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# Is N an integer ? (1) N^2 is an integer. (2) SQRT(N) is an

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Director
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Is N an integer ? (1) N^2 is an integer. (2) SQRT(N) is an [#permalink]

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12 Dec 2003, 18:38
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Is N an integer ?
(1) N^2 is an integer.
(2) SQRT(N) is an integer.

Can any one give me an number whose square is an integer?
Manager
Joined: 12 Oct 2003
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12 Dec 2003, 20:25
vote for B as well.

Can any one give me an number whose square is an integer?

SQRT(3)
Director
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12 Dec 2003, 20:44
why is it not D. i feel like a cretin
Manager
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12 Dec 2003, 20:58
2 is an integer, but sqrt(2) is not ...

I had the same idea as well, but I am trying to train myself to plug in atleast these numbers for any DS question : -2, -1, 0, 1, 2 and sqrt(2) ..
Director
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12 Dec 2003, 21:21
bluefox420 wrote:
2 is an integer, but sqrt(2) is not ...

I had the same idea as well, but I am trying to train myself to plug in atleast these numbers for any DS question : -2, -1, 0, 1, 2 and sqrt(2) ..

gosh..! it 's gotta be the friday.

thanks, bluefox.
SVP
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12 Dec 2003, 21:35
I tried to explain that A also is sufficient. ( pitts20042006 corrected me - so I am modifying my post )
Choice A - if square N is integer then sqrt of N may or may not be integer.
Choice B - if sqrt of N is integer then N has to be integer. If we consider 2 or 3 as integers(n=2 or N=3) then their sqrt is not an integer. That does not mean that the sqrt(N) if it is integer then N is not integer. B would have been wrong if the question were is sqrt(N) integer ? given N as integer.
For example sqrt(4) = 2 which an integer meaning N=4 which is definitely integer.

Last edited by anandnk on 12 Dec 2003, 21:47, edited 1 time in total.
Manager
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12 Dec 2003, 21:40
Dear anand,

A is NOT sufficient.

A says N^2 is an integer.

take, N^2 = 5 --> which is definitely an integer

take SQRT of both side

thus we have N = SQRT(5)

Now is N an integer here?? NO
So A is not sufficient.
CEO
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12 Dec 2003, 23:59
Is N an integer ?
(1) N^2 is an integer.
(2) SQRT(N) is an integer.

Can any one give me an number whose square is an integer?

any integer if squared will give you an integer.

(1) clearly insufficient
(2) sufficient.. its can only be a perfect square.

B
Director
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13 Dec 2003, 07:29
Thanks Guys.

After posting the question, I relaised what was the mistake I made.

13 Dec 2003, 07:29
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