Explanation
The first box has a volume of 320 cubic meters, and this
could be obtained through various different possible cases of exact dimensions.
For example, the box could be or .
But there is something interesting about this question: the correct answer,
evidently, doesn't depend on the exact dimension of the first box, because we
don't know what they are, and there is a single, definitive, correct answer to
this question. This type of situation crops up frequently on GMAT questions: we
are dealing with a range of possible cases and an outcome that is the same for
all the cases. When this is the case, we are free to choose any particular case
we want, for our own convenience. For example, since we are going to be taking
a half, a half, and a quarter, we can imagine a box that has a volume
Then, the volume of the second box is
Therefore, the correct answer is (A).
This technique might seem too good to be true. Or it might
strike you as clear enough, but you doubt that you'll be able to replicate it.
The key is, before automatically jumping into algebra, to consider the range of
possible cases. Analysis by cases is critical in data sufficiency, and it's
useful anywhere logical thinking is required. It's a useful step in most
questions to consider briefly what the range of possible cases is for the
question. Sometimes, you'll find that you can choose any one of those possible
cases, or you can choose two cases and compare them. The correct answer is (A).
If you believe you have found an error in this question or explanation, please contact us and include the question title or URL in your message.