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## Official Guide Explanation:Problem Solving #160

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: 160
Page: 175
Difficulty: 5 (Moderate)
Category 1: Word Problems > Geometry Problems >
Category 2: Geometry > Circles > Multiple figures

Explanation: The easiest (perhaps the only reasonable) way to find the area of the path is to find the area of the inner (unshaded) circle and the area of the outer circle, then find the diffferent. The area of a circle is given by π r2, so since the inner circle's radius is 8, the area is 82 π =64 π . The path is 3 feet wide, so the radius of the larger circle is 8 + 3 = 11, so the outer circle's area is given by 112 π =121 π . The difference is 121 π -64 π =57 π , choice (D).

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