GMATPrep number properties

[lilu]

Please let me know how to solve this question.
I'll post the OA after a few replies.

[kanha81]

Please let me know how to solve this question.
I'll post the OA after a few replies.

e=even, o=odd

(i) n + m = odd
a) n=e, m=o: lhs=e+o = o = o = rhs
b) n=o, m=e: lhs=o+e= o = o = rhs

insuff

(ii) n + m = (n^2) + 5
n=e: rhs=(n^2) + 5 = o => lhs=e+o = o. true
n=o: rhs=(n^2) + 5 = e => lhs=o+o = e. true;

suff. hence, [spoiler][/spoiler]

[lilu]

Thank you, kanha!!
The OA is B