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## Official Guide Explanation:Problem Solving #154

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: 154
Page: 82
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Arithmetic > Percents > Percent Change

Explanation: This is essentially a weighted average question. We need to figure out what "weight" is assigned to salary costs and fringe - benefit costs. We're given an equation, where s is salary costs and f is fringe - benefit costs.

3.5(s + f) = 3s + 5.5f

We want the relationship between f and s + f. Simplify:

3.5s + 3.5f = 3s + 5.5f

0.5s = 2f

s = 4f

In other words, s has four times the weight of f. We're looking for ((f)/(s + f)), so substitute:

((f)/(s + f)) = ((f)/((4f) + f)) = ((f)/(5f)) = (1/5) = 20%, choice (B).

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