Official Guide Explanation:
Data Sufficiency #D36

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Solution and Metadata

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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