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Official Guide Explanation:Data Sufficiency #42

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: 42
Page: 276
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Geometry Problems >
Category 2: Geometry > Circles > other
Category 3: Arithmetic > Ratio and Proportion >

Explanation: The real - life scenario of the water pipe makes this question look more complicated than it is. We've got two circles with the same center; the smaller one has a radius of r; the larger has a radius of t.

Statement (1) is sufficient. We're told that ((t - r)/(r)) = 0.5 and t - r = 0.3. So combining them, we get:

((0.3)/(r)) = 0.5

That's enough to find r. (No need on DS to worry about handling the decimals.)

Statement (2) is insufficient. The area of the cross section is the difference between the area of the larger circle and the area of the smaller circle, or:

π t2- π r2 = 1.29 π

That's not enough to find a value for r. Choice (A) is correct.

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