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Is s an odd integer?

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Is s an odd integer? [#permalink] New post 11 Feb 2012, 18:50
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A
B
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D
E

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  35% (medium)

Question Stats:

69% (01:39) correct 31% (00:25) wrong based on 16 sessions
Is s an odd integer?

(1) \(\sqrt{s}\) is not an even integer.
(2) \(s^2\) is not an even integer.

[Reveal] Spoiler:
How can the answer be E?

Considering statement 1 --> s is ODD i.e 9, 81 etc.. -----------------------------(Why this is not sufficient)

Considering Statement 2 --> S is ODD-------------------------------------------(Why this is not sufficient)?
[Reveal] Spoiler: OA

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Re: Is s an odd integer? [#permalink] New post 11 Feb 2012, 20:45
S can be 0.

Statement 1: S could be 10 and root 10 therefore is an irrational number. This means S is neither odd or even. S could also be 0.

Statement 2: S could be root 9. Also S could be 0.

!+2) Still could be 0 or a root number. If this is a GMAT question it will tell you if it's an integer or not. If it doesn't there are endless possibility that exist for numbers that match both of those statements.

Answer is E.
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Re: Is s an odd integer? [#permalink] New post 11 Feb 2012, 21:14
kys123 wrote:
S can be 0.

Statement 1: S could be 10 and root 10 therefore is an irrational number. This means S is neither odd or even. S could also be 0.

Statement 2: S could be root 9. Also S could be 0.

!+2) Still could be 0 or a root number. If this is a GMAT question it will tell you if it's an integer or not. If it doesn't there are endless possibility that exist for numbers that match both of those statements.

Answer is E.


Isn't 0 an even integer? I agree with the explanation otherwise since integers have to be whole numbers with no decimals. I can see the answer is E. But when you say S can be 0, isn't \(s^2=0\) which is an even integer?
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Re: Is s an odd integer? [#permalink] New post 11 Feb 2012, 22:48
omerrauf your right 0 is an even integer, so it's my mistake. Everything else holds the same, so answer still E.
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Re: Is s an odd integer? [#permalink] New post 12 Feb 2012, 00:13
Expert's post
Is s an odd integer?

(1) \(\sqrt{s}\) is not an even integer. Notice we are not told that \(\sqrt{s}=odd\), we are told that \(\sqrt{s}\neq{even}\), those ARE NOT the same. \(\sqrt{s}\) might be an odd integer, for example 1, 3, ... and in this case \(s\) will be an odd integer, but \(\sqrt{s}\) might as well be a fraction, for example 1/3, 7/5 and in this case \(s\) won't be an integer at all. \(\sqrt{s}\) also might be an irrational number, for example \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{{\frac{1}{3}}}\) ... and in this case \(s\) might or might not be an odd integer. Not sufficient.

(2) \(s^2\) is not an even integer. Notice again that we are not told that \(s^2=odd\), we are told that \(s^2\neq{even}\), those ARE NOT the same. The same here: \(s^2\) might be a square of an odd integer, for example 1, 9, ... and in this case \(s\) will be an odd integer, but \(s^2\) might as well not be a perfect square, for example 1/3, 17, and in this case \(s\) won't be an integer at all. Not sufficient.

(1)+(2) When combined still insufficient: if \(s=1\) then the answer will be YES but if \(s=\frac{1}{3}\) then the answer will be NO.

Answer: E.

Hope it's clear.
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Re: Is s an odd integer?   [#permalink] 12 Feb 2012, 00:13
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