Official Guide Explanation:
Data Sufficiency #117




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Solution and Metadata

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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