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

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

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New post Updated on: 24 Oct 2017, 22:18
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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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New post 15 Aug 2016, 09:10
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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.

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

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New post 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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New post 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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New post 30 May 2017, 02:06
1
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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New post 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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