Geometry

[mattnyc15]

No clue on this one:


No idea how they got to 27 on this one.

OA: 1 to 27[/img]

[Brent@GMATPrepNow]

The volume of a rectangular solid (aka box) = (length)(width)(height), but the volume of a cube = (length of one side)^3

To solve this question, let's assign some nice dimensions to each cube.

Let's say that cube A has dimensions 1 x 1 x 1
This means that cube B has dimensions 3 x 3 x 3 [since the length of an edge of cube A is 1/3 the length of an edge of cube B]

The volume of cube A = 1x1x1 = 1
The volume of cube B = 3x3x3 = 27

So, the ratio of the volume of cube A to the volume of cube B = 1/27

The question is very similar to this one - https://www.beatthegmat.com/geometry-t269674.html

Cheers,
Brent

[MartyMurray]

Notice that in answering this question Brent took advantage of a key thing.

In questions such as this one that basically state that if you do something with any set of numbers that fit the constraints described in the question you will always get the same result, it is safe to plug in any numbers that fit the constraints of the question.

In this case, the implication of the question is that in tripling the lengths of the sides of the cube you will always get a larger cube the volume of which is a particular multiple of the volume of the smaller cube.

Since no matter what the numbers are, as long as the greater length is triple the shorter length, you will always get the same result, then you can select any numbers that fit that constraint.

This principle can be applied to answering many different types of GMAT questions, sometimes making questions that seem insanely challenging rather easy to answer.