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

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Expert Post
Math Expert
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V
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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New post 29 Aug 2017, 01:54
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A
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C
D
E

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  55% (hard)

Question Stats:

52% (00:44) correct 48% (01:38) wrong based on 71 sessions

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

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

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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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New post 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

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Director
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Joined: 18 Aug 2016
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If (a^2)(b) is an integer which of the following must be an integer? [#permalink]

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New post 29 Aug 2017, 02:46
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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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Kudos [?]: 140 [1], given: 123

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Status: Head GMAT Instructor
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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]

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New post 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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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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