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Re: Is n^2 an even integer? [#permalink]
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05 Nov 2013, 22:42
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 noninteger, 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.
