the surface area of the cube?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Nov 04, 2011 4:55 am

The ratio of the number of cubic units in the volume of a cube to the number of square units in the surface area of the cube is 2:3. What is the surface area of the cube?
(A) 16 square units
(B) 24 square units
(C) 64 square units
(D) 96 square units
(E) 144 square units

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Source: Beat The GMAT — Problem Solving | Fri Nov 04, 2011 4:55 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Fri Nov 04, 2011 5:00 am

Volume of a cube of side a = a*a*a cubic units
Surface area of the same cude = 6*a*a square units

From the question (a*a*a)/(6*a*a) = 2/3 => a/6=2/3 => a = 4
Surface area of the same cude = 6*a*a square units = [spoiler]6*4*4 = 96 square units[/spoiler] IMO Option D

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Nov 04, 2011 5:51 am

sanju09 wrote:The ratio of the number of cubic units in the volume of a cube to the number of square units in the surface area of the cube is 2:3. What is the surface area of the cube?
(A) 16 square units
(B) 24 square units
(C) 64 square units
(D) 96 square units
(E) 144 square units

Let each side of the cube = s units
Then volume of cube = s^3
Surface area of cube = 6s^2
Volume of cube : Surface area of cube = s^3 : 6s^2 = 2 : 3
s : 6 = 2 : 3 implies s = 4
Therefore, Surface area of cube = 6 * (4 ^ 2) = 6 * 16 = 96 sq units

The correct answer is D.

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vaibhavgupta: Master | Next Rank: 500 Posts; Posts: 416; Joined: Tue Aug 30, 2011 2:18 pmFollowed by: 9 members; Location: Delhi, India; Thanked: 13 times

by vaibhavgupta » Sat Nov 05, 2011 8:53 am

sanju09 wrote:The ratio of the number of cubic units in the volume of a cube to the number of square units in the surface area of the cube is 2:3. What is the surface area of the cube?
(A) 16 square units
(B) 24 square units
(C) 64 square units
(D) 96 square units
(E) 144 square units

First looked at ratios. all of them divisible by 3 are to be left.
then chose d cos the other one has to be a cube!

Hence D it is!

If OA is A, IMO B
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A

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