Answer: C

Use even and odd identities to evaluate each expression:
(A) 2(odd) = even
(B) 2(odd)^2 = 2(odd) = even
(C) n^2 + 2n = (odd)^2 + 2(odd) = odd + even = odd
(D) n^2 + 3n = (odd)^2 + 3(odd) = odd + odd = even
(E) n^2 + 2n + 3 = (odd)^2 + 2(odd) + odd = odd + even + odd = even
(C) is the only odd answer, so it is correct.