If \(a, b\) and \(n\) are positive integers such that \(n=3a-b^3,\) is \(n^2+3\) divisible by \(2?\)

[Vincen]

If \(a, b\) and \(n\) are positive integers such that \(n=3a-b^3,\) is \(n^2+3\) divisible by \(2?\)

(1) \(a^2 -4b^3-5=0\)

(2) \(3b^3 -a^2 +6=0\)

Answer: B

Source: e-GMAT