GMAT For Dummies 7th Edition

411 Pages·2017·0.56 MB·English

by  Lisa Zimmer Hatch

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
Copyright © 2018 by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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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 on the 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 Write a GMAT 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 and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
PART 1: GETTING STARTED WITH THE GMAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
CHAPTER 1: Getting the Lowdown on the 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 figure 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 Effective Business-School Essays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Table of Contents  v
PART 2: VANQUISHING THE VERBAL SECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Applying What You Learned (We Hope) in Grammar Class:
CHAPTER 4:
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
vi GMAT For Dummies, 7th Edition with Online Practice
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
Analyze This: What to Expect from the Analytical
CHAPTER 8:
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 Write a GMAT 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
Defining 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
Table of Contents  vii
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, and Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Defining numerators, denominators, and other stuff
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: Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
CHAPTER 13: Considering All the Variables: Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Defining 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 of functions . . . . . . . . . . . . . . . . . . . . . . . 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 stuff about right triangles . . . . . . . . . . 204
A striking resemblance: Similar triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
viii GMAT For Dummies, 7th Edition with Online Practice