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## 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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**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).

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