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Bunuel
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scrantonstrangler
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Bunuel
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chandnik3
Bunuel can you please explain why ans in E and not C?

Of course. However, just a small correction – the correct answer is A, not E.

Is an integer n even?

Firstly, please note that the question explicitly states that n is an integer: Is an integer n...

(1) n(n + 2) = even

In order for the product of two integers to be even, at least one of them must be even. If n is even, then we get a definitive YES. Likewise, if n + 2 is even, n must be even, so we again have a YES. So, we can conclude that n must be even for n(n + 2) to be even. Sufficient.

Alternatively, we can reason this way: if n were odd, then n(n + 2) would be the product of two odd numbers, which results in an odd number, not even. Therefore, n must be even. Sufficient.

(2) n(n + 3) = even

Similarly, in this case either n is even, or n + 3 is even. However, if n + 3 is even, then n must be odd. Therefore, n can be either even or odd. Not sufficient.

Answer: A.
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