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## Official Guide Explanation:Data Sufficiency #95

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 95
Page: 160
Difficulty: 5 (Moderate)
Category 1: Geometry > Circles > Multiple figures
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: Statement (1) is insufficient: the total areas does not tell you the specific area of each circle. Statement (2) is also insufficient, as the ratio is not attached to any actual numbers.

Taken together, the statements are sufficient. If we assume that P is the larger of the regions (it doesn't matter which is which, as the question doesn't ask for P or Q, it asks for the larger of the two) the radius of P is r and the radius of Q is s, then (1) implies the following equation:

π r2+ π s2 = 90

while (2) provides another equation:

r = 3s

The two equations can be combined as follows:

π (3s)2+ π s2 = 90

There's only one variable in the equation, so we can solve for that variable. Because s is squared, there may be two possible values of s, but one will be negative, and the radius of a circle can't be negative, so we can eliminate that value. Choice (C) is correct.

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