### 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 #117

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: 117
Page: 76
Difficulty: 5 (Moderate)
Category 1: Algebra > Inequalities > other
Category 2: Arithmetic > Real Numbers >

Explanation: If xy > 0, either both are positive or both are negative. If yz < 0, then one of the variables is positive and one is negative. Thus, we have two possibilities:

(i) x is positive, y is positive, and z is negative

(ii) x is negative, y is negative, and z is positive

Consider each choice:

(A)    With (i), xyz is negative. With (ii), it's positive.

(B)    With (i), xyz2 is positive. With (ii), it's also positive.

(C)    With (i), xy2z is negative. With (ii), it's also negative.

(D)    With (i), xy2z2 is positive. With (ii), it's negative.

(E)    With (i), x2y2z2 is positive. With (ii), it's also positive.

Choice (C) is correct. Note that you don't have to go through all of that work: If you find a scenario in which one of the choices is positive, you know it isn't ALWAYS negative, and you can move on to the next choice.

 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.