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# If a and b are positive integers, is ³√ab an an integer?

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Intern
Joined: 20 Jul 2014
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GMAT 1: 710 Q46 V41
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If a and b are positive integers, is ³√ab an an integer?  [#permalink]

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Updated on: 24 Oct 2017, 22:18
2
17
00:00

Difficulty:

75% (hard)

Question Stats:

45% (01:22) correct 55% (01:30) wrong based on 486 sessions

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If a and b are positive integers, is $$\sqrt[3]{ab}$$ an an integer?

(1) $$\sqrt{a}$$ is an integer

(2) $$b=\sqrt{a}$$

I think this is from OG 2017 quant review, I found it in "New questions from OG 17 Review" file that was shared here by a member. So, I don't have the OA. If someone could please post the OA and solution, would be appreciated.

Thanks.

Originally posted by Neeraj91 on 15 Aug 2016, 08:53.
Last edited by Bunuel on 24 Oct 2017, 22:18, edited 2 times in total.
Edited the question and added the OA.
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Re: If a and b are positive integers, is ³√ab an an integer?  [#permalink]

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15 Aug 2016, 09:10
12
11
If a and b are positive integers, is $$\sqrt[3]{ab}$$ an an integer?

(1) $$\sqrt{a}$$ is an integer. No info about b. Not sufficient.

(2) $$b=\sqrt{a}$$ --> square: $$b^2 = a$$ --> substitute: $$\sqrt[3]{ab}=\sqrt[3]{b^2*b}=b=integer$$. Sufficient.

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Intern
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Re: If a and b are positive integers, is ³√ab an an integer?  [#permalink]

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15 Aug 2016, 09:57
Aah. I chose E, since i substituted the value for b in the original question, to get a^1/7. Didn't think of just squaring it! Thanks Bunnuel!
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Re: If a and b are positive integers, is ³√ab an an integer?  [#permalink]

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20 Aug 2016, 06:39
1
Neeraj91 wrote:
If a and b are positive integers, is $$\sqrt[3]{ab}$$ an an integer?

(1) $$\sqrt{a}$$ is an integer

(2) $$b=\sqrt{a}$$

I think this is from OG 2017 quant review, I found it in "New questions from OG 17 Review" file that was shared here by a member. So, I don't have the OA. If someone could please post the OA and solution, would be appreciated.

Thanks.

1. If a=4 and b=2 then Yes If a=4 and b=1 then No. Insufficient
2. Since both a and b are positive we can square both sides and get a=(b^2) Substitute to have $$\sqrt[3]{b^3}$$ Sufficient
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Re: If a and b are positive integers, is ³√ab an an integer?  [#permalink]

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30 May 2017, 02:06
2
I have a question.
No doubt that stat1 is not sufficient.
BUT - if I take stat2 and replace b by SQRT(a) in the original question, I get (a*SQRT(a))^(1/3) = (a^(3/2))^(1/3) = SQRT(a).
In this case, I will need both statements to have a definitive answer and thus, the answer is C.
How can I differentiate between my reasoning and Bunuel's?
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Re: If a and b are positive integers, is ³√ab an an integer?  [#permalink]

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30 May 2017, 02:16
5
Mike2805 wrote:
I have a question.
No doubt that stat1 is not sufficient.
BUT - if I take stat2 and replace b by SQRT(a) in the original question, I get (a*SQRT(a))^(1/3) = (a^(3/2))^(1/3) = SQRT(a).
In this case, I will need both statements to have a definitive answer and thus, the answer is C.
How can I differentiate between my reasoning and Bunuel's?

We are given that a and b are positive integers. (2) says that $$b=\sqrt{a}$$, thus $$b=\sqrt{a}=integer$$. So, when you get $$\sqrt{a}$$, you already know that it must be an integer.

Hope it's clear.
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Re: If a and b are positive integers, is ³√ab an an integer?  [#permalink]

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10 Jun 2018, 20:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a and b are positive integers, is ³√ab an an integer? &nbs [#permalink] 10 Jun 2018, 20:17
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