A certain clay cube has volume 64 cubic inches

[SpencerP]

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

[Brent@GMATPrepNow]

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

[Max@Math Revolution]

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.


www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.

l The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.

l The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare

l Hitting a score of 45 is very easy and points and 49-51 is also doable.

l Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson

Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8