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

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Re: A perfect cube is an integer whose cube root is an integer. For exampl [#permalink]
Bunuel 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

p = a^3
q = b^3
where a and b are integers

A. 8p = 8a^3 = (2a)^3 - Perfect cube
B. pq = a^3 * b^3 = (ab)^3 - Perfect cube
C. pq + 27 = (ab)^3 + 27 - Not necessarily perfect cube
D. -p = -a^3 - Perfect cube
E. (p - q)^6 = [(p-q)^2]^3 - Perfect cube

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Re: A perfect cube is an integer whose cube root is an integer. For exampl [#permalink]
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Bunuel 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

A. since p is a perfect cube and 8 is a perfect cube, 8p will be a perfect cube. reject.
B. since p is a perfect cube and q is a perfect cube, pq will be a perfect cube. reject.
C. Hold.
D. since p is a perfect cube, -p will also be a perfect cube. reject.
E. (p-q)^6, is a perfect cube, so reject.

By elimination C is the answer.

Check say p = 1, q=8, then 8+27 = 35 --> not a perfect cube.
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Re: A perfect cube is an integer whose cube root is an integer. For exampl [#permalink]
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Bunuel 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

A) 8p

If p = 8, then 8p = 64, which is a perfect cube.

B) If p = 8 and q = 8, then pq = 64, which is a perfect cube.

C) If pq = 8, then pq + 27 = 8 + 27 = 35, which is not a perfect cube.

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Re: A perfect cube is an integer whose cube root is an integer. For exampl [#permalink]
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Re: A perfect cube is an integer whose cube root is an integer. For exampl [#permalink]
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