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## Official Guide Explanation:Data Sufficiency #D36

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: D36
Page: 25
Difficulty: 5 (Moderate)
Category 1: Geometry > Circles > other

Explanation: Before considering the statements, consider the possible locations of X and Y. In a circle with a radius of 2, the furthest apart two points can be and still be within the circle is a little under 4, the diameter.

Statement (1) is insufficient. If XY is 3 and X is inside the circle, it's possible that Y is also inside the circle--as noted, the two could be close to 4 apart and still both be inside the circle. However, that's no guarantee. If, say, X is near the top of the circle and Y is 3 above that, Y is not within the circle.

Statement (2) is sufficient. If the radius is 2, every point that is less than 2 away from the center of the circle (O) is inside the circle. If OY is 1.5, Y is less than 2 away from the center, so Y is inside the circle. Choice (B) is correct.

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