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A certain clay cube has volume 64 cubic inches

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by SpencerP » Thu Aug 20, 2015 10:43 am
A certain clay cube has volume 64 cubic inches. If a smaller clay cube is formed and has half the volume of the original cube, how many inches long is an edge of the smaller cube?

A) 2
B) 4
C) 8
D) 4^1/3
E) 2 4^1/3

Correct Answer: E
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by Brent@GMATPrepNow » Thu Aug 20, 2015 10:51 am
SpencerP wrote:A certain clay cube has volume 64 cubic inches. If a smaller clay cube is formed and has half the volume of the original cube, how many inches long is an edge of the smaller cube?

A) 2
B) 4
C) 8
D) ∛4
E) 2∛4
When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

Volume of smaller cube is HALF of original cube.
So, volume of smaller cube = (1/2)(64) = 32

Volume of cube = (length of one side)³ [aside: edge is the same as side]
So, (length of one side)³ = 32
This means length of one side = ∛32

None of the answer choices matches this, so we must simplify ∛32
∛32 = ∛(8 x 4)
= (∛8)(∛4)
= [spoiler]2∛4[/spoiler]
= E
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by Max@Math Revolution » Fri Aug 21, 2015 7:05 pm
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


A certain clay cube has volume 64 cubic inches. If a smaller clay cube is formed and has half the volume of the original cube, how many inches long is an edge of the smaller cube?

A) 2
B) 4
C) 8
D) 4^1/3
E) 2 4^1/3

Correct Answer: E

==> Since the new cube has half the volume of the original cube, assuming the individual side of the cube has length a, a^3=64/2=32.

a=(32)^1/3, (2^3*2^2)^1/3=2(2^2)^1/3=2(4)^1/3, therefore E is the answer.


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