Official Guide Explanation:
Data Sufficiency #122




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Solution and Metadata

Question: 122
Page: 283
Difficulty: 5 (Moderate)
Category 1: Geometry > Rectangular Solids and Cylinders > Rectangular Solids

Explanation: To find the volume of a rectangular solid, we need the three dimensions--usually described as length, width, and height.

Statement (1) is insufficient. It doesn't matter which face has which name (e.g. "length"), so we can say:

lw = 15

wh = 24

That's three variables but only two equations--not enough information.

Statement (2) is also insufficient. Knowing the area of two of the faces (in this case, two corresponding faces) isn't enough.

Taken together, we have enough information. There are three distinct faces, each of which occurs twice (for instance, the top and bottom have the same dimensions). We're given the measurements of each:

lw = 15

wh = 24

lh = 40

We have three variables and now three equations. It takes some work to find the values, but they can be guessed at based on the factors of the numbers. Since 40 and 15 are both multiples of 5, we can guess that l = 5, meaning that w = 3 and h = 8, which is confirmed by wh = 24. With the three dimensions, we can calculate the volume of the solid. Choice (C) is correct.

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