What is the volume of cube C?
(1) The total surface area of C is greater than 24 and less than 150.
(2) The edge length of C is 5.
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Free GMAT Data Sufficiency Practice Question
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Answer & Explanation
Correct answer
B
A cube's volume is its edge length cubed, so a single exact edge length fixes the volume.
Statement (1): a surface area greater than 24 and less than 150 means each of the 6 faces has area greater than 4 and less than 25, so the edge is between 2 and 5, and the volume is between 8 and 125. That is a range, not a single value. Not sufficient.
Statement (2): an edge of 5 gives volume 5³ = 125, a single value. Sufficient.
So statement (2) alone is sufficient while statement (1) alone is not, and the answer is (B).
Trap notes. Choices (A) and (D) over-trust the surface-area range as if it pinned the volume to one value, but a range of edges (2 to 5) gives a range of volumes (8 to 125), a range, not a value. Choice (C) treats the range as if it had to be combined with the edge, but statement (2)'s exact edge already fixes the volume on its own. Choice (E) dismisses statement (2)'s exact edge as if no single statement could pin the cube, when an edge of 5 alone yields volume 125.