MANHATTAN PREP Algebra GMAT Strategy Guide This essential guide covers algebra in all its various forms (and disguises) on the GMAT. Master fundamental techniques and nuanced strategies to help you solve for unknown variables of every type. guide 2 Algebra GMAT Strategy Guide, Sixth Edition 10-digit International Standard Book Number: 1-941234-00-3 13-digit International Standard Book Number: 978-1-941234-00-6 eISBN: 978-1-941234-21-1 Copyright © 2014 MG Prep, Inc. ALL RIGHTS RESERVED. No part of this work may be reproduced or used in any form or by any means —graphic, electronic, or mechanical, including photocopying, recording, taping, or web distribution— without 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 of the Graduate Management Admission Council, which neither sponsors nor is affiliated in any way with this product. Layout Design: Dan McNaney and Cathy Huang Cover Design: Dan McNaney and Frank Callaghan Cover Photography: Alli Ugosoli INSTRUCTIONAL GUIDE SERIES GMAT Roadmap Number Properties (ISBN: 978-1-941234-09-9) (ISBN: 978-1-941234-05-1) Fractions, Decimals, & Critical Reasoning Percents (ISBN: 978-1-941234-01-3) (ISBN: 978-1-941234-02-0) Algebra Reading (ISBN: 978-1-941234-00-6) Comprehension (ISBN: 978-1-941234-06-8) Word Problems Sentence Correction (ISBN: 978-1-941234-08-2) (ISBN: 978-1-941234-07-5) Geometry Integrated Reasoning (ISBN: 978-1-941234- & Essay 03-7) (ISBN: 978-1-941234-04-4) SUPPLEMENTAL GUIDE SERIES Math GMAT Supplement Verbal GMAT Guides Supplement Guides Foundations of GMAT Math Foundations of GMAT (ISBN: 978-1-935707-59-2) Verbal (ISBN: 978-1-935707-01-9) Advanced GMAT Quant Official Guide Companion (ISBN: 978-1-935707-15-8) for Sentence Correction (ISBN: 978-1-937707-41-5) Official Guide Companion (ISBN: 978-0-984178-01-8) December 2nd, 2014 Dear Student, Thank you for picking up a copy of Algebra. I hope this book gives you just the guidance you need to get the most out of your GMAT studies. A great number of people were involved in the creation of the book you are holding. First and foremost is Zeke Vanderhoek, the founder of Manhattan Prep. Zeke was a lone tutor in New York City when he started the company in 2000. Now, well over a decade later, the company contributes to the successes of thousands of students around the globe every year. Our Manhattan Prep Strategy Guides are based on the continuing experiences of our instructors and students. The overall vision of the 6th Edition GMAT guides was developed by Stacey Koprince, Whitney Garner, and Dave Mahler over the course of many months; Stacey and Dave then led the execution of that vision as the primary author and editor, respectively, of this book. Numerous other instructors made contributions large and small, but I'd like to send particular thanks to Josh Braslow, Kim Cabot, Dmitry Farber, Ron Purewal, Emily Meredith Sledge, and Ryan Starr. Dan McNaney and Cathy Huang provided design and layout expertise as Dan managed book production, while Liz Krisher made sure that all the moving pieces, both inside and outside of our company, came together at just the right time. Finally, we are indebted to all of the Manhattan Prep students who have given us feedback over the years. This book wouldn't be half of what it is without your voice. At Manhattan Prep, we aspire to provide the best instructors and resources possible, and we hope that you will find our commitment manifest in this book. We strive to keep our books free of errors, but if you think we've goofed, please post to manhattanprep.com/GMAT/errata. If you have any questions or comments in general, please email our Student Services team at