Includes 6 ^ Free Online Exams & More! Covers Divisibility & Primes, Probability; & More Teaches Problem Solving & Data Sufficiency Strategies Includes Practice Problems with Detailed Explanations Updated for The Official Guide for GMAT® Review, 13th Ed. H em anth V e n ka ta ra m a n , M an ha tta n GM AT Instructor mmm 99th Percentile Instructors • Content-Based Curriculum Number Properties GMAT and GMAC are registered trademarks of the Graduate Management Admission Council which neither sponsors nor endorses this product. MANHATTAN GMAT Number Properties GMAT Strategy Guide This foundational guide provides a comprehensive analysis of the properties and rules of integers tested on the GMAT. Learn, practice, and master everything from prime products to perfect squares. Number Properties GMAT Strategy Guide, Fifth Edition 10-digit International Standard Book Number: 1-935707-65-5 13-digit International Standard Book Number: 978-1-935707-65-3 elSBN: 978-1-937707-06-4 Copyright © 2012 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, 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: Evyn Williams and Dan McNaney Cover Photography: Alii Ugosoli Certified Chain of Custody ^ FORESTRY Promot'n9 Sustainable Forestry INITIATIVE www.sfiprogram.org SFI-00756 J INSTRUCTIONAL GUIDE SERIES □ 0 0 0 □ GMAT Roadmap Number Properties (ISBN: 978-1-935707-69-1) (ISBN: 978-1-935707-65-3) Fractions, Decimals, & Percents 0 Critical Reasoning (ISBN: 978-1-935707-63-9) (ISBN: 978-1-935707-61-5) Algebra H Reading Comprehension (ISBN: 978-1-935707-62-2) ZJB (ISBN: 978-1-935707-66-0) Word Problems n Sentence Correction (ISBN: 978-1-935707-68-4) LJ (ISBN: 978-1-935707-67-7) Geometry n Integrated Reasoning & Essay (ISBN: 978-1-935707-64-6) (ISBN: 978-1-935707-83-7) SUPPLEMENTAL GUIDE SERIES Math GMAT Supplement Guides Foundations of GMAT Math (ISBN: 978-1-935707-59-2) Advanced GMAT Quant (ISBN: 978-1-935707-15-8) Official Guide Companion (ISBN: 978-0-984178-01-8) Verbal GMAT Supplement Guides Foundations of GMAT Verbal (ISBN: 978-1-935707-01-9) MANHATTAN GMAT April 24th, 2012 Dear Student, Thank you for picking up a copy of Number Properties. I hope this book provides just the guidance you need to get the most out of your GMAT studies. As with most accomplishments, there were many people involved in the creation of the book you are holding. First and foremost is Zeke Yanderhoek, the founder of Manhattan GMAT. Zeke was a lone tutor in New York when he started the company in 2000. Now, 12 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 volume, we are particularly indebted to Stacey Koprince and Dave Mahler. Dave deserves special recognition for his contributions over the past number of years. Dan McNaney and Cathy Huang provided their design expertise to make the books as user-friendly as possible, and Noah Teitelbaum and Liz Krisher made sure all the moving pieces came together at just the right time. And there’s Chris Ryan. Beyond providing additions and edits for this book, Chris continues to be the driving force behind all of our curriculum efforts. His leadership is invaluable. Finally, thank you to all of the Manhattan GMAT students who have provided input and feedback over the years. This book wouldn’t be half of what it is without your voice. At Manhattan GMAT, we continually aspire to provide the best instructors and resources possible. We hope that you’ll find our commitment manifest in this book. If you have any questions or comments, please email me at