A rectangular box has a volume of 320 cubic meters, and a second box

Question

A rectangular box has a volume of 320 cubic meters, and a second box is half as long, half as wide, and one quarter as high as the first one. What is the volume, in cubic meters, of the second box?

A. 20
B. 40
C. 64
D. 80
E. 160

Kinshook · Answer

Given:  A rectangular box has a volume of 320 cubic meters, and a second box is half as long, half as wide, and one quarter as high as the first one.

Asked:  What is the volume, in cubic meters, of the second box?

A rectangular box has a volume of 320 cubic meters, and a second box is half as long, half as wide, and one quarter as high as the first one.

LWH = 320
olume, in cubic meters, of the second box=  \frac{L}{2}*\frac{W}{2}*\frac{H}{4} = \frac{LWH}{16} = \frac{320}{16} = 20

IMO A

Archit3110 · Answer

given ; x*y*z = 320
and also x*y*z/16 ; so 320/16 = 20
IMO A

Bunuel · Answer

Official 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 16*2*10 or 8*4*10. 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

320 = 8*10*4

Then, the volume of the second box is

1/2*8*1/2*10*1/2*4 = 20

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).

Bunuel · Answer

Video Explanation

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TheNightKing · Answer

1/2*1/2*1/4*320=20

A rectangular box has a volume of 320 cubic meters, and a second box

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A rectangular box has a volume of 320 cubic meters, and a second box

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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