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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A certain clay cube has volume 64 cubic inches
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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.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
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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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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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
