### 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!

1,800 Practice Math Questions

GMAT Official Guide
OG Math | OG Verbal

Guides To the Official Guide
Free: OG12 explanations!

GMAT Question of the Day

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 #196

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th 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: 196
Page: 180
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-Two Unk >
Category 2: Word Problems > Data Interpretation >

Explanation: The chart gives you three equations: x + y = 80, y + z = 120, and x + z = 160. With three variables and three equations, it's just a matter of combining the equations to find z, the number of green marbles in jar R. Start by combining the first two equations by setting each one equal to y:

y = 80 - x

y = 120 - z

80 - x = 120 - z

z - x = 40

Now, combine this equation with the third equation by adding them:

x + z = 160

(-x) + z = 40

2z = 200

z = 100, choice (D).

 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.