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

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

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New post 17 May 2016, 02:44
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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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Re: A perfect cube is an integer whose cube root is an integer. For exampl  [#permalink]

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New post 16 Jun 2016, 11:28
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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


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

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New post 17 May 2016, 09:25
A. 8p
= 2^3 * p
Perfect cube
B. pq will be a perfect cube since its a product of 2 perfect cubes
C. pq + 27
Not necessarily a perfect cube
if p = 8 and q= 27
pq+ 27 = 8*27 + 27 = 27(8+1)
=3^3 * 3^2
=3^5
Not a perfect cube
D. -p
Perfect cube
E. (p - q)^6
Difference of p and q will be an integer and when its raised to 6th power , it will be 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]

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New post 16 Jun 2016, 22:45
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

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

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New post 17 Jun 2016, 00:47
1
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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New post 20 Jun 2017, 18:06
1
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


Let’s test our answer choices.

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.

Answer: C
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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 &nbs [#permalink] 14 Jul 2018, 00:38
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