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Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an

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Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink] New post 31 Aug 2010, 13:04
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Is n an integer?

(1) n^2 is an integer

(2) n^(1/2) is an integer
[Reveal] Spoiler: OA

Last edited by Bunuel on 05 Apr 2012, 02:48, edited 1 time in total.
Edited the question and added the OA
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Re: N [#permalink] New post 31 Aug 2010, 13:18
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vwjetty wrote:
Is n an integer?

(1) n^2 is an integer

(2) n^(1/2) is an integer

Please explain. Thanks.


Is n an integer?

(1) n^2 is an integer --> not sufficient, as if n^2=4 answer is YES, but if n^2=3 answer is NO.

(2) n^(1/2) is an integer --> \sqrt{n}=integer --> n=integer^2=integer. Sufficient.

Answer: B.
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Re: N [#permalink] New post 31 Aug 2010, 13:20
oh wow. i feel dumb now. for some reason i was thinking something else. tricky tricky. thx. +1 kudo's good sir.
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Re: OG 11th edition [#permalink] New post 12 Dec 2011, 12:31
Answer is indeed B.

stmt 1: says that n^2 is an integer. So n could be 4, which n^16 or n could be 5.477 and n^2 would be 30. This gives us two different options so insuff

stmt 2: says that sqrt n is an integer. that means n is the square of an (or integer x integer) which will always give you an integer. suff
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Re: OG 11th edition [#permalink] New post 23 Dec 2011, 00:16
Is n an integer?

(1) n^2 is an integer

(2) sqrt(n) is an integer

S1: If n^2 is an integer, is n an integer?

Is n rational or irrational?

If rational, then n can be expressed as p/q,
where p and q are non-zero integers.
Further, if n^2 = (p/q)^2 is an integer, n = p/q is an integer.

If irrational, then n could be the non-integer square root of an integer, whose square is an integer.

S2: An integer multiplied by another integer is an integer.
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Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink] New post 05 Apr 2012, 03:31
Thank you for the explanations. I know have an understanding of the question.
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Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an [#permalink] New post 20 Jun 2013, 14:07
Stament 1 : n^2=integer
n=+/- sqrt(integer)
=> Sqrt of integer may or may not be integer depending on whether chose integer is perfect square
or not. insufficient

Statement 2: sqrt (n) = integer
=> Squaring both sides
=> n= integer^2 = some other integer (as intg*intg=intg)
= sufficient

Ans B
Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an   [#permalink] 20 Jun 2013, 14:07
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