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# Is s an odd integer?

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Is s an odd integer? [#permalink]

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11 Feb 2012, 19:50
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Difficulty:

35% (medium)

Question Stats:

65% (00:38) correct 35% (00:39) wrong based on 40 sessions

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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]

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11 Feb 2012, 21:45
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.

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Re: Is s an odd integer? [#permalink]

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11 Feb 2012, 22:14
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.

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]

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11 Feb 2012, 23:48
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]

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12 Feb 2012, 01:13
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.

Hope it's clear.
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Re: Is s an odd integer?   [#permalink] 12 Feb 2012, 01:13
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