GMAT CAT ® 8th Edition Jerry Bobrow, Ph.D. Test-prep essentials from the experts at The fast track to your best score Proven test-taking strategies Focused reviews and exercises Computer adaptive- style practice test Test-taking tips and tricks at cliffsnotes.com CliffsTestPrep™ GMAT® CAT (Computer-Adaptive Graduate Management Admission Test) 8th Edition by Jerry Bobrow, Ph.D. Contributing Authors/Consultants Allan Casson, Ph.D. Jean Eggenschwiler, M.A. Rajiv Rimal, Ph.D. Peter Z Orton, Ph.D. William A. Covino, Ph.D. Michele Spence, M.A. Harold Nathan, Ph.D. David A. Kay, M.S. Dale Johnson, M.A. IDG Books Worldwide, Inc. An International Data Group Company Foster City, CA(cid:2) Chicago, IL(cid:2) Indianapolis, IN (cid:2) New York, NY About the Author Publisher’s Acknowledgments Dr. Jerry Bobrow, Ph.D., is a national authority in the field Editorial of test preparation. As executive director of Bobrow Test Project Editor:Joan Friedman Preparation Services, he has been administering the test preparation programs at over 25 California institutions for Copy Editor:Corey Dalton, Janet M. Withers the past 27 years. Dr. Bobrow has authored over 30 national Editorial Assistant:Carol Strickland best-selling test preparation books, and his books and pro- grams have assisted over two million test-takers. Each year, Production Dr. Bobrow personally lectures to thousands of students on Proofreader:Vicki Broyles preparing for graduate, college, and teacher credentialing exams. IDG Books Indianapolis Production Department CliffsTestPrep™GMAT®CAT,8th Edition Note:If you purchased this book without a cover, Published by you should be aware that this book is stolen prop- erty. 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THE PUBLISHER AND AUTHOR MAKE NO REPRESENTATIONS OR WARRANTIES WITH RESPECTTO THE ACCURACYOR COMPLETE- NESS OF THE CONTENTS OF THIS BOOK AND SPECIFICALLYDISCLAIM ANYIMPLIED WARRANTIES OF MERCHANTABILITYOR FITNESS FOR APARTICULAR PURPOSE. THERE ARE NO WARRANTIES WHICH EXTEND BEYOND THE DESCRIPTIONS CONTAINED IN THIS PARA- GRAPH. NO WARRANTYMAYBE CREATED OR EXTENDED BYSALES REPRESENTATIVES OR WRITTEN SALES MATERIALS. THE ACCURACY AND COMPLETENESS OF THE INFORMATION PROVIDED HEREIN AND THE OPINIONS STATED HEREIN ARE NOTGUARANTEED OR WAR- RANTED TO PRODUCE ANYPARTICULAR RESULTS, AND THE ADVICE AND STRATEGIES CONTAINED HEREIN MAYNOTBE SUITABLE FOR EVERYINDIVIDUAL. NEITHER THE PUBLISHER NOR AUTHOR SHALLBE LIABLE FOR ANYLOSS OF PROFITOR ANYOTHER COMMERCIAL DAMAGES, INCLUDING BUTNOTLIMITED TO SPECIAL, INCIDENTAL, CONSEQUENTIAL, OR OTHER DAMAGES. NOTE: THIS BOOK IS INTENDED TO OFFER GENERALINFORMATION ON THE GMATCAT. THE AUTHOR AND PUBLISHER ARE NOTENGAGED IN RENDERING LEGAL, TAX, ACCOUNTING, INVESTMENT, REALESTATE, OR SIMILAR PROFESSIONALSERVICES. ALTHOUGH LEGAL, TAX, ACCOUNTING, INVESTMENT, REALESTATE, AND SIMILAR ISSUES ADDRESSED BYTHIS BOOK HAVE BEEN CHECKED WITH SOURCES BE- LIEVED TO BE RELIABLE, SOME MATERIALMAYBE AFFECTED BYCHANGES IN THE LAWS AND/OR INTERPRETATION OF LAWS SINCE THE MANUSCRIPTIN THIS BOOK WAS COMPLETED. THEREFORE, THE ACCURACYAND COMPLETENESS OF THE INFORMATION PROVIDED HEREIN AND THE OPINIONS THATHAVE BEEN GENERATED ARE NOTGUARANTEED OR WARRANTED TO PRODUCE PARTICULAR RESULTS, AND THE STRATEGIES OUTLINED IN THIS BOOK MAYNOTBE SUITABLE FOR EVERYINDIVIDUAL. IF LEGAL, ACCOUNTING, TAX, INVEST- MENT, REALESTATE, OR OTHER EXPERTADVICE IS NEEDED OR APPROPRIATE, THE READER IS STRONGLYENCOURAGED TO OBTAIN THE SERVICES OF APROFESSIONALEXPERT. Trademarks:GMATis a registered trademark of Graduate Management Admission Council. Cliffs, CliffsTestPrep, CliffsNote-a-Day, CliffsNotes, and all related logos and trade dress are registered trademarks or trademarks of IDG Books Worldwide, Inc., in the United States and other countries. All other trademarks are the property of their respective owners. IDG Books Worldwide is not associated with any product or vendor mentioned in this book. is a registered trademark under exclusive license to IDG Books Worldwide, Inc., from International Data Group, Inc. Author’s Acknowledgments I would like to thank former Cliffs Notes Editor Michele Spence for her meticulous editing of the original manuscript and Joan Friedman and the IDG editorial staff for reviewing and editing this newest edition of my work. I would also like to extend my sincere appreciation to the following authors and publications for permission to use excerpts from their fine writings: Dr. Albert Upton, Design for Thinking, Stanford University Press. Sy Montgomery, “Sharks,” Los Angeles Times, February 23, 1991, p. B-3. And finally, I would like to thank my wife Susan, daughter Jennifer (22), and sons Adam (19) and Jonathan (15) for their patience, moral support, and comic relief. iii Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Study Guide Checklist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv PART I: INTRODUCTION TO THE GMAT CAT: THE COMPUTER-ADAPTIVE GRADUATE MANAGEMENT ADMISSION TEST General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Questions Commonly Asked about the Computer-Adaptive GMAT (GMAT CAT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Taking the GMAT CAT: An Overview of the Process. . . . . . . . . . 9 Test Center Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Using the Interactive Tutorials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 The Answer-Selection and Word-Processing Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Typing Essays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Selecting an Answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 The Functions Tutorials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Using a Mouse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Using the Screen Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Using the Scroll Bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Scratch Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Test-Taking Strategies: The Approach. . . . . . . . . . . . . . . . . . . . . . 15 Don’t Get Stuck. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Eliminate Wrong Answers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Working from Multiple-Multiple-Choice Answers. . . . . . . . . . . . . . . . . . . . . . 16 PART II: ANALYSIS OF EXAM AREAS The Analytical Writing Assessment. . . . . . . . . . . . . . . . . . . . . . . . 21 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Ability Tested. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Basic Skills Necessary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Analysis of an Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Analysis of an Argument. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Scoring the Analytical Writing Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Analyzing the Scores. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Grading the Analysis of an Issue Response. . . . . . . . . . . . . . . . . . . . . . . . . 24 Score of 6: Excellent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Score of 5: Good. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Score of 4: Competent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Score of 3: Limited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Score of 2: Weak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 v CliffsTestPrep GMAT CAT, 8th Edition Score of 1: Poor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Score of 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Score of NR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Grading the Analysis of an Argument Response . . . . . . . . . . . . . . . . . . . . 26 Score of 6: Excellent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Score of 5: Good. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Score of 4: Competent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Score of 3: Limited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Score of 2: Weak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Score of 1: Poor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Score of 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Score of NR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Suggested Approach with Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Analysis of an Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Preparing to Write. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Writing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Proofreading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 One Approach: The “Why” Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Sample: Analysis of an Issue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Analysis of an Argument. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Sample: Analysis of an Argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Another Sample: Analysis of an Argument . . . . . . . . . . . . . . . . . . . . . . 35 Extra Practice Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Analysis of an Issue Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Analysis of an Argument Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Response Scoring Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Analysis of an Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Analysis of an Argument. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 The Quantitative Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Introduction to Problem Solving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Basic Skills Necessary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Suggested Approach with Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Practice Problem Solving Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Easy to Moderate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Average. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Above Average to Difficult. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Answers and Explanations for the Practice Problem Solving Questions. . . . . 67 Easy to Moderate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Average. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Above Average to Difficult. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Introduction to Data Sufficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Basic Skills Necessary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Suggested Approach With Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Practice Data Sufficiency Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Easy to Moderate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Average. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Above Average to Difficult. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 vi Table of Contents Answers and Explanations for the Practice Data Sufficiency Questions. . . . . 90 Easy to Moderate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Average. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Above Average to Difficult. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Introduction to Graphs and Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Basic Skills Necessary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Suggested Approach with Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Charts and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Practice Graphs and Chart Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Set 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Set 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Set 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Answers and Explanations for the Graphs and Charts Practice Problems. . . 111 Set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Basic Math Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Symbols, Terminology, Formulas, and General Mathematical Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Common Math Symbols and Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Math Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Important Equivalents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Customary System, or English System . . . . . . . . . . . . . . . . . . . . . . . . . 115 Metric System, or The International System of Units. . . . . . . . . . . . . . 116 Math Words and Phrases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Mathematical Properties and Basic Statistics . . . . . . . . . . . . . . . . . . . . . . . 118 Some Properties (Axioms) of Addition . . . . . . . . . . . . . . . . . . . . . . . . . 118 Some Properties (Axioms) of Multiplication . . . . . . . . . . . . . . . . . . . . . 119 A Property of Two Operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Some Basic Terms in Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Arithmetic Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Arithmetic Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Rounding Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Common Fractions and Improper Fractions . . . . . . . . . . . . . . . . . . . . 123 Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Reducing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Adding Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Adding Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Subtracting Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Subtracting Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Multiplying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Multiplying Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Dividing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Simplifying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 vii CliffsTestPrep GMAT CAT, 8th Edition Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Adding and Subtracting Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Multiplying Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Dividing Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Changing Decimals to Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Changing Percents to Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Changing Fractions to Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Changing Percents to Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Changing Fractions to Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Changing Decimals to Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Finding Percent of a Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Other Applications of Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Percentage Increase or Decrease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Arithmetic Mean, or Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Squares and Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Square Root Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Approximating Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Simplifying Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Signed Numbers (Positive Numbers and Negative Numbers) . . . . . . . . 135 Adding Signed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Subtracting Signed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Multiplying and Dividing Signed Numbers . . . . . . . . . . . . . . . . . . . . . . . 136 Parentheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Algebra Diagnostic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Answers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Algebra Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Understood Multiplying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Literal Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Cross Multiplying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Proportions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Evaluating Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Monomials and Polynomials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Adding and Subtracting Monomials. . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Multiplying and Dividing Monomials. . . . . . . . . . . . . . . . . . . . . . . . . . 142 Adding and Subtracting Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Multiplying Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Factoring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Factoring out a common factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Factoring the difference between two squares. . . . . . . . . . . . . . . . . . . 143 Factoring Polynomials That Have Three Terms: Ax2+ Bx+ C . . . . . . 143 Solving Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Geometry Diagnostic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Answers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Geometry Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 viii