Official Guide Explanation:
Problem Solving #109




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Solution and Metadata

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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