Official GRE Quantitative Reasoning Practice Questions

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Welcome toOfficial GRE Quantitative ReasoningPractice Questions, Volume 1The book you are holding offers 150 real GRE practice questions directly from the maker ofthe GRE revised General Test. This book is specially created to give you in-depth practiceand accurate test preparation for the Quantitative Reasoning measure.Here’s what you will find inside: Authentic GRE Quantitative Reasoning test questions arranged by content andquestion type—to help you build your test-taking skills. Plus, mixed practice sets. Answers and explanations for every question! ETS’s own test-taking strategies. Learn valuable hints and tips that can help youget your best score. GRE Math Review covering math topics you need to know for the test. Official information on the GRE Quantitative Reasoning measure. Get the factsabout the test content, structure, scoring, and more—straight from ETS.About ETSAt ETS, we advance quality and equity in education for people worldwide by creatingassessments based on rigorous research. ETS serves individuals, educational institutions,and government agencies by providing customized solutions for teacher certification,English language learning, and elementary, secondary, and post-secondary education,as well as conducting educational research, analysis, and policy studies. Founded as anonprofit in 1947, ETS develops, administers, and scores more than 50 million testsannually—including the TOEFL and TOEIC tests, the GRE tests, and The PraxisSeriesTM assessments—in more than 180 countries at over 9,000 locations worldwide.For more information, visit www.ets.org.

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IMPORTANTETS makes available free test preparation materials for individuals planning to take a GRE test.POWERPREP II software is available for individuals planning to take the computer-deliveredGRE revised General Test, and the Practice Book for the Paper-based GRE revised General Test,Second edition, is available for individuals planning to take the paper-delivered test. Theinformation about how to prepare for the Quantitative Reasoning measure of the GRE revisedGeneral Test, including test-taking strategies, question strategies, etc., that is included in thefree test preparation is also included in this publication. This publication also provides youwith 150 brand new practice questions with answers and explanations.For more information about the GRE revised General Test, free and low-costGRE test preparation materials, and other GRE products and services,please visit the GRE website at:www.ets.org/greInquiries concerning the practice test questions in this bookshould be sent to the GRE testing program at:GRETestQuestionInquiries@ets.org

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Copyright 2014 by Educational Testing Service. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publicationmay be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher, with theexception that the program listings may be entered, stored, and executed in a computer system, but they may not be reproduced for publication.ISBN: 978-0-07-183431-5MHID: 0-07-183431-1The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-183432-2,MHID: 0-07-183432-X.eBook conversion by codeMantraVersion 2.0All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in aneditorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, theyhave been printed with initial caps.McGraw-Hill Education eBooks are available at special quantity discounts to use as premiums and sales promotions or for use in corporate trainingprograms. To contact a representative, please visit the Contact Us page at www.mhprofessional.com.ETS, the ETS logo, LISTENING, LEARNING, LEADING, E-RATER, GRADUATE RECORD EXAMINATIONS, GRE, POWERPREP, SCORESELECT, TOEFL, andTOEIC are registered trademarks of Educational Testing Service in the United States and other countries and are used under license. THE PRAXIS SERIES is a trademarkof Educational Testing Service and is used under license.TERMS OF USEThis is a copyrighted work and McGraw-Hill Education and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify,create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill Education’s prior consent.You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if youfail to comply with these terms.THE WORK IS PROVIDED “AS IS.” McGRAW-HILL EDUCATION AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THEACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATIONTHAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS ORIMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-HillEducation and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted orerror free. Neither McGraw-Hill Education nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work orfor any damages resulting therefrom. McGraw-Hill Education has no responsibility for the content of any information accessed through the work. Under no circumstancesshall McGraw-Hill Education and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of orinability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoeverwhether such claim or cause arises in contract, tort or otherwise.

Contents1How to Use This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiOverview of the GRE Quantitative ReasoningMeasure1Introduction to the GRE revised General Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1The Quantitative Reasoning Measure of the Computer-deliveredGRE revised General Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2The Quantitative Reasoning Measure of the Paper-deliveredGRE revised General Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Score Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Test Content7Overview of the Quantitative Reasoning Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7General Problem-solving Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Quantitative Reasoning Question Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Using the Calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393Arithmetic43Quantitative Comparison Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Multiple-choice Questions—Select One Answer Choice . . . . . . . . . . . . . . . . . . . . . . . . . 47Multiple-choice Questions—Select One or More Answer Choices . . . . . . . . . . . . . . . . . 49Numeric Entry Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4Algebra65Quantitative Comparison Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Multiple-choice Questions—Select One Answer Choice . . . . . . . . . . . . . . . . . . . . . . . . . 69Multiple-choice Questions—Select One or More Answer Choices . . . . . . . . . . . . . . . . . 71Numeric Entry Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745Geometry85Quantitative Comparison Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Multiple-choice Questions—Select One Answer Choice . . . . . . . . . . . . . . . . . . . . . . . . . 89Multiple-choice Questions—Select One or More Answer Choices . . . . . . . . . . . . . . . . . 91Numeric Entry Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946Data Analysis105Quantitative Comparison Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Multiple-choice Questions—Select One Answer Choice . . . . . . . . . . . . . . . . . . . . . . . . 110Multiple-choice Questions—Select One or More Answer Choices . . . . . . . . . . . . . . . . 112Numeric Entry Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Data Interpretation Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

7Mixed Practice Sets139Practice Set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Practice Set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Practice Set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209Answers and Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210Appendix A: GRE Math Review2291. Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2302. Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2453. Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2734. Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288Appendix B: Mathematical Conventions for theQuantitative Reasoning Measure of theGRE revised General Test329

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How to Use This BookThis book provides important information about the Quantitative Reasoning measure ofthe GRE revised General Test, including the knowledge and skills that are assessed and thetypes of questions that appear. The book will help you: Familiarize yourself with the test format and test question typesLearn valuable test-taking strategies for each question typeReview the math topics you need to know for the testCheck your progress with Quantitative Reasoning practice questionsThe following four-step program has been designed to help you make the best use ofthis book.STEP 1 Learn About the GRE Quantitative Reasoning MeasureChapter 1 of this book provides an overview of the GRE Quantitative Reasoning measure.Read this chapter to learn about the number of questions, time limits, and the test designfeatures. You will also find valuable test-taking strategies from ETS and importantinformation about how the measure is scored.STEP 2 Study the Different GRE Quantitative ReasoningQuestion TypesChapter 2 of this book describes the types of questions you will encounter in the Quantitative Reasoning measure. You will learn what the questions are designed to measure,and you will get tips for answering each question type. You will also see samples of eachquestion type, with helpful explanations.STEP 3 Practice Answering GRE QuantitativeReasoning QuestionsChapters 3, 4, 5, and 6 contain sets of authentic Quantitative Reasoning practice questions inthe content areas of Arithmetic, Algebra, Geometry, and Data Analysis, respectively. Answerthe questions in each set, and then read through the explanations to see which questions youfound most challenging. Look for patterns. Did specific content areas give you trouble? Youcan refresh your math skills in these areas with the GRE Math Review in Appendix A. TheGRE Math Review is a review of the math topics that are likely to appear on the QuantitativeReasoning measure. Each section of the GRE Math Review ends with exercises that will helpyou see how well you have mastered the material. Note that Appendix B provides informationabout the mathematical conventions that are used on the Quantitative Reasoning measure.Prior to answering the practice questions, it might be helpful to review these conventions.xi

STEP 4 Test Yourself With the Mixed Practice SetsOnce you have completed the practice sets for each content area in Chapters 3–6, it is time topractice with authentic GRE questions in the Mixed Practice Sets in Chapter 7. Each MixedPractice Set includes the question types and content areas contained in an actual QuantitativeReasoning section of the GRE revised General Test.xii

Overview of the GRE Quantitative ReasoningMeasureYour goal forthis chapter Review basic information on the structure of the GREQuantitative Reasoning measure, test-taking strategies,and scoringIntroduction to the GRE revised General TestT he GRE revised General Test—the most widely accepted graduate admissionstest worldwide—measures verbal reasoning, quantitative reasoning, criticalthinking, and analytical writing skills that are necessary for success in graduateand business school.Prospective graduate and business school applicants from all around the world takethe GRE revised General Test. Although applicants come from varying educational andcultural backgrounds, the GRE revised General Test provides a common measure forcomparing candidates’ qualifications. GRE scores are used by admissions committeesand fellowship panels to supplement undergraduate records, recommendation letters,and other qualifications for graduate-level study.The GRE revised General Test is available at test centers in more than 160 countries.In most regions of the world, the computer-delivered test is available on a continuousbasis throughout the year. In areas of the world where computer-delivered testing is notavailable, the test is administered in a paper-delivered format up to three times a year.Before taking the GRE revised General Test, it is important to become familiar withthe content and structure of the test, and with each of the three measures—VerbalReasoning, Quantitative Reasoning, and Analytical Writing. This book provides a closelook at the GRE Quantitative Reasoning measure. Chapter 1 provides an overview of thestructure and scoring of the Quantitative Reasoning measure. In Chapters 2 through 7,you will find information specific to the content of the Quantitative Reasoning measure.You can use the information in this publication to help you understand the type ofmaterial on which you will be tested. For the most up-to-date information about theGRE revised General Test, visit the GRE website at www.ets.org/gre.1

Overview of the GRE Quantitative Reasoning MeasureThe Quantitative Reasoning Measure of the Computer-deliveredGRE revised General TestStructure of the Quantitative Reasoning MeasureMeasureQuantitative Reasoning(Two sections)Number of Questions20 questions per sectionAllotted Time35 minutes per sectionThe Quantitative Reasoning sections may appear anytime in the test after section 1. Thedirections at the beginning of each Quantitative Reasoning section specify the totalnumber of questions in the section and the time allowed for the section.Test Design FeaturesThe Quantitative Reasoning measure of the computer-delivered GRE revised General Testis section-level adaptive. This means the computer selects the second section of a measurebased on your performance on the first section.The advanced adaptive design also means you can freely move forward and backward throughout an entire section. Specific features include: Preview and review capabilities within a section“Mark” and “Review” features to tag questions, so you can skip them and returnlater if you have time remaining in the sectionThe ability to change/edit answers within a sectionAn on-screen calculator (More information about the calculator is given inChapter 2.)Test-taking StrategiesThe questions in the Quantitative Reasoning measure are presented in a variety of formats. Some require you to select a single answer choice, others require you to select oneor more answer choices, and yet others require you to enter a numeric answer. Makesure when answering a question that you understand what response is required. An onscreen calculator will be provided at the test center for use during the QuantitativeReasoning sections.When taking the Quantitative Reasoning measure of the computer-delivered GRErevised General Test, you are free to skip questions that you might have difficultyanswering within a section. The testing software has a “Mark” feature that enables you tomark questions you would like to revisit during the time provided to work on thatsection. The testing software also has a “Review” feature that lets you view a completelist of all the questions in the section on which you are working, that indicates whetheryou have answered each question, and that identifies the questions you have marked forreview. Additionally, you ca

Practice Questions, Volume 1 The book you are holding offers 150 real GRE practice questions directly from the maker of the GRE revised General Test. This book is specially created to give you in-depth practice and accurate test preparation for the Quantitative Reasoning measure. Here’s what you will find inside:

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For the Verbal Reasoning and Quantitative Reasoning Measures of the computer-based GRE revised General Test, the reported scores are based on the number of correct responses to the questions included in the operational sections of the measure. The Verbal Reasoning and Quantitative Reasoning Measures are section-level adaptive. This means

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