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# Is n^2 an even integer?

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Is n^2 an even integer? [#permalink]

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02 Nov 2013, 00:56
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Is n^2 an even integer?

(1) n/2 is an odd integer.

(2) (n^2)/2 is not an even integer.

GH-06.12.13 | OE to follow
[Reveal] Spoiler: OA
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Re: Is n^2 an even integer? [#permalink]

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02 Nov 2013, 04:56
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Expert's post
Is n^2 an even integer?

Notice that we are NOT told that n is an integer.

(1) n/2 is an odd integer --> $$\frac{n}{2}=odd$$ --> $$n=2*odd=even$$ --> n^2=even^2=even. Sufficient.

(2) (n^2)/2 is not an even integer --> if n=1, then the answer is NO but if $$n=\sqrt{2}$$, then the answer is YES. Not sufficient.

Hope it's clear.
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Re: Is n^2 an even integer? [#permalink]

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05 Nov 2013, 22:42
Official Explanation

- Statement (1) is sufficient. If n/2 is an odd integer, we can find n by multiplying both sides by 2. n is 2 times an odd integer, which is always an even. If n is an even, then n^2 is an even -- an even times an even is always an even.

Statement (2) is not sufficient. Note that "not an even integer" does not mean "an odd integer." It could also refer to any non-integer, such as 4.5. If n = 3, then n^2 = 9 and n^2/2 = 4.5, which is not an even integer. In that case, the answer is "no." However, if n^2 = 2, then n^2/2 = 1, which is not an even integer. But in this case, n^2 is even, so the answer is "yes." Choice (A) is correct.
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Re: Is n^2 an even integer? [#permalink]

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22 Aug 2016, 02:59
Excellent Question
Here we don't know if N is an integer or not
Statement 1 => n/2=odd => n must be an integer and that too even as n=odd*2
suff
Staement 2 => n^2/2≠even =z(say)
Now for z=>
case 1 => let it be odd => n^2 will be even=> YES
case 2 => let it be 4.5 => n^2/2=4.5 => n^2 is odd => NO
case 3 => let it be 3434850948540.324334314343 (anything) clearly here n wont be an integer forget it being odd/even=> NO
hence insuff
Smash that A
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Re: Is n^2 an even integer? [#permalink]

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23 Aug 2016, 14:37
I do not agree with A being the answer.
Please correct me if i am wrong

If N = 1/2, then for statement 1

1/2 /2 = 1 which is an odd integer which makes then N^2 is not even
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Re: Is n^2 an even integer? [#permalink]

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23 Aug 2016, 14:42
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Tmoni26 wrote:
I do not agree with A being the answer.
Please correct me if i am wrong

If N = 1/2, then for statement 1

1/2 /2 = 1 which is an odd integer which makes then N^2 is not even

Hi mate
The mistake you made here is as follows => 1/2 /2 = 1/4 not 1
If x/2=odd integer => x=2*odd now as we know that the product of two integers is always an integer => x is an integer and that too even as 2 is its factor.
Smash that A
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Re: Is n^2 an even integer? [#permalink]

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24 Aug 2016, 02:01
stonecold,

Thanks a lot....
Re: Is n^2 an even integer?   [#permalink] 24 Aug 2016, 02:01
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