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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: 41892

Kudos [?]: 128992 [0], given: 12185

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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Question Stats:

52% (00:44) correct 48% (01:38) wrong based on 71 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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128992 [0], given: 12185

Director
Joined: 21 May 2013
Posts: 535

Kudos [?]: 71 [0], given: 487

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

Take a=1/2, b=4 for option A
For option B,C,D, take a=4, b =1/16

Kudos [?]: 71 [0], given: 487

Director
Joined: 18 Aug 2016
Posts: 512

Kudos [?]: 140 [1], given: 123

GMAT 1: 630 Q47 V29
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
KUDOS
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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Luckisnoexcuse

Kudos [?]: 140 [1], given: 123

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 837 [0], given: 5

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.

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Jeffery Miller

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Kudos [?]: 837 [0], given: 5

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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