Official Guide Explanation:
Data Sufficiency #43




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Solution and Metadata

Question: 43
Page: 156
Difficulty: 5 (Moderate)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Pythag

Explanation: Statement (1) is insufficient. The diagonal is the hypotenuse of a right triangle with legs equal to the length and width of the rectangle. We can use the pythagorean theorem to represent what the statement tells us:

l2 + w2 = 52

Statement (2) is also insufficient. We're looking for lw, but we're told that 2l + 2w = 14, or l + w = 7.

Taken together, the statements are sufficient. We have two equations and two variables. Note that the first equation doesn't meet the usual standard of "linear" equations--having an exponent in one of the equations is a recipe for multiple results. However, there's a sort of twist on that twist. The multiple results in a case like this result in one positive and one negative answer (for instance, if x2 = 16, x = 4 or x= - 4). But since this question deals with a rectangle, all of the values must be positive. Choice (C) is correct.

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