Official Guide Explanation:
Data Sufficiency #135




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Solution and Metadata

Question: 135
Page: 285
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Pythag

Explanation: To find the area of this quadrilateral, we would need to break it up into three parts: first, the triangle on the left (SRW), a rectangle bounded by S, T, W, and a point along RU directly below T, and the triangle left over on the right side. We know the dimensions of the first two of those parts, but need to know one more dimension of the triangle on the right to find its area.

Statement (1) is sufficient: if the length of RU is 80, then that leaves 80 - 45 - 15 = 20 for the base of the triangle on the right. Given a base of 20 and a height of 60, we can find the area of that triangle. Statement (2) is also sufficient: we know the height of the triangle on the right, so if we also know the hypotenuse, we can solve for the base, and then find the area. Choice (D) is correct.

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