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## Official Guide Explanation:Problem Solving #109

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: 109
Page: 167
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Percents > Percent Change
Category 2: Arithmetic > Ratio and Proportion >

Explanation: This is a percent change question. Before we can calculate the percent change, we'll need to calculate the two percents.

The initial percent is \$3MM on sales of \$20MM:

(3/20) = 0.15 = 15%

Next, it's \$9MM on sales of \$108MM:

(9/108) = (1/12)

(1/12) is approximately 8.3%, but given the decimal point, it may be easier to finish this question with decimals instead of percents.

Now that we know the two ratios (or percents, or fractions) of royalties to sales, we can calculate the percent decrease. We'll do that by dividing the change in the ratio by the original ratio:

(((3/20) - (1/12))/((3/20)))

= (((9/60) - (5/60))/((9/60)))

= ((9 - 5)/9) = (4/9) ≈ 45%, choice (C).

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