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A perfect cube is an integer whose cube root is an integer. For exampl

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Carcass
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A perfect cube is an integer whose cube root is an integer. For exampl [#permalink] New post   01 Feb 2021, 06:00
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A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

A. 8p
B. pq
C. pq + 27
D. -p
E. \((p - q)^6\)

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C
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Re: A perfect cube is an integer whose cube root is an integer. For exampl [#permalink] New post   01 Feb 2021, 06:57
Carcass wrote:
A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

A. 8p
B. pq
C. pq + 27
D. -p
E. \((p - q)^6\)

Kudos for the right answer and explanation


Test some super easy values.
How about p = 1 and q = 1 (both are perfect cubes since 1³ = 1)

A. 8(1) = 8 = perfect cube
B. (1)(1) = 1 = perfect cube
C. (1)(1) + 27 = 28 = NOT a perfect cube
STOP TESTING VALUES. We've found an answer choice that is not necessarily a perfect cube

Answer:C
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Re: A perfect cube is an integer whose cube root is an integer. For exampl [#permalink] New post   02 Oct 2024, 16:53
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A perfect cube is an integer whose cube root is an integer. For exampl [#permalink]
02 Oct 2024, 16:53
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