Problem Solving

If m & n are positive integers, is n even ?

1) m(m +2) + 1 = mn
2) m(m + n) is odd

1. if m is odd, then m(m+2)+1 is even, then m(m+2)+1=nm must be even---> n is even
if m is even, then m(m+2)+1 is odd, and mn must be even. There is a contradiction, then m must be odd and n must be even.
sufficient

2. m(m+n) is odd, then m is odd, m+n is even---> n is even
sufficient

The correct answer is D!