Official Guide Explanation:
Data Sufficiency #149




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Solution and Metadata

Question: 149
Page: 286
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Coordinate Geometry > Other
Category 2: Geometry > Triangles > Multiple figures

Explanation: The height of triangle OPQ is a line parallel to the y - axis between P and the x - axis. Because OP < PQ, the distance between that line and O is not as long as the distance between that line and Q. As a corollary, the triangle to the right of that line has a greater area than the triangle to the left of the line.

Statement (1) is sufficient: if the y - coordinate of P is 8, the height of the triangle is 8. If the x - coordinate of P is 6, the base of the triangle must be greater than 12, as the triangle to the right of the height is larger than the one to its left. Since the area is greater than (1/2)(12)(8), it must be greater than 48.

Statement (2) is insufficient: while it provides the base of the triangle, it does not offer anything about the height, which is necessary to determine the area. Choice (A) is correct.

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