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Geometry

This topic has 1 expert reply and 2 member replies
vinay1983 Legendary Member
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Geometry

Post Wed Sep 18, 2013 7:15 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post 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\

    Cheers,
    Brent

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    theCodeToGMAT Legendary Member
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    Post 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!

    Post 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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