Is n^2 an even integer?

Question

(1) n/2 is an odd integer.

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

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Bunuel · Accepted Answer

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.

Answer: A.

Hope it's clear.

avohden · Answer

Official Explanation

Answer: A   - 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.

stonecold · Answer

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

Tmoni26 · Answer

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

stonecold · Answer

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

Hoozan · Answer

Bunuel  Aren't both the statements contradicting each other? Could you provide a value of "n" that satisfies (1) and (2)?

Bunuel · Answer

You are right. The statements contradict each other. From (1) n = 2*odd and if we plug this into (n^2)/2, we'd get (4*odd^2)/2 = 2*odd^2, which is an even number. So, the question is flawed.

Is n^2 an even integer?

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Is n^2 an even integer?

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