### 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 #66

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: 66
Page: 161
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Ratio and Proportion >

Explanation: This question gives us three ratios and asks us to combine them to generate a fourth. There are a total of four variables: The number of first, second, third, and fourth graders. To avoid the confusion of "first" and "fourth" starting with the same letter, call the variables a, b, c, and d, respectively.

Here are the given ratios:

b:d = 8:5

a:b = 3:4

c:d = 3:2

We're looking for a:c.

Combining ratios is much like finding common denominators. To combine the first two, we'll need the value for b to be the same. If a:b = 3:4, the ratio is equivalent to 6:8. Now the first two ratios have the same value of b, 8. Thus, the ratio of a:b:d = 6:8:5, or:

a:d = 6:5

Now, to relate a and c, combine this new ratio with c:d = 3:2. Since d is the common term, multiply each ratio so that d = 10:

a:d = 12:10

c:d = 15:10

Now, a:d:c = 12:10:15, or a:c = 12:15, which simplifies to 4:5, choice (E).

 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.