn’t work because the argument doesn’t set up a
rival theory in a deliberate ploy to attack it. Choice (C) is right.
376 PART 6 Practice Makes Perfect
38. B. we intuitively try to imagine what they would have looked like in real life and to visualize
their physical features
The easiest issue to spot is the improper use of “he or she” to refer to the plural noun peo-
ples. The proper plural pronoun is they, so Choices (A) and (C) are out. Choice (D) corrects the
pronoun problem, but it replaces “their physical features” with the wordy “what their phys-
ical features were like,” a phrasing that is not only awkward but also constructed dierently
from the rest of the nouns in the series. Choice (E) improperly changes the verb from the
conditional perfect tense “would have looked” to the conditional present tense “would
look,” a construction that projects the appearance of past peoples in the yet-to-be-realized
future rather than from a place in the past. Choice (B) applies the proper pronoun without
creating additional errors, so it’s the best answer.
39. A.My European client calls once a week, always in the evening, after everyone has left the
oce. I’ll be sure to get his messages if I turn on my telephone’s answering machine once
aweek.
The aw in the argument is the mistaken belief that the odds of an event occurring can tell
you how often you need to do a certain act. Odds of 1in 1,000 don’t mean that every 1,000th
trip will realize a certain event. It means that an accident could happen in any trip out of
1,000, and you can’t predict which one. The awed reasoning in Choice (A) is similar; turn-
ing on the answering machine on just one particular day won’t necessarily catch a weekly
phone call because the call could come on any day of the week. Choice (B) is wrong. The con-
clusion is mistaken but in a dierent way from the original argument. It’s about proportion-
ality, not probability. Choice (C) isn’t the same as the original argument because you’re not
trying to guess which one of the 1,000 games will result in the jackpot; instead you’re cover-
ing them all. That’s closer to wearing the helmet for all 1,000 rides on the assumption that
one of them will involve a wreck. Choice (D) is totally wrong because the second sentence is
nothing like the original argument’s conclusion; it doesn’t state how many times people in
cars should wear seat belts based on seat-belt statistics. Choice (E) is awed but not in the
same way as the original argument. The aw would be more similar to the original argument
if the MBA student applied to only one of 20 business schools because the odds are 1in 20 of
being chosen. Choice (A) is the closest and is correct.
40. A.Even though Carter had fewer quarters in his piggybank than did his brother Clark, Clark
had less money overall.
This question requires you to access your knowledge of the correct usage of fewer and less.
Use fewer when referring to plural entities, such as M&Ms, students, sunowers, and quar-
ters. Use less to reference singular entities, such as water, damage, appreciation, and money.
So the proper construction in this sentence is “fewer quarters” and “less money”; eliminate
Choices (B), (C), and (D). The language in Choice (E) is potentially confusing. The descriptive
phrase “in his piggybank” seems to refer to Clark rather than the quarters. Choice (A) pres-
ents clearer construction.
41. C.Rugby is somewhat like American football in that both involve downs, tackles, and
touchdowns, but it also combines elements from other sports, such as soccer and hurling.
Because the sentence makes a comparison between only two sports, both is proper and all is
improper. Eliminate Choices (B) and (D). Choice (E) contains a subject/verb agreement prob-
lem: the plural noun both shouldn’t be paired with the singular verb involves. The dierence
between Choices (A) and (C) is the use of “like” or “such as.” Generally, you use like to com-
pare nouns rather than to introduce examples. So the comma before like in Choice (A) is a big
clue that it’s used incorrectly. The comma sets up examples. Therefore, Choice (C) is a better
option than Choice (A).
CHAPTER 22 Practice Test Answers andExplanations 377
Answers at a Glance
Section3: Quantitative
1. E
2. D
3. A
4. D
5. D
6. D
7. C
8. C
9. A
10. C
11. B
12. B
13. D
14. D
15. A
16. A
17. C
18. B
19. B
20. E
21. D
22. A
23. D
24. C
25. B
26. E
27. D
28. B
29. C
30. D
31. A
32. C
33. C
34. B
35. A
36. C
37. C
Section4: Verbal
1. A
2. C
3. D
4. A
5. E
6. E
7. D
8. B
9. D
10. A
11. A
12. C
13. E
14. D
15. B
16. A
17. E
18. C
19. D
20. B
21. A
22. D
23. E
24. A
25. E
26. A
27. E
28. C
29. E
30. D
31. D
32. C
33. B
34. E
35. A
36. D
37. C
38. B
39. A
40. A
41. C
7
The Part of Tens
IN THIS PART ...
Discover ten question types that are easiest to master.
Find out ten errors to avoid in your analytical writing
essay (and to look for in the sentence-correction
questions).
Go beyond just mastering the GMAT and discover ten
things you can do to increase your chances of getting
accepted to an MBA program.
CHAPTER23 Ten Question Types You’ve Got a Good Shot At 381
IN THIS CHAPTER
» Revealing the kinds of questions
you’ve got a good chance to get
right
» Taking advantage of the easier
questions
Ten Question Types You’ve
Got a Good Shot At
W
ith all that math, grammar, and logical reasoning, you can develop a headache just
thinking about the GMAT.And knowing that you have only a half hour to write an essay
doesn’t help! Why can’t the GMAT cut you some slack? Well, it does...sort of. You see,
certain GMAT questions may be a little easier to answer than others. In this chapter, we lay out
ten types of questions you have a greater chance of answering correctly with greater consistency
so you can buy yourself a little time to use on the tougher questions in each section.
Main-Theme Reading Questions
In general, reading-comprehension questions are a little easier than critical-reasoning ques-
tions. For reading-comprehension questions, the answers are right there on the screen; you just
need to nd them. One reason main-theme questions in particular are easier is that 90 percent of
the passages present you with one. Identifying the main theme should become automatic, so you
don’t even have to refer to a passage to answer a question. And usually, three of the ve answer
choices are clearly o topic or too specic, so all you have to do is choose the best answer of the
remaining two.
Specic-Information Reading Questions
Specic-information questions appear in every reading-comprehension passage, so you’ll get
used to them. You have a great shot at these questions because the computer highlights the text
that contains the answer. Just read the highlighted part of the passage (and maybe the text around
it) to nd the correct answer. As long as you stay focused, you should bat a thousand on these
beauties!
Chapter23
382 PART 7 The Part of Tens
Sentence Corrections
Although sentence-correction questions may not seem easy at rst, they get easier with practice.
The GMAT tends to focus on the same sentence errors, so taking practice tests can help you get
familiar with the errors you need to know about. Answers frequently contain more than one error,
providing you with more than one reason to eliminate an answer. You’ll notice the same kinds of
errors appearing frequently, so you’ll be able to give the right answers frequently, too.
Exception Questions for Reading Passages
Exception questions ask you to choose the answer that isn’t stated in the passage. Usually, all you
have to do is eliminate each answer choice that appears in the text. The choice left standing is the
correct answer.
Strengthening or Weakening Critical
Arguments
Critical-reasoning questions that ask you what strengthens or weakens the argument tend to rely
on cause-and-eect relationships or analogies. If an author reaches a conclusion by cause and
eect, you choose an answer that either shows other causes for the eect (to weaken the argu-
ment) or that emphasizes that no other causes for the eect exist (to strengthen the argument).
To weaken analogy arguments, choose an answer that shows the compared entities are dissimi-
lar. An answer that highlights similarities strengthens the argument.
Data-Suciency Math Questions
Data-suciency questions usually take less time to answer than problem-solving math ques-
tions. You don’t have to actually solve the problem to answer the question correctly. Just follow
the step-by-step process outlined in Chapter15 to stay focused.
Math Problem-Solving with Figures
One of the hardest parts of a problem-solving question is getting started. You may have trouble
sifting through the information you get from word problems, but a gure presents known infor-
mation clearly. Examine the information in the gure and solve the problem.
CHAPTER 23 Ten Question Types You’ve Got a Good Shot At 383
Math Problems Involving Basic Operations
Some problem-solving questions present you with an equation or a simple word problem involv-
ing arithmetic, exponents, or other basic operations. You’ve been applying these basics since
childhood, so all you have to do is read carefully!
Substitution Math Problems
Problem-solving questions that ask you to substitute values for symbols can be simple after you
understand what you’re supposed to do. In most cases, you just need to exchange a value for a
symbol in an otherwise simple equation.
Graph- and Table-Analysis Questions
The questions that require you to analyze graphs and tables in the integrated-reasoning section
primarily test your ability to read data. Finding the correct answer is rarely based on your ability
to read lengthy paragraphs or perform complex calculations. As long as you pay attention to how
the chart categorizes the data, you should sail through these questions fairly smoothly. Just don’t
complicate matters by reading more into these questions than you have to.
CHAPTER24 Ten Writing Errors to Avoid 385
IN THIS CHAPTER
» Being aware of ten writing
practices you should shun
» Finding ways to ace the analytical
writing assessment
Ten Writing Errors to Avoid
C
hapter10 gives you what you need to know to develop a good writing style for the analyti-
cal writing assessment, but becoming a better writer takes practice. Fortunately, you can
rapidly improve your writing style (and your analytical writing assessment score) if you
avoid the ten common writing mistakes we share in this chapter.
Composing Complicated Sentences
The chances of making multiple grammar and punctuation errors increase with the length and
complexity of your sentences. If you need to improve your writing in a hurry, concentrate on
simplicity. Make your point, end your sentence, and move on. Remember that the readers have to
grade many exams. Don’t make your reader work too hard to understand your sentences. You can
(and should) use a variety of sentence structures, but keep them simple.
Presenting Your Text in Passive Voice
Active voice is clearer and more powerful than passive voice. Passive voice uses more words than
necessary and clouds the main action. You’re much more likely to make errors in verb usage with
a passive sentence. Remember that the passive voice is really only appropriate when the doer of
the action is unknown or unimportant, such as in scientic writing. For business writing and the
GMAT, use active voice. (See Chapter4 for more about active and passive voice.)
Wasting Time with Unfamiliar Words
Trying to impress the essay readers with your advanced vocabulary is tempting. But if you aren’t
completely familiar with a word’s meaning, don’t use it on the GMAT.GMAT readers focus more
on how you organize and support your thoughts than on the reading level of your essay, and
they’ll take points o your score if you misuse words. You have only 30 minutes to develop your
argument, so don’t waste time coming up with ve-syllable words unless you just happen to use
them in your normal conversation.
Chapter24
386 PART 7 The Part of Tens
Using Unclear (Or Zero) Transitions
Tell your reader where your argument is going by including clear transitions. With just one or two
words, you can tell the reader whether the next paragraph continues the current idea, refutes it,
or moves in a new direction. Using transition words and phrases can really improve your assess-
ment score.
Going Overboard with Generic Terms
To clarify your points and excite your reader, pack your sentences with lively and unambiguous
descriptions rather than fuzzy generalities (like interesting, great, and awful). Your writing makes
a greater impact and will receive a higher score when you fortify it with expressive language.
Writing in Informal English
Save slang and creative capitalization and punctuation for the text messages you send to your
friends and co-workers. For the GMAT, apply the rules of standard written English you learned in
grammar class.
Giving a Laundry List of Examples
Satisfy essay readers with a few clearly developed illustrations to back up your points rather than a
list of undeveloped examples. Readers are more concerned with the depth of your supporting evidence
than they are with its quantity. In fact, you can earn a 6 with just one example if you develop it well.
Succumbing to Sentence Fragments
Your essay shouldn’t read like an outline. Fully develop your thoughts with properly punctuated,
complete sentences and well-organized paragraphs.
Announcing a Position without Explanation
The essay prompt requires you to adopt a position. But merely stating your position and jumping
into your argument is insucient. Introduce your essay with a brief analysis of the argument to
show the readers you understand what you’re writing about.
Putting Aside Proofreading
Leave yourself enough time at the end of the 30 minutes to quickly read through your essay and
correct any obvious errors. Set aside about three minutes to proofread your masterpiece and
eliminate careless errors. Doing so can raise your score by a complete point.
CHAPTER25 Ten Ways to Increase Your Chances of Getting into Business School 387
IN THIS CHAPTER
» Discovering what’s important to
admissions committees
» Finding out how to make the
most of your MBA admissions
application
Ten Ways to Increase Your
Chances of Getting into
Business School
T
he number of business school applications continues to increase, but quantity doesn’t nec-
essarily mean quality. And the quality of your application remains your single best bet for
standing out among the crowd. A great application emphasizes your academic prepara-
tion, strong work experience, and a clear sense of what you hope to gain from your quest for an
MBA.This chapter highlights what you can do to make sure your application process provides
what it takes to impress the decision makers.
Accumulate a Little Work Experience
You don’t have to get your MBA right after you graduate. In fact, waiting and working for a while
may be to your advantage. Many admissions ocers like to see at least three years of managerial
work experience when you apply for an MBA program so they can be sure you’re cut out for a
career in business. They also look for signs of competence and career progress, such as promo-
tions, the acquisition of new skills, and increased responsibilities in the workplace.
Ace the Interview
Some programs require an interview; others may recommend them. If a business school states
that an interview is optional, grab this opportunity to demonstrate your social skills and highlight
your passions. To make a good impression, heed the following advice:
»
Dress in business attire.
»
Smile, look your interviewer in the eye, and answer questions honestly.
Chapter25
388 PART 7 The Part of Tens
»
Exude condence without arrogance.
»
Ask questions of the interviewer that demonstrate your knowledge of the program.
»
Follow up with a thank-you note.
Apply Early
Applying early to an MBA program demonstrates strong planning skills and a signicant interest
in the program. Submitting your application before the rest of the crowd also increases the
chances of your application getting the time and attention from admissions ocers it rightfully
deserves!
Apply While You’re Upwardly Mobile
Business schools want go-getters, and what better time to catch someone than on the way up?
Show your school of choice that you’re a force to be reckoned with by highlighting any recent
promotions, achievements, accolades, or anything that helps suggest that it had better snatch you
up while you’re in your prime before another school beats it to the punch.
Capitalize on What Makes You Unique
Don’t waste too much time trying to t into some imaginary mold of the ideal business student.
Business school admissions ocers are seeking students with varying life experiences and from
a broad variety of backgrounds, so embrace who you are and avoid trying to present a false per-
sona that may ultimately backre. In fact, your non-traditional prole may make you even more
desirable to a program that seeks to diversify its class.
Demonstrate Interest
Business schools want to know that if they accept you, you’ll actually attend. Admissions com-
mittees equate communication with interest, so the more you reach out to them, the more inter-
ested they’ll be in you. Contact your admissions representative regularly with pertinent questions.
Just make sure you don’t become a pest!
Focus on Fit
Just as you want to know what school is the best t for you, admissions ocers seek the students
who are the best t for them. Do your research about what a particular school is known for and
what sorts of skills and personality traits it embraces, and tailor your application, essay, and
interview accordingly. You can nd out a lot about a particular business school’s personality by
researching its website, searching the Internet for articles about the program and its graduates,
and visiting the campus.
CHAPTER 25 Ten Ways to Increase Your Chances of Getting into Business School 389
Get the Right Recommendations
Business school applicants commonly xate so much on the essay process that they diminish the
importance of securing solid recommendations. Don’t undervalue the crucial role of recommen-
dations. Choose supervisors who know you well, both personally and professionally. Admissions
ocers focus on how well your reference knows your strengths and weaknesses. Find someone
who can expound on how well you interact with others and provide evidence of your academic
prowess and leadership abilities.
The person who knows you best is more likely to be your direct supervisor than the company CEO.
Study for the GMAT
Your GMAT score matters. The test was designed to determine how well you’ll likely do in an MBA
program in comparison to a plethora of other applicants, so scoring sky-high on the GMAT can
place you head and shoulders above the rest of the crowd. Use this book’s step-by-step instruc-
tion for each area of the test to help you prepare, and be sure to take the practice tests to help you
identify areas where you could benet from a bit of a refresher.
Write a Memorable Admissions Essay
When crafting your admissions essay, keep in mind that the admissions committee already knows
your facts and gures— what you studied, where you worked, and your scores on the GMAT.The
point of the essay is to give application readers a glimpse of the real you— what makes you stand
out from the crowd, what motivates you, what you have overcome, and what you want to achieve
in life. Keep in mind that admissions committees are reading thousands of responses to the same
questions, so avoid falling into the trap of writing what you think they want to hear and instead
shift your focus to self-revelation through vivid details and thoughtful anecdotes.
Index 391
Index
A
absolute value, 157–158
acute angle, 200
addition, 155, 160, 167, 177–179
adjectives, 39
admissions essays, 389
adverbs, 40
aordability, of business
schools,30
algebra
about, 175
factoring polynomials, 181–183
functions, 183–188
operations, 177–181
problem-solving, 188–197
terms, 175–177
alumni network, of jobs out of
business schools, 31
ambiance, 61
analogy arguments, 85–86
analytical writing assessment (AWA)
section
about, 123
analyzing arguments, 124–125
preparing for, 123–124
scores for, 133–134
scoring essays, 125–126
writing tools for, 124
angles, 199–202
answers and explanations
analytical writing assessment,
347–348
critical-reasoning section practice
questions, 98–102
data-suciency practice
questions, 255–259
eliminating choices for answers,
20–24, 52–53, 66–67
integrated-reasoning section, 348
problem-solving practice
questions, 263–265
quantitative section, 274–283,
349–367, 377
quantitative section practice
questions, 274–283
reading-comprehension practice
questions, 74–78
recognizing wrong answers, 21–24
sentence-correction practice
questions, 56–58
verbal section, 113–119, 367–376,
377
verbal section practice questions,
113–119
apostrophe, 129
applying to business schools,
31–33, 388
arcs, 212–213
area, 204, 212
arguments, 81, 84–88, 124–125, 382
associative property, 155
assumptions, seeking, 84, 89–91
author style/tone, 61, 66
automatic corrections, 124
average, 241
average starting salary, of jobs out
of business schools, 31
AWA. see analytical writing
assessment (AWA) section
axis of symmetry, 227
B
bar graphs, 305–307
bases, 160–162
basic operations, 155–159, 383
binomial, 177
bisect, 200
business passages, 63
business schools, 29–34, 387–389
C
calculator, 289–290
canceling score, 14–15
CAT (computer-adaptive test)
format, 11–12
cause-and-eect arguments,
83,86–87
central angle, of a circle, 213
cheating, 26
chords, 213
circle graphs, 310–311
circles, 212–215, 227
circumference, 212
circumscribed gures, 213–214
clauses, 41–42, 45, 46
coecient, 176
collinear, 200
combinations, 239–241
comma splices, 128
commas, 128
common factors, nding, 182
common sense, 22
commutative property, 155
complementary angle, 201
complex scatter plots, 309–310
composite numbers, 154
computer skills, 12
computer-adaptive test (CAT)
format, 11–12
computerized format, 11–12
concentrations, of business
schools, 30
conclusions, drawing from
premises, 84, 88–89
congruent, 201
conjunctions, 40
constants, 175–176
construction, errors in, 45–48
coordinate geometry, 219–232
coordinates, 220, 225
correlative expressions, 50
critical-reasoning section
about, 79, 104
answer explanations for practice
questions, 98–102
answering questions in, 80–81
critical concepts, 79–81
logical arguments, 81–83
practice questions, 94–98
question examples, 22
question types, 80, 83–84
strategies for approaching
questions in, 84–94
392 GMAT For Dummies, 7th Edition with Online Practice
cube root, 162
cubes, working with, 216–217
cylinders, working with, 217–218
D
data-suciency questions
about, 249, 382
answer explanations for practice
questions, 255–259
practice questions, 253–255
solutions for, 250
steps for approaching, 250–253
decagon, 211
decimals, 164–171
deductive reasoning, 81–82, 88
denominator, 161, 165
dependent clauses, 41–42, 45
dependent variables, 184
descriptions, precision in, 130
diameter, 212
dierence of perfect squares,
193–194
disjoint sets, 235
dispersion, 243
distance, calculating, 226–227
distance problems, 197
distributing terms, 179–180
division, 155–157, 160–161,
167–169, 179–181
domain, 184
domain of a function, 185–187,
230–232
E
elements, 235
eliminating answer choices, 20–24,
52–53, 66–67
empty set, 235
English Grammar For Dummies
(Woods), 127
equations, 188–194
equilateral triangle, 202
errors, 42–48, 52, 385–386
essays
about, 127
creating for business school
applications, 33–34
example, 134–141
examples, 134–141, 143–149
grammar errors, 127–130
mechanics errors, 127–130
punctuation errors, 127–130
requesting a rescore, 126
tips for improving score for,
131–132
writing, 127–132
even numbers, 158–159
example questions
absolute value, 157–158
algebraic problem, 178–179
calculating distance, 226–227
circles, 215
combinations, 241
critical-reasoning, 22
cylinders, 218
data-suciency, 252
distance problems, 197
domain of the function, 186–187,
232
drawing conclusions from
premises, 89
exception, 68, 69
exponents, 162
expressions, 50–51, 179–180
factoring polynomials, 183
FOIL method, 181
45:45:90-degree triangle, 207
fractions, 168–169
functions, 184–185
General Rule of Multiplication,
247–248
graphics interpretation, 298
groups, 234
lines, 202
making inferences, 91–92
mean, 242–243
method-of-reasoning, 93–94
multi-source reasoning, 301–302
noun-pronoun agreement
errors, 44
number ranges, 192
numbers, 155
odd numbers, 159
parallel structure, 47
percent change, 170
permutations, 238–239
problem-solving, 23, 260
Pythagorean theorem, 204–205
range of a function, 187
ratios, 172, 205–206
ratios of right triangles, 205–206
rhetorical construction errors, 48
Roman numerals, 24
roots, 163
scientic notation, 173
seeking assumptions, 90
sentence-correction, 51
similar triangles, 208
simultaneous equations, 190–191
slope-intercept form, 224
standard deviation, 245
subject-verb agreement errors, 44
table analysis, 292–294
trapezoids, 210–211
triangles, 203
two-part analysis, 294–296
Venn diagrams, 236
vertex, 228
vertical line test, 230
word problems, 195
work problems, 196
examples, 85–87, 386
exception questions, 67–70, 382
explanations. see answers and
explanations
exponents, 160–162
expressions, 49–51, 130, 176–177
F
factorial, 237
factoring, 181–183, 193
factors, 181
t, of business schools, 388
focus, loss of, 25
FOIL method, 180–181
format, 10–12
45:45:90-degree triangle, 206–207
fourth root, 162
fractional exponents, 161
fractions, 164–171
framework, nding for passages, 61
functions
about, 183
domain of, 185–187, 230–232
graphing, 228–232
range of, 187–188, 230–232
terminology, 184–185
Index 393
G
General Rule of Addition, 246–247
General Rule of Multiplication, 246,
247–248
generic terms, 386
geometry
about, 199
angles, 199–202
circles, 212–215
lines, 199–202
polygons, 211–212
quadrilaterals, 208–211
three-dimensional, 215–218
triangles, 202–208
GMAT. see also specic topics
format, 10–12
importance of, 7–8
preparing for, 27
retaking, 15
things to avoid, 25–26
what it tests, 10–11
what to take for, 10
when to take, 8–9
Graduate Management Admission
Test (GMAT). see GMAT
grammar, 38–42, 124, 127–130
graph-analysis questions, 383
graphics interpretation, 288,
296–298
graphing functions and lines,
223–225, 228–232
GRE, 32
groups, 233–235
guessing, 17–18, 53
H
heptagon, 211
hexagon, 211
horizontal, 200
I
icons, explained, 2–3
idiomatic expressions, 49–51
imaginary numbers, 154
improper fractions, 166
indenite pronouns, 39
independent clauses, 41, 46
independent variables, 184
inductive reasoning, 82–83
inequalities, 191–192
inference questions, 65
inferences, making, 84, 91–92
informal English, 386
informal logic, 81–83
inscribed gures, 213–214
integers, 154
integrated-reasoning (IR) section
about, 287, 303
approaching data in, 303–304
bar graphs, 305–307
circle graphs (pie charts), 310–311
line graphs, 308–310
question types in, 288–302
scoring, 290
skills tested on, 288
time management for, 290–291
translating table information,
304–305
Venn diagrams, 311–313
interest, demonstrating your, 388
intersect, 200
intersecting lines, 201
intersection, 235
interviews, 387–388
intransitive verb, 41
IR. see integrated-reasoning (IR)
section
irrational numbers, 154
isolating variables, 188–189
isosceles triangle, 202
L
line graphs, 308–310
line segment, 199
linear equations, 188–189
lines, 199–202, 223–225
location, of business schools, 31
logical arguments, 81–83
logical thought, origins of, 82
M
main point, 60
main-theme reading questions,
64, 381
major arc, 212
massage, 26
math section. see quantitative
section
mean, 241–243
mechanics errors, avoiding in
essays, 127–130
median, 241–243
members, 235
method-of-reasoning questions,
92–94
midpoint, 200
midpoint coordinates, 225
minor arc, 212
mixed fractions, 166
mode, 241–243
modier errors, 129
monomial, 176
multiplication, 155, 156, 160–161,
167–169, 179–181
multi-source reasoning, 288,
298–302
N
natural science passages, 62
negative exponents, 161–162
negative numbers, 159
negative slope, 222
nonagon, 211
nonrestrictive clauses, 42
normal distribution, 244
noun-pronoun agreement, 43–45
nouns, 38–39, 41, 129
null set, 235
numbers, 153–155, 192
numerator, 161, 165
O
obtuse angle, 200, 201
octagon, 211
odd numbers, 158–159
operations
algebraic, 177–181
basic, 383
order of, 164
performing with inequalities, 191
ordered pair, 220
origin, 220
outline, of passages, 61
394 GMAT For Dummies, 7th Edition with Online Practice
P
parabolas, on coordinate plane,
227
parallel, 200
parallel lines, 201
parallel structure, 46–47
parallelograms, 209–210
parts of sentences, 40–42
parts of speech, 38–40
passages, reading, 60–63
passive voice, 385
PEMDA acronym, 164
pentagon, 211
percent change, 169–171
percentages, 164–171
perfect squares, dierence of,
193–194
permutations, 237–239
perpendicular, 200
perpendicular angle, 200
personal pronouns, 39
phrases, 41, 45
pie charts, 310–311
polygons, 211–212
polynomials, 177, 181–183
population, 243
positions, announcing, 386
positive numbers, 159
positive slope, 222
positive thinking, 26
possessives, faulty forming of, 129
powers, 161
practice questions
analytical writing assessment
section, 322
critical-reasoning section, 94–98
data-suciency, 253–255
integrated-reasoning section, 323
problem-solving, 261–263
quantitative section, 267–274,
324–332
reading-comprehension, 70–74
sentence-correction, 53–55
verbal section, 104–112, 333–345
practice test
about, 317
analytical writing assessment
section answers and
explanations, 347–348
analytical writing assessment
section questions, 322
answer sheet, 319–321
integrated-reasoning section
answers and explanations, 348
integrated-reasoning section
questions, 323
quantitative section answers and
explanations, 349–367, 377
quantitative section questions,
324–332
verbal section answers and
explanations, 367–376, 377
verbal section questions, 333–345
prepositions, 40
prestige, of business schools, 30
prime numbers, 154
private status, of business
schools,31
probability, 245–248
problem-solving questions
about, 259–261, 382
answer explanations for practice
questions, 263–265
examples, 23
practice questions, 261–263
quantitative section, 188–197
pronouns, 39, 129
proofreading, 386
proper fractions, 166
proportions, 171–172
public status, of business schools,
31
punctuation errors, avoiding in
essays, 127–130
Pythagorean theorem, 204–205
Q
quadrants, identifying, 220–221
quadratic equations, 193–194
quadratic formula, 194
quadratic polynomial, 177, 182–183
quadrilaterals, 208–211
quality of life, of jobs out of
business schools, 31
quantitative section
about, 153, 175, 267
algebra, 175–197
answer explanations for practice
questions, 274–283
bases, 160–162
basic operations, 155–159
coordinate geometry, 219–232
data-suciency questions, 382
decimals, 164–171
exponents, 160–162
fractions, 164–171
geometry, 199–218
number types, 153–155
order of operations, 164
percentages, 164–171
practice questions, 267–274
problem-solving questions, 382
proportions, 171–172
question types, 249–265
ratios, 171–172
roots, 162–163
scientic notation, 172–173
statistics and probability, 233–248
table-analysis questions, 383
quantitative skills, 11
questions. see also example
questions; practice questions
in critical-reasoning section, 80,
83–84
exception, 67–70
identifying types of, 63–66
in integrated-reasoning (IR)
section, 288–290
in quantitative section, 249–265
types of, 381–383
R
radicals, 162
radius, 212
range, 184, 192, 243
range of a function, 185, 230–232
rational numbers, 154
ratios, 171–172, 205–206
ray, 200
reading passages, 60–61
reading-comprehension section
about, 59, 104
answer explanations for practice
questions, 74–78
main-theme questions, 381
practice questions, 70–74
question types, 59–60
specic-information questions,
381
strategies for reading passages,
60–61
strategies for reading-
comprehension questions,
63–70
types of passages, 62–63
Index 395
real numbers, 154, 157–159
reasoning, 81–84
reasoning skills, 11
reciprocal, 166
recommendations, 389
rectangle, 209
rectangular solids, 215–217
registering, 8–9
relative pronouns, 39
relaxation techniques, 26
repeated percent change, 170–171
reporting scores, 13–14
requesting essays be rescored, 126
rereading sentences, 53
restrictive clauses, 42
retaking, 15
rhetorical construction, errors in,
47–48
rhombus, 210
right angle, 200, 201
right rectangular prism, 215–217
right triangles, 202, 205–206
Roman numerals, 23–24
roots, 162–163
run-on sentences, 45–46, 128
S
sample, 243
scalene triangle, 202
scatter plots, 308–310
schedule considerations, 9
scientic notation, 172–173
scores
analytical writing assessment
(AWA), 133–134
calculating, 13
canceling, 14–15
essays in analytical writing
assessment, 125–126
integrated-reasoning (IR)
section,290
interpreting, 126
maximizing, 17–27
reporting, 13–14
tips for improving for essays,
131–132
sections, completing, 19
segmented bar graphs, 306–307
selectivity, of business schools, 30
semicircle, 212
sentence fragments, 45, 129, 386
sentence-correction section
about, 37, 104
answer explanations to practice
problems, 56–58
common errors in, 42–51
grammar basics, 38–42
practice problems, 53–55
question types, 382
strategy for, 51–53
sentences, 40–42, 53, 130, 385
sentence-structure problems, 129
sets, 235–236
similar, 201
similar triangles, 207–208
simultaneous equations, 189–191
slang expressions, 130
slope, 220–223
slope-intercept form, 223–225
social science passages, 62–63
special programs, of business
schools, 30
Special Rule of Addition, 246
Special Rule of Multiplication,
246,247
specialties, of business schools, 30
specic-information questions,
64–65
specic-information reading
questions, 381
speech, parts of, 38–40
speed reading, 25
spell check, 124, 129–130
spelling issues, 129–130
square root, 162, 209
stacking terms, 180
standard deviation, 243–245
standard expressions, 49–51
standard-issue nouns, 129
statistical arguments, 83, 87
statistics
about, 233
combinations, 239–241
groups, 233–235
mean, 241–243
median, 241–243
mode, 241–243
permutations, 236–239
range, 243
sets, 235–236
standard deviation, 243–245
straight angle, 200
stretching, 26
studying, 389
style, author, 66
subject, 41
subject-verb agreement, 43
subset, 235
substitution, 189–191, 383
subtraction, 155, 156, 160, 167,
177–179
supplementary angle, 201
surface area (SA), 216
symbols, for inequalities, 191
synonym nder, 124
T
table analysis, 288, 291–294, 383
tables, translating information in,
304–305
tangents, 214–215
tense, 46
terms, 176, 179–180
test banks, 3
30:60:90-degree triangle, 206
three-dimensional geometry,
215–217
time management, 12, 19–20, 25,
290–291
tone, author’s, 61, 66
transitions, clarity in, 130, 386
transitive verb, 41
trapezoids, 210–211
triangles, 202–208
trinomial, 177
two-part analysis, 288, 294–297
U
union, 235
uniqueness, stressing your, 388
V
vacation, 26
variables, 175–176, 184, 188–189
variation, 243
Venn diagrams, 235–236, 311–313
verb tense, 46
verbal section, 103–119
verbal skills, 11
verbs, 38, 41
vertex, 227
396 GMAT For Dummies, 7th Edition with Online Practice
vertical, 200
vertical line test, 228–230
volume (V), 216
W
weighted mean, 242
Woods, Geraldine (author)
English Grammar For Dummies,
127
word problems, 194–196
words, using unfamiliar, 385
work experience, 387
work problems, 196
writing ability, 11
writing essays, 127–132
writing prompts, 143–149
X
x, factoring to nd, 193
x-axis, 220
x-intercept, 220
Y
y-axis, 220
y-intercept, 220
About the Authors
Lisa Zimmer Hatch, M.A. and Scott A.Hatch, J.D. have prepared teens and adults since 1987 to
excel on standardized tests, gain admission to colleges of their choice, and secure challenging and
lucrative professional careers. For virtually 30 years, they have created and administered award-
winning standardized test preparation and professional career courses worldwide for live lecture,
online, and other formats through more than 500 universities worldwide.
Scott and Lisa have written the curriculum for all formats, and their books have been translated
for international markets. Additionally, they wrote, produced, and appeared in the landmark
weekly PBS “Law for Life” series. They continue to develop new courses for a variety of careers
and extend their college admissions expertise to assist those seeking advanced degrees in law,
business, and other professions. Together they have authored numerous law and standardized test
prep texts, including ACT For Dummies, 1,001 ACT Practice Problems For Dummies, LSAT For Dummies,
SAT II U.S.History For Dummies, SAT II Biology For Dummies, SAT II Math For Dummies, Catholic High
School Entrance Exams For Dummies, and Paralegal Career For Dummies (Wiley).
Lisa is currently an independent educational consultant and the president of College Primers,
where she applies her expertise to guiding high-school and college students through the under-
graduate and graduate admissions and nancial aid processes and prepares students for entrance
exams through individualized coaching and small group courses. She prides herself in maximiz-
ing her students’ nancial aid packages and dedicates herself to helping them gain admission to
the universities or programs that best t their goals, personalities, and nancial resources. She
graduated with honors in English from the University of Puget Sound and received a master’s
degree in humanities with a literature emphasis from California State University. She holds a
certicate in college counseling from UCLA and is for a member of the Higher Education Consul-
tants Association (HECA) and the Rocky Mountain Association of College Admissions Counselors
(RMACAC).
Scott received his undergraduate degree from the University of Colorado and his Juris Doctorate
from Southwestern University School of Law. He is listed in Who’s Who in California and Who’s Who
Among Students in American Colleges and Universities and is one of the Outstanding Young Men of
America as determined by the United States Jaycees. He was also a contributing editor to McGraw-
Hill’s Judicial Proler series and The Colorado Law Annotated series published by Lawyers Cooperative
Publishing. He also served as editor of the Freedom of Information Committee Newsletter and func-
tioned as editor of several national award-winning periodicals. His current law books include A
Legal Guide to Probate and Estate Planning and A Legal Guide to Family Law in B & B Legal Publica-
tion’s Learn the Law series.
In addition to writing law books, periodical articles, television scripts, and college curricula, Scott
was editor of his law school’s nationally award-winning legal periodical, winner of two rst-place
awards from the Columbia University School of Journalism, and another rst-place award from
the American Bar Association. He also contributed to Los Angeles’s daily newspaper, The Metro-
politan News, was an editorial assistant during the formation of the Los Angeles Press Club’s
Education Foundation, and served on the Faculty of Law at the City University of Los Angeles.
Dedication
We dedicate GMAT For Dummies to our children, Alison, Andrew, Zachary, and Zoe and to Dan,
Paige, and Ryan Welch, Miarra Jackson, and John Gilchrist. Our family demonstrated patience,
understanding, and editorial assistance while we wrote this book, and we’re very blessed to have
them in our lives.
Authors’ Acknowledgments
This book would not be possible without the contributions of Julia Brabant, Hank Zimmer,
Jackson Sutherland, Zachary Hatch, and Zoe Hatch, who provided practice test material and help-
ful input. We also acknowledge the input of thousands of our students who have completed our
test preparation courses over the last 30 years. The classroom and online contributions oered by
these dedicated and motivated learners have provided us with a signicant amount of informa-
tion about those subject areas that require the greatest amount of preparation for success on the
GMAT.
Our project organization and attempts at wit were greatly facilitated by the editing professionals
at Wiley. Our thanks go out to Chrissy Guthrie for her patience and guidance throughout the editing
process and to copy editor Christy Pingleton. Thanks also to technical editor Bill Kenworthy for
his attention to detail and helpful suggestions during the editing process.
Finally, we wish to thank our literary agent, Margo Maley Hutchinson, at Waterside Productions
in Cardi for her support and assistance and for introducing us to the innovative For Dummies
series.
We thrive on feedback from our students and encourage our readers to provide comments and
critiques at
Publisher’s Acknowledgments
Executive Editor: Lindsay Sandman Lefevere
Editorial Project Manager
and Development Editor:
Christina N.Guthrie
Copy Editor: Christine Pingleton
Technical Editor: Bill Kenworthy
Production Editor: Antony Sami
Cover Photos: ©phototechno/iStockphoto
