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Geometry

by vinay1983 » Wed Sep 18, 2013 7:15 am
If the length of an edge of cube X is twice the length of an edge of cube Y, what is the ratio of the volume of cube Y to the volume of cube X?

(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/8
(E) 1/27

How can the length be considered as the volume of the cube?
Volume of a cube is l*w*h!
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by Brent@GMATPrepNow » Wed Sep 18, 2013 7:21 am
vinay1983 wrote:If the length of an edge of cube X is twice the length of an edge of cube Y, what is the ratio of the volume of cube Y to the volume of cube X?

(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/8
(E) 1/27

How can the length be considered as the volume of the cube?
Volume of a cube is l*w*h!
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 Y has dimensions 1x1x1
This means that cube X has dimensions 2x2x2 [since the length of an edge of cube X is twice the length of an edge of cube Y]

The volume of cube Y = 1x1x1 = 1
The volume of cube X = 2x2x2 = 8

So, the ratio of the volume of cube Y to the volume of cube X = 1/8 = D\

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Brent
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by theCodeToGMAT » Wed Sep 18, 2013 9:02 am
Volume of Cube is (Side)^3 and not L*B*H.

Let Side of CUBE Y be y
The Side of CUBE X is 2y

Ratio of Volume of Cube y to Cube x = (y)^3/(2y)^3
= 1/8

Answer [D]
vinay1983 wrote:If the length of an edge of cube X is twice the length of an edge of cube Y, what is the ratio of the volume of cube Y to the volume of cube X?

(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/8
(E) 1/27

How can the length be considered as the volume of the cube?
Volume of a cube is l*w*h!
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by [email protected] » Wed Sep 18, 2013 10:51 am
Hi vinay1983,

Brent's approach, TESTing values, is straight-forward and easy to duplicate on Test Day; it's exactly how I would have done it.

Here's the Number Property behind this question.

This question asks us to double each side of a cube (the fact that it's a cube is irrelevant though, the solution would be the same even if it was any type of "box")

Initial Volume = (side)(2nd side)(3rd side)

Since we're doubling each side, we'd have

New Volume = (double)(double)(double)(Initial Volume)

When you "double" and "double again" and "double again", you end up with (2)(2)(2)(what you started with) = 8(what you started with).

This is why the answer is D.

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