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## Official Guide Explanation:Data Sufficiency #117

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: 117
Page: 283
Difficulty: 5 (Moderate)
Category 1: Geometry > Circles > Multiple figures
Category 2: Geometry > Circles > other

Explanation: To find the area of the region inside the larger circle and outside the smaller circle, we'll need to find the areas of each of the two circles. To do that, we'll need some measurement of each circle. Finding the radius of each is a typical way of solving this sort of problem.

Statement (1) is sufficient. AB is the radius of the smaller circle, so we can find the area of the smaller circle. AC is the radius of the larger circle and is equal to the sum of AB and BC. Given AC, we can find the area of the larger circle as well.

Statement (2) is also sufficient. The sum of CD and DE is CE, the radius of the larger circle. Given that, we can find the area of the larger circle. Knowing the radius of the larger circle (CD + DE =1 + 4 = 5), we know that AC is 5 as well. The diameter of the smaller circle is AD, which is the sum of AC and CD. AC is 5 and CD is 1, so the diameter is 6. That means the radius of 3, so we can find the area of the smaller circle. Choice (D) is correct.

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