### Bookshelf

 Total GMAT Math Jeff's complete Quant guide, on sale now!
 Total GMAT Verbal Everything you need to ace GMAT Verbal!
 New: GMAT 111 Improve every aspect of your GMAT prep!

Guides To the Official Guide
(Updated for new editions!)

1,800 Practice Quant Questions

GMAT Question of the Day

GMAT Official Guide
OG Math | OG Verbal

Beginner's Guide to the GMAT

GMAT Hacks Affiliate Program

### Resources

MBA.com
GMAC Official Site
Free GMATPrep Practice Tests

Stacy Blackman Consulting
Book | Essay Guides

GRE HQ
Total GRE Math

Ultimate SAT Verbal

## Official Guide Explanation:Problem Solving #106

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 106
Page: 75
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Real Numbers >
Category 2: Algebra > Equations >

Explanation: Trying to simplify the equation x2 = xy raises an important point. Generally, you can divide both sides by x, leaving x = y. However, this question specifies that x and y are different integers, so x ≠ y. Whenever you divide both sides of an equation by a variable, there's always the possibility that the variable is 0. (If both sides are multiplied by zero, both sides are equal to zero, and they are equal.) In this case, if x = 0, y could be any number. So, if x2 = xy and x ≠ y, it must be the case that x = 0. Now, we can look at the statements:

I.    Yes, we've established that x = 0.

II.    This cannot be true: if x = 0 and x ≠ y, y cannot be 0.

III.    Since x = 0, if x= - y, then y = 0, and we've just seen that y cannot be 0.

I is the only statement that must be true, so the correct choice is (A).

 You should follow me on Twitter. While you're at it, take a moment to subscribe to GMAT Hacks via RSS or Email.

 Total GMAT Math The comprehensive guide to the GMAT Quant section. It's "far and away the best study material available," including over 300 realistic practice questions and more than 500 exercises! Click to read more.