FROM THE GRADUATE MANAGEMENT ADMISSION COUNCIL® 2O17 OUANTITATIVE Advance your skills with 300 additional practice questions unique to this guide I n c l u d e s Problem Solving and Data Suffi ciency 5 4 questions with answer explanations n e v e rq- ub ee sf ot iroen- ss e e n Create your own practice sets online at gmat.wiley.com Exclusive online videos with study tips and test-taking strategies mba.com THE OFFICIAL GUIDE FOR GMAT® QUANTITATIVE REVIEW 2017 Copyright © 2016 by the Graduate Management Admission Council. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. 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Table of Contents 1.0 What Is the GMAT®? 4 1.0 What Is the GMAT®? 5 1.1 Why Take the GMAT® Exam? 5 1.2 GMAT® Exam Format 6 1.3 What Is the Content of the Test Like? 7 1.4 Quantitative Section 8 1.5 Verbal Section 8 1.6 What Computer Skills Will I Need? 9 1.7 What Are the Test Centers Like? 9 1.8 How Are Scores Calculated? 9 1.9 Analytical Writing Assessment Scores 9 1.10 Test Development Process 10 2.0 How to Prepare 12 2.0 How to Prepare 13 2.1 How Can I Best Prepare to Take the Test? 13 2.2 What About Practice Tests? 13 2.3 Where Can I Get Additional Practice? 14 2.4 General Test-Taking Suggestions 14 3.0 Math Review 16 3.0 Math Review 17 3.1 Arithmetic 18 3.2 Algebra 29 3.3 Geometry 37 3.4 Word Problems 49 4.0 Problem Solving 58 4.0 Problem Solving 59 4.1 Test-Taking Strategies 60 4.2 The Directions 60 4.3 Sample Questions 62 4.4 Answer Key 87 4.5 Answer Explanations 89 5.0 Data Suffi ciency 148 5.0 Data Suffi ciency 149 5.1 Test-Taking Strategies 150 5.2 The Directions 152 5.3 Sample Questions 154 5.4 Answer Key 166 5.5 Answer Explanations 167 Appendix A Answer Sheets 212 Problem Solving Answer Sheet 213 Data Suffi ciency Answer Sheet 214 Visit gmat.wiley.com to access web‐based supplemental features available in the print book as well. Th ere you can access a question bank with customizable practice sets and answer explanations using 300 Problem Solving and Data Suffi ciency questions and review topics like Arithmetic, Algebra, Geometry, and Word Problems. Watch exclusive videos stressing the importance of big data skills in the real world and off ering insight into math skills necessary to be successful on the Quantitative section of the exam. 1.0 What Is the GMAT® Exam? 4 1.0 What Is the GMAT® Exam? 1 .0 What Is the GMAT ® Exam? Th e Graduate Management Admission Test ® (GMAT ® ) is a standardized, three‐part test delivered in English. Th e test was designed to help admissions officers evaluate how suitable individual applicants are for their graduate business and management programs. It measures basic verbal, mathematical, and analytical writing skills that a test‐taker has developed over a long period of time through education and work. Th e GMAT exam does not measure a person’s knowledge of specific fields of study. Graduate business and management programs enroll people from many diff erent undergraduate and work backgrounds, so rather than test your mastery of any particular subject area, the GMAT exam will assess your acquired skills. Your GMAT score will give admissions officers a statistically reliable measure of how well you are likely to perform academically in the core curriculum of a graduate business program. Of course, there are many other qualifications that can help people succeed in business school and in their careers—for instance, job experience, leadership ability, motivation, and interpersonal skills. Th e GMAT exam does not gauge these qualities. Th at is why your GMAT score is intended to be used as one standard admissions criterion among other, more subjective, criteria, such as admissions essays and interviews. 1 .1 Why Take the GMAT ® Exam? GMAT scores are used by admissions officers in over 6,000 graduate business and management programs worldwide. Schools that require prospective students to submit GMAT scores in the application process are generally interested in admitting the best‐qualified applicants for their programs, which means that you may find a more beneficial learning Myth -vs- FACT environment at schools that require GMAT scores as part of your application. M – If I don’t score in the 90th percentile, I won’t get into any Because the GMAT exam gauges skills that are important school I choose. to successful study of business and management at the graduate level, your scores will give you a good indication F – Very few people get very high scores. of how prepared you are to succeed academically in a graduate management program; how well you do on Fewer than 50 of the more than 200,000 the test may also help you choose the business schools people taking the GMAT exam each year to which you apply. Furthermore, the percentile table get a perfect score of 800. Thus, while you you receive with your scores will tell you how your may be exceptionally capable, the odds performance on the test compares to the performance are against your achieving a perfect score. Also, the GMAT exam is just one piece of of other test‐takers, giving you one way to gauge your your application packet. Admissions offi cers competition for admission to business school. use GMAT scores in conjunction with undergraduate records, application essays, interviews, letters of recommendation, and other information when deciding whom to accept into their programs. 5 The Offi cial Guide for GMAT® Quantitative Review 2017 Schools consider many diff erent aspects of an application before making an admissions decision, so even if you score well on the GMAT exam, you should contact the schools that interest you to learn more about them and to ask about how they use GMAT scores and other admissions criteria (such as your undergraduate grades, essays, and letters of recommendation) to evaluate candidates for admission. School admissions offi ces, web sites, and materials published by schools are the key sources of information when you are doing research about where you might want to go to business school. For more information on the GMAT, test preparation materials, exam registration, how to use and send your GMAT scores to schools, and applying to business school, visit mba.com. 1 .2 GMAT ® Exam Format Th e GMAT exam consists of four separately timed sections (see the table on the next page). Th e test starts with one Analytical Writing Assessment (AWA) essay prompt, and you will have 30 minutes to type your essay on a computer keyboard. Th e AWA is followed immediately by the 30‐minute Integrated Reasoning section, which features 12 question prompts in four diff erent question formats. Th e test ends with two 75‐minute, multiple‐choice sections: the Quantitative section, with 37 questions, and the Verbal section, with 41. Th e GMAT is a computer‐adaptive test (CAT), which means that in the multiple‐choice sections of the test, the computer constantly gauges how well you are doing on the test and presents you with questions that are appropriate to your ability level. Th ese questions are drawn from a huge pool of possible test questions. So, although we talk about the GMAT as one test, the GMAT exam you take may be completely diff erent from the test of the person sitting next to you. Here’s how it works. At the start of each GMAT multiple‐choice section (Verbal and Quantitative), you will be presented with a Myth FACT -vs- question of moderate difficulty. Th e computer uses your response to that first question to determine which question to present next. M – Getting an easier question If you respond correctly, the test usually will give you questions means I answered the last one of increasing difficulty. If you respond incorrectly, the next wrong. question you see usually will be easier than the one you answered incorrectly. As you continue to respond to the questions presented, F – Getting an easier question the computer will narrow your score to the number that best does not necessarily mean characterizes your ability. When you complete each section, the you got the previous question wrong. computer will have an accurate assessment of your ability. To ensure that everyone receives the same Because each question is presented on the basis of your answers to content, the test selects a specifi c number all previous questions, you must answer each question as it appears. of questions of each type. The test may call You may not skip, return to, or change your responses to previous for your next question to be a relatively hard problem-solving item involving arithmetic questions. Random guessing can significantly lower your scores. operations. But, if there are no more If you do not know the answer to a question, you should try to relatively diffi cult problem-solving items eliminate as many choices as possible, then select the answer you involving arithmetic, you might be given an think is best. If you answer a question incorrectly by mistake—or easier item. correctly by lucky guess—your answers to subsequent questions Most people are not skilled at estimating will lead you back to questions that are at the appropriate level of item diffi culty, so don’t worry when taking difficulty for you. the test or waste valuable time trying to determine the diffi culty of the questions you are answering. 6 1.3 What Is the GMAT® Exam? What Is the Content of the Test Like? Each multiple‐choice question used in the GMAT exam has been thoroughly reviewed by professional test developers. New multiple‐choice questions are tested each time the test is administered. Answers to trial questions are not counted in the scoring of your test, but the trial questions are not identified and could appear anywhere in the test. Th erefore, you should try to do your best on every question. Th e test includes the types of questions found in this guide, but the format and presentation of the questions are diff erent on the computer. When you take the test: • Only one question at a time is presented on the computer screen. • Th e answer choices for the multiple‐choice questions will be preceded by circles, rather than by letters. • Diff erent question types appear in random order in the multiple‐choice sections of the test. • You must select your answer using the computer. • You must choose an answer and confirm your choice before moving on to the next question. • You may not go back to change answers to previous questions. Format of the GMAT® Exam Questions Timing Analytical Writing Analysis of an Argument 1 30 min. Integrated Reasoning 12 30 min. Multi‐Source Reasoning Table Analysis Graphics Interpretation Two‐Part Analysis Optional break Quantitative 37 75 min. Problem Solving Data Sufficiency Optional break Verbal 41 75 min. Reading Comprehension Critical Reasoning Sentence Correction Total Time: 210 min. 1 .3 What Is the Content of the Test Like? It is important to recognize that the GMAT exam evaluates skills and abilities developed over a relatively long period of time. Although the sections contain questions that are basically verbal and mathematical, the complete test provides one method of measuring overall ability. Keep in mind that although the questions in this guide are arranged by question type and ordered from easy to difficult, the test is organized diff erently. When you take the test, you may see diff erent types of questions in any order. 7 The Offi cial Guide for GMAT® Quantitative Review 2017 1 .4 Quantitative Section Th e GMAT Quantitative section measures your ability to reason quantitatively, solve quantitative problems, and interpret graphic data. Two types of multiple‐choice questions are used in the Quantitative section: • Problem Solving • Data Sufficiency Problem solving and data sufficiency questions are intermingled throughout the Quantitative section. Both types of questions require basic knowledge of: • Arithmetic • Elementary algebra • Commonly known concepts of geometry To review the basic mathematical concepts that will be tested in the GMAT Quantitative questions, see the math review in chapter 3. For test‐taking tips specific to the question types in the Quantitative section of the GMAT exam, sample questions, and answer explanations, see chapters 4 and 5. 1 .5 Verbal Section Th e GMAT Verbal section measures your ability to read and comprehend written material, to reason and evaluate arguments, and to correct written material to conform to standard written English. Because the Verbal section includes reading sections from several diff erent content areas, you may be generally familiar with some of the material; however, neither the reading passages nor the questions assume detailed knowledge of the topics discussed. Th ree types of multiple‐choice questions are used in the Verbal section: • Reading Comprehension • Critical Reasoning • Sentence Correction Th ese question types are intermingled throughout the Verbal section. For test‐taking tips specific to each question type in the Verbal section, sample questions, and answer explanations, see Th e Offi cial Guide for GMAT Review, 2017 Edition, or Th e Offi cial Guide for GMAT Verbal Review , 2017 Edition; both are available for purchase at mba.com. 8