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# Is s an odd integer?

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Is s an odd integer? [#permalink]

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19 Dec 2010, 19:45
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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.

When not mentioned do we consider irrational numbers as well? Please clarify. Thanks !
[Reveal] Spoiler: OA

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Re: ODD vs EVEN Trick Question? [#permalink]

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20 Dec 2010, 00:38
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MasterGMAT12 wrote:

Is s an odd integer?
(1) sqrt(s) is not an even integer.
(2) s^2 is not an even integer.

GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers. So, if there is no restriction then you must consider irrational numbers as well.

Note that only integers can be even or odd. So, for example there is no difference in asking "is s an odd integer" and "is s odd".

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Back to the original question:

Is s an odd integer?

(1) sqrt(s) is not an even integer --> $$\sqrt{s}$$ 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. $$s$$ 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 --> 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 if $$s=\frac{1}{3}$$ then the answer will be NO.

Hope it's clear.
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Re: ODD vs EVEN Trick Question? [#permalink]

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02 Jul 2012, 02:44
Bunuel wrote:
MasterGMAT12 wrote:

Is s an odd integer?
(1) sqrt(s) is not an even integer.
(2) s^2 is not an even integer.

GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers. So, if there is no restriction then you must consider irrational numbers as well.

Note that only integers can be even or odd. So, for example there is no difference in asking "is s an odd integer" and "is s odd".

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Back to the original question:

Is s an odd integer?

(1) sqrt(s) is not an even integer --> $$\sqrt{s}$$ 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. $$s$$ 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 --> 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 if $$s=\frac{1}{3}$$ then the answer will be NO.

Hope it's clear.

Dear Bunuel

Can you please elaborate a bit further... not clear with the explanation.
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Re: ODD vs EVEN Trick Question? [#permalink]

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02 Jul 2012, 02:47
narangvaibhav wrote:
Can you please elaborate a bit further... not clear with the explanation.

Can you please tell what exactly didn't you understand?
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Re: ODD vs EVEN Trick Question? [#permalink]

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03 Jul 2012, 07:47
Bunuel wrote:
narangvaibhav wrote:
Can you please elaborate a bit further... not clear with the explanation.

Can you please tell what exactly didn't you understand?

Couldn't get why option1 and 2 together are not sufficient

Posted from my mobile device
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Re: ODD vs EVEN Trick Question? [#permalink]

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03 Jul 2012, 07:50
narangvaibhav wrote:
Bunuel wrote:
narangvaibhav wrote:
Can you please elaborate a bit further... not clear with the explanation.

Can you please tell what exactly didn't you understand?

Couldn't get why option1 and 2 together are not sufficient

Posted from my mobile device

It's explained in the solution.

Consider two cases: if $$s=1$$ then the answer will be YES but if if $$s=\frac{1}{3}$$ then the answer will be NO.
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Re: Is s an odd integer? [#permalink]

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29 Jul 2014, 20:58
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Re: Is s an odd integer? [#permalink]

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27 Sep 2015, 09:14
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Re: Is s an odd integer? [#permalink]

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23 Dec 2016, 09:38
Hello from the GMAT Club BumpBot!

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Re: Is s an odd integer?   [#permalink] 23 Dec 2016, 09:38
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