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

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Wed May 20, 2020 7:21 am

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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

[spoiler]OA=D[/spoiler]

Source: Official Guide

Source: Beat The GMAT — Problem Solving | Wed May 20, 2020 7:21 am

anonylfc: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed May 20, 2020 9:34 pm

Re: 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

by anonylfc » Thu May 21, 2020 9:50 am

Area of cube = (side)^3

As side of X is twice of Y-> X=2Y

Ratio of cube Y to cube X will be
=Y^3/X^3
=Y^3/ (2Y)^3
=Y^3/ 8Y^3
=1/8
Hope this helps. Please upvote if you found this helpful !

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: 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

by Scott@TargetTestPrep » Mon May 25, 2020 11:13 am

M7MBA wrote: ↑
Wed May 20, 2020 7:21 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

[spoiler]OA=D[/spoiler]

Source: Official Guide

Solution:

Let y = the edge length of cube Y. Thus, 2y = the edge length of cube X. The volume of cube Y is therefore y^3, and that of cube X is (2y)^3 = 8y^3. So the ratio of the volume of cube Y to that of cube X is x^3 / (8x^3) = 1/8.

Answer: D

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