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Strategy Guide MANHATTAN Supplement GM/ Foundations of GMAT Math Builds Core Skills in Algebra, Arithmetic, Geometry, & More Includes Strengthens Comprehension of GMAT Math Principles Online Bonus < Questions -mf 700+ Practice Problems with Step-by-Step Explanations Kate M cKeon, M anhattan GMAT Instructor 9 9 t h P e r c e n t i l e I n s t r u c t o r s • C o n t e n t - B a s e d Cu r r i c u l um GMAT and GMAC are registered trademarks of the Graduate Management Admission Council which neither sponsors nor endorses this product. MANHATTAN GMAT Foundations of GMAT Math GMAT Strategy Guide This supplemental guide provides in-depth and easy-to-follow explanations o f the fundamental m ath skills necessary for a strong performance on the GMAT. Foundations of GMAT Math, Second Edition 10-digit International Standard Book Number: 1-935707-59-0 13-digit International Standard Book Number: 978-1-935707-59-2 elSBN: 978-0-979017-59-9 Copyright © 2011 MG Prep, Inc. ALL RIGHTS RESERVED. No part o f this work may be reproduced or used in any form or by any means— graphic, electronic, or mechanical, including photocopying, recording, taping, W eb distribution— w ithout the prior written permission of the publisher, MG Prep Inc. Note: GMAT, Graduate Management Admission Test, Graduate Management Admission Council, and GMAC are all registered trademarks o f the Graduate Managem ent Admission Council, which neither sponsors nor is affiliated in any way with this product. Layout Design: Dan M cNaney and Cathy Huang Cover Design: Evyn Williams and Dan McNaney Cover Photography: Adrian Buckmaster INSTRUCTIONAL GUIDE SERIES GM AT R oadm ap G eom etry (ISBN: 978 -1-935707-69-1) (ISBN: 978-1-935707-64-6) Fractions, Decim als, & Percents Critical Reasoning (ISBN: 978 -1-935707-63-9) (ISBN: 978-1-935707-61-5) A lgebra Reading C om prehension (ISBN: 978-1-935707-62 -2 ) (ISBN: 978-1-935707-66-0) W ord Problem s Sentence Correction (ISBN: 978-1 -935707-68-4) (ISBN: 978-1-935707-67-7) N u m b er Properties In te g ra ted Reasoning (ISBN: 978 -1-935707-65-3) (ISBN: 978-1-935707-83-7) SUPPLEMENTAL GUIDE SERIES Math GMAT Supplement Guides Verbal GMAT Supplement Guides Foundations o f G M A T M ath Foundations o f G M AT Verbal (ISBN: 978-1 -935707-59 -2 ) (ISBN: 978-1-935707-01 -9) A dvanced G M A T Q u an t (ISBN: 978-1 -935707-15 -8 ) O fficial G uide C om pan ion (ISBN: 978-0 -984178-01 -8 ) MANHATTAN GMAT November 15th, 2011 Dear Student, Thank you for picking up a copy of Foundations o f GMAT Math. Think of this book as the foundational tool that will help you relearn all of the math rules and concepts you once knew but have since forgotten. Its all in here, delivered with just the right balance of depth and simplicity. Doesn’t that sound good? As with most accomplishments, there were many people involved in the creation of the book you’re holding. First and foremost is Zeke Vanderhoek, the founder of Manhattan GMAT. Zeke was a lone tutor in New York when he started the company in 2000. Now, eleven years later, the company has Instructors and offices nationwide and contributes to the studies and successes of thousands of students each year. Our Manhattan GMAT Strategy Guides are based on the continuing experiences of our Instructors and students. For this Foundations o f GMAT Math book, we are particularly indebted to a number of Instructors, starting with the extraordinary Dave Mahler. Dave rewrote practically the entire book, having worked closely with Liz Ghini Moliski and Abby Pelcyger to reshape the books conceptual flow. Together with master editor/writer/organizer Stacey Ko- prince, Dave also marshalled a formidable army of Instructor writers and editors, including Chris Brusznicki, Dmitry Farber, Whitney Garner, Ben Ku, Joe Lucero, Stephanie Moyerman, Andrea Pawliczek, Tim Sanders, Mark Sullivan, and Josh Yardley, all of whom made excellent contributions to the guide you now hold. In addition, Tate Shafer, Gilad Edelman, Jen Dziura, and Eric Caballero provided falcon-eyed proofing in the final stages of book production. Dan McNaney and Cathy Huang provided their design expertise to make the books as user-friendly as possible, and Liz Krisher made sure all the moving pieces came together at just the right time. And theres Chris Ryan. Beyond provid ing additions and edits for this book, Chris continues to be the driving force behind all of our curriculum efforts. His leadership is invaluable. At Manhattan GMAT, we continually aspire to provide the best Instructors and resources possible. We hope that you 11 find our commitment manifest in this book. If you have any questions or comments, please email me at HOWTO ACCESS YOUR ONLINE RESOURCES If you... ® are a registered Manhattan GMAT student and have received this book as part of your course materials, you have AUTOMATIC access to ALL of our online resources. This includes all practice exams, question banks, and online updates to this book. To access these resources, follow the instructions in the Welcome Guide provided to you at the start of your program. Do NOT follow the instructions below. ® purchased this book from the Manhattan GMAT Online store or at one of our Centers 1. Go to: http://www.manhattangmat.com/practicecenter.cfm 2. Log in using the username and password used when your account was set up. ® purchased this book at a retail location 1. Create an account with Manhattan GMAT at the website: https://www.manhattangmat.com/createaccount.cfm 2. Go to: http://www.manhattangmat.com/access.cfm 3. Follow the instructions on the screen. Your one year of online access begins on the day that you register your book at the above URL. You only need to register your product ONCE at the above URL. To use your online resources any time AFTER you have completed the registration process, log in to the following URL: http://www.manhattangmat.com/practicecenter.cfm Please note that online access is non-transferable. This means that only NEW and UNREGISTERED copies of the book w ill grant you online access. Previously used books will NOT provide any online resources. ® purchased an e-book version of this book 1. Create an account with Manhattan GMAT at the website: https://www.manhattangmat.com/createaccount.cfm 2. Email a copy of your purchase receipt to YOUR ONLINE RESOURCES Your purchase includes ONLINE ACCESS to the following: ® Foundations o f GMAT Math Online Question Bank The Bonus Online Drill Sets for FOUNDATIONS OF GMAT MATH consist of 400+ extra prac tice questions (with detailed explanations) tha t test the variety of Foundational Math concepts and skills covered in this book. These questions provide you with extra practice beyond the problem sets contained in this book. You may use our online timer to practice your pacing by setting time lim its for each question in the bank. ® Online Updates to the Contents in this Book The content presented in th is book is updated periodically to ensure tha t it reflects the GMAT’s most current trends. You may view all updates, including any known errors or changes, upon registering for online access. TABLE Ot CONTENTS 1. Arithmetic 11 Drill Sets 49 2. Divisibility 59 Drill Sets 89 3. Exponents & Roots 103 Drill Sets 133 4. Fractions 147 Drill Sets 181 5. Fractions, Decimals, Percents, & Ratios 197 Drill Sets 229 6. Equations 255 Drill Sets 285 7. Quadratic Equations 301 Drill Sets 331 8. Beyond Equations: Inequalities & Absolute Value 339 Drill Sets 355 9. Word Problems 367 Drill Sets 395 10. Geometry 419 Drill Sets 479 Glossary 507 0 Foundations of GMAT Math Arithmetic Quick-Start Definitions Basic Numbers Greater Than and Less Than Adding and Subtracting Positives and Negatives Multiplying and Dividing Distributing and Factoring Multiplying Positives and Negatives Fractions and Decimals Divisibility and Even and Odd Integers Exponents and Roots (and Pi) Variable Expressions and Equations PEMDAS PEMDAS Overview Combining Like Terms Distribution Pulling Out a Common Factor Long Multiplication Long Division