Official Guide Explanation:
Data Sufficiency #22

 

 

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.

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Solution and Metadata

Question: 22
Page: 154
Difficulty: 5 (Moderate)
Category 1: Geometry > Coordinate Geometry > Other
Category 2: Geometry > Circles > other

Explanation: For a circle with the center at the origin, the value of r2 + s2 is always the same for any point (r,s) on the circle. Thus, all we need is to find one point on the circle, and we'll get the value we're looking for.

Statement (1) is sufficient. Given the radius and the fact that the center is at the origin, we can find any number of points. The easiest are the ones on the axes: For instance, on the x - axis, the point 2 from the origin is (2,0). That gives us a r2 + s2 = 22 + 02 = 4.

Statement (2) is also sufficient. Given a point, we can calculate the square of each coordinate and sum them to get the answer. Choice (D) is correct.

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