Hi TARGET730,

This DS question has a number of interesting "restrictions" to it (and you have to pay careful attention to the restrictions to get the correct answer).

Here, we have a rectangular solid that has 4 faces with the same dimensions. In real basic terms, we have a box (NOT a cube), with the dimensions X, X and Y. We're also told that each dimension is an INTEGER. We're asked for the VOLUME of the solid.

Volume = (length)(width)(height)

Fact 1: Two of the faces have areas of 32 and 16

Since this rectangular solid has 4 faces with the same dimensions, the other 2 faces will have dimensions that match (but are different from the other 4 faces).

With the above values, we have just 2 possibilities:

The 4 sides are 32s and the 2 sides are 16s

The 4 sides are 16s and the 2 sides are 32s

While many Test Takers might dismiss this as insufficient, we need to do a bit more work to PROVE whether it's sufficient or insufficient.

If the 2 sides are 16s, then the two dimensions are 4 and 4

Since the others sides are 32s, those dimensions are 4 and 8

The volume of this solid is (4)(4)(8) = 126

If the 2 sides are 32s, then the two dimensions are (root32) and (root32).

The prompt stated that the dimensions had to be INTEGERS though, so this set of dimensions does NOT MATCH the restrictions given. Thus, there is only one answer in Fact 1.

Fact 1 is SUFFICIENT

Fact 2: One of the edges is twice the length of another.

We could have (4)(4)(8) =126

We could have (1)(1)(2) = 2

Fact 2 is INSUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,

Rich

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