E R G ® G e n e r a l Te s t TM proadfCbodrlraiat en imoomVdnni lss Pamii,llt na ao eptc nr hrtaee caiC cv cGeeitsRntsiE ict et eeos r , E R G ® G e n e r a l Te s t TM Carolyn Wheater and Catherine McMenamin About the Authors Editorial Carolyn Wheater teaches middle-school and upper- Acquisition Editor: Greg Tubach school mathematics at the Nightingale-Bamford School Project Editor: Elizabeth Kuball in New York City. Educated at Marymount Manhattan College and the University of Massachusetts, Amherst, Copy Editor: Elizabeth Kuball she has taught math and computer technology for Technical Editor: Abraham Mantell 30 years to students from preschool through college. Catherine McMenamin has an M.A. in Art History from Composition Columbia University. She lives and teaches in New York City. Proofreader: ConText Editorial Services, Inc. Wiley Publishing, Inc., Composition Services CliffsNotes® GRE® General Test Cram Plan™ Note: If you purchased this book without a Published by: cover, you should be aware that this book is Wiley Publishing, Inc. stolen property. It was reported as “unsold and destroyed” to the publisher, and neither the 111 River Street author nor the publisher has received any Hoboken, NJ 07030-5774 payment for this “stripped book.” www.wiley.com Copyright © 2009 Wiley, Hoboken, NJ Published by Wiley, Hoboken, NJ Published simultaneously in Canada Library of Congress Cataloging-in-Publication Data Wheater, Carolyn C., 1957– CliffsNotes GRE general test Cram Plan / by Carolyn Wheater and Catherine McMenamin. p. cm. ISBN-13: 978-0-470-46591-2 ISBN-10: 0-470-46591-3 1. Graduate Record Examination—Study guides. I. McMenamin, Catherine. II. Title. III. Title: Cliffs Notes GRE general test Cram Plan. 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Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii About the Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii About This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .viii Online Extras at CliffsNotes.com . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .x I. Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Section 1: Verbal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 Section 2: Quantitative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 Scoring the Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 II. Two-Month Cram Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 III. One-Month Cram Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 IV. One-Week Cram Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 V. Antonyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43 VI. Analogies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 VII. Sentence Completion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 VIII. Reading Comprehension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 IX. Analytical Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 Analytical Writing Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 The Scoring of the Analytical Writing Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 Test-Taking Strategies for the Analytical Writing Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 Sample Essay Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 X. Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 A. Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 B. Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74 C. Number Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78 D. Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83 v CliffsNotes GRE General Test Cram Plan E. Ratio and Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92 F. Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96 G. Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102 H. Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 I. Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114 XI. Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 A. Linear Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121 B. Simultaneous Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130 C. Multiplying and Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .139 D. Applications of Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146 XII. Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 A. Lines, Rays, Segments, and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155 B. Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .161 C. Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169 D. Other Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175 E. Areas of Shaded Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180 F. Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .184 G. Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .190 H. Coordinate Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .194 XIII. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 A. Data Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .203 B. Functions and Invented Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .210 C. Combinatorics and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .214 D. Common Problem Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .220 E. Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .224 F. Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227 XIV. Full-Length Practice Test with Answer Explanations . . . . . . . . . . . . . . 231 Section 1: Analytical Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .244 Section 2: Quantitative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .248 Section 3: Verbal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256 Section 4: Quantitative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .265 Section 5: Verbal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .273 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .281 Answer Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .283 vi Introduction If you’re preparing to take the GRE, this is not your first encounter with standardized testing. You’ve likely taken the SAT or ACT for your undergraduate admission, so you have some expectations for the GRE. From your previous test-taking experience, you probably realize that the goal is to test your reasoning and critical thinking skills, and the content, whether verbal or mathematical, is only the vehicle for that assessment. Without firm control of that vehicle, however, you won’t be able to demonstrate your reasoning skills effectively. To approach the GRE with confidence, you need to review the content and practice the style of questions you’ll find on the test. CliffsNotes GRE General Test Cram Plan is designed to help you achieve your best possible score on the GRE, whether you have two months, one month, or only one week to prepare. About the Test The GRE is comprised of three sections: Analytical Writing, Verbal Reasoning, and Quantitative Reasoning. Within the Analytical Writing section, you’ll be asked to complete two writing tasks: an issue task and an argument task; you’ll have 45 minutes to complete the issue task and 30 minutes for the argument. The Verbal Reasoning section includes critical reading, analogies, antonyms, and sentence completions; 30 minutes are allotted for this section. The Quantitative Reasoning questions may appear as multiple choice or quantitative comparison questions; you’re given 45 minutes for this section. Paper-based versions of the test were once the standard, but today they’re used only in areas where computer- based testing is not available. They offered a predetermined number of questions of each type for the Verbal Reasoning and Quantitative Reasoning sections. The chart at the end of this section shows the breakdown of the paper-based test on which our final test was patterned. The current computer adaptive version of the test allots a set time for each section and bases your score on the number of questions you answer in that time period and on their level of difficulty. You’re presented first with medium-difficulty questions, which are scored immediately as you answer them. Based on your responses, the computer assigns you questions of higher, lower, or equal difficulty. It is difficult to predict exactly how many questions of each type you’ll find on the computer adaptive test, but the chart at the end of this section gives you an idea of what to expect. Because questions are scored as soon as you submit your answers, you can’t return to previous questions. Unlike other testing situations, in which you might choose to skip over a question and return to it later, on the computer adaptive GRE you must answer each question as it is presented (or leave it unanswered permanently). Because you can’t return to a previous question to change an answer, it may be wise to pause a moment before moving on to the next question, just to be certain that you’re satisfied with your answer. For the Analytical Writing section, you’ll type your essays on the computer, using a simplified word processor that includes basic functions common to all word processing software (such as inserting, deleting, cutting, and pasting). The issue task presents you with a choice of two essay topics, while the argument task provides a single subject. vii CliffsNotes GRE General Test Cram Plan The GRE is administered year-round, by appointment, at computer test centers. When paper-based tests were used, they were administered to large groups of people simultaneously, but for the computer-based test, you’ll be able to choose a day and time to take the test, subject to availability. Test centers may offer appointments at Sect different times during the day, but whenever your appointment may be, you’ll need to arrive at the test center 30 1 minutes before your appointment. Bring your admission ticket and a photo ID. Except for pens and pencils, no personal items may be brought into the testing room. You’ll be provided with a place to store other items, 2 including cellphones, calculators, and electronic devices, but you won’t be able to access them again until the testing is over. You’ll be given scratch paper, and you may not remove that paper from the testing room. You 3 aren’t permitted to use a calculator during the test. About This Book 4 CliffsNotes GRE General Test Cram Plan is designed to guide you through a thorough and well-organized preparation for the GRE general test. Whether your test date is two months away, one month away, or just a week away, CliffsNotes GRE General Test Cram Plan will show you how to address your weaknesses and approach the test with confidence. 5 Begin with the diagnostic test, a compact simulation of the questions you can expect to find on the Verbal Reasoning and Quantitative Reasoning sections of the GRE general test. Check your work against the answers and 6 solutions provided. The Verbal Reasoning questions are organized by type, allowing you to determine which style of question you need to practice. The Quantitative Reasoning questions are mixed by subject and the solutions include references to the section number that reviews the content of the question. After you’ve scored your diagnostic test, look for patterns of strength and weakness. As you begin your review, pay special attention to any areas of weakness you’ve identified. After you’ve identified your target areas, the two-month, one-month, and one-week study plans will show you how to do a systematic study of the subject reviews, while practicing the question formats included in the test. The Sect two-month study plan gives you seven weekly tasks and a day-by-day study plan for the week before the test. Like 1 the two-month study plan, the one-month study plan includes weekly assignments and a daily breakdown for the 2 last week, but it organizes the material and highlights key areas to make best use of the available time. If you have 3 only one week to prepare for the test, the one-week study plan will guide you day by day through the essential topics and practice. 4 After you’ve had time to read and practice the material in the subject reviews, the final test will give you a clear 5 assessment of your readiness. Patterned after the former paper-based GRE, this simulated GRE includes directions and timings that mimic the real test, as well as solutions and explanations to help you correct your errors. With diagnosis, planning, practice, and assessment, CliffsNotes GRE General Test Cram Plan will provide the Note information, skills, and tactics you need to approach the GRE with confidence and to achieve your best possible four score. work Your the b coun maxi viii