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# If (a^2)(b) is an integer which of the following must be an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 46280
If (a^2)(b) is an integer which of the following must be an integer? [#permalink]

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29 Aug 2017, 01:54
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Difficulty:

55% (hard)

Question Stats:

56% (00:52) correct 44% (01:37) wrong based on 86 sessions

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If (a^2)(b) is an integer which of the following must be an integer?

A. a
B. b
C. ab
D. b^2
E. None of the above

_________________
Director
Joined: 21 May 2013
Posts: 646
Re: If (a^2)(b) is an integer which of the following must be an integer? [#permalink]

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29 Aug 2017, 02:13
Bunuel wrote:
If (a^2)(b) is an integer which of the following must be an integer?

A. a
B. b
C. ab
D. b^2
E. None of the above

Answer E

Take a=1/2, b=4 for option A
For option B,C,D, take a=4, b =1/16
Director
Joined: 18 Aug 2016
Posts: 634
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
If (a^2)(b) is an integer which of the following must be an integer? [#permalink]

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29 Aug 2017, 02:46
1
Bunuel wrote:
If (a^2)(b) is an integer which of the following must be an integer?

A. a
B. b
C. ab
D. b^2
E. None of the above

consider a as $$\sqrt{2}$$ and b as 1/2

E
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Re: If (a^2)(b) is an integer which of the following must be an integer? [#permalink]

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01 Sep 2017, 12:08
Bunuel wrote:
If (a^2)(b) is an integer which of the following must be an integer?

A. a
B. b
C. ab
D. b^2
E. None of the above

Here is one example that allows us to check the answer choices: If we let a = ∛2 and b = ∛2, we see that (a^2)(b) = (∛2)^2 x ∛2 = ∛4 x ∛2 = ∛8 = 2 is an integer. However, none of a, b, ab, or b^2 will be an integer. So, the correct answer choice is E.

Answer: E
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Re: If (a^2)(b) is an integer which of the following must be an integer?   [#permalink] 01 Sep 2017, 12:08
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# If (a^2)(b) is an integer which of the following must be an integer?

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