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## Official Guide Explanation:Problem Solving #220

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: 220
Page: 184
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Percents > Percent Change
Category 2: Word Problems > Rate Problems > other

Explanation: This is a question where assigning numbers to unknown values comes in handy. Say the employee's original number of hours per week was 10, and the original pay rate was \$8 per hour. That's \$8(10) = \$80 per week. If the pay rate increases by 25%, that's an increase of 25%(\$8) = \$2 to \$8 + \$2 = \$10 per hour. To make \$80 per week at an hourly rate of \$10 per hour, the employee needs to work ((\$80)/(\$10)) = 8. Percent change is ((change)/(original)), so in this case, when the hours decreased from 10 to 8, that's ((10 - 8)/10) = (2/10) = 20%, choice (B).

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