If \(m, n,\) and \(p\) are integers, is \(m + n\) odd?

[VJesus12]

If \(m, n,\) and \(p\) are integers, is \(m + n\) odd?

(1) \(m = p^2 + 4p + 4\)
(2) \(n = p^2 + 2m + 1\)

Answer: C

Source: Manhattan GMAT