If x is a positive integer, is x an integer? : GMAT Data Sufficiency (DS)
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If x is a positive integer, is x an integer?

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If x is a positive integer, is x an integer? [#permalink]

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If x is a positive integer, is \sqrt{x} an integer?

(1) \(\sqrt{4x}\) is an integer.
(2) \(\sqrt{3x}\) is not an integer.
[Reveal] Spoiler: OA

Last edited by ezinis on 29 Sep 2010, 08:39, edited 1 time in total.
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Re: Q 31, OG 12 DS [#permalink]

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New post 29 Sep 2010, 06:29
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ezinis wrote:
If x is a positive integer, is \sqrt{x} an integer?
(1) \(\sqrt{4x}\) is an integer4.
(2) \(\sqrt{3x}\) is an integer.

I am not satisfied with the official explanation. Please give yours, thanks.


I think (2) should be \(\sqrt{3x}\) is NOT an integer.

If \(x=integer\), is \(\sqrt{x}=integer\)?

(1) \(\sqrt{4x}\) is an integer --> \(2\sqrt{x}=integer\) --> \(2\sqrt{x}\) to be an integer \(\sqrt{x}\) must be an integer or integer/2, but as \(x\) is an integer, then \(\sqrt{x}\) can not be integer/2, hence \(\sqrt{x}\) is an integer. Sufficient.

(2)\(\sqrt{3x}\) is not an integer --> if \(x=9\), condition \(\sqrt{3x}=\sqrt{27}\) is not an integer satisfied and \(\sqrt{x}=3\) IS an integer, BUT if \(x=2\), condition \(\sqrt{3x}=\sqrt{6}\) is not an integer satisfied and \(\sqrt{x}=\sqrt{2}\) IS NOT an integer. Two different answers. Not sufficient.

Answer: A.
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Re: Q 31, OG 12 DS [#permalink]

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New post 29 Sep 2010, 07:10
ezinis wrote:
If x is a positive integer, is \sqrt{x} an integer?
(1) \sqrt{4x} is an integer4.
(2) \sqrt{3x} is an integer.

I am not satisfied with the official explanation. Please give yours, thanks.


(1) \(\sqrt{4x} = 2 * \sqrt{x}\)
If this is an integer, then \(\sqrt{x}\) has to be an integer

(2) \(\sqrt{3x} = \sqrt{3} * \sqrt{x}\)
For this to be an integer, \(\sqrt{x}\) must be of the form \(\sqrt{3} * Integer\)
So \(\sqrt{x}\) is not an integer

I am not sure if the question is correct as (1) and (2) are contradicting. Is it supposed to say \(\sqrt{3x}\) is not an integer ?
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Re: If x is a positive integer, is x an integer? [#permalink]

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Re: If x is a positive integer, is x an integer? [#permalink]

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New post 27 Sep 2015, 07:36
Bunuel wrote:
ezinis wrote:
If x is a positive integer, is \sqrt{x} an integer?
(1) \(\sqrt{4x}\) is an integer4.
(2) \(\sqrt{3x}\) is an integer.

I am not satisfied with the official explanation. Please give yours, thanks.


I think (2) should be \(\sqrt{3x}\) is NOT an integer.

If \(x=integer\), is \(\sqrt{x}=integer\)?

(1) \(\sqrt{4x}\) is an integer --> \(2\sqrt{x}=integer\) --> \(2\sqrt{x}\) to be an integer \(\sqrt{x}\) must be an integer or integer/2, but as \(x\) is an integer, then \(\sqrt{x}\) can not be integer/2, hence \(\sqrt{x}\) is an integer. Sufficient.

(2)\(\sqrt{3x}\) is not an integer --> if \(x=9\), condition \(\sqrt{3x}=\sqrt{27}\) is not an integer satisfied and \(\sqrt{x}=3\) IS an integer, BUT if \(x=2\), condition \(\sqrt{3x}=\sqrt{6}\) is not an integer satisfied and \(\sqrt{x}=\sqrt{2}\) IS NOT an integer. Two different answers. Not sufficient.

Answer: A.


i think it does not matter whether statement 2 is integer or not, as in both the cases we are getting different solution. and answer will be one in both the cases.
Re: If x is a positive integer, is x an integer?   [#permalink] 27 Sep 2015, 07:36
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