Is the product of two integers \(A\) and \(B\) odd?
(1) \(A\) is the number of factors of \(N,\) where \(N\) is a perfect square and \(B=A^3-1.\)
(2) \(A\) is a product of two consecutive prime numbers and when \(B+3^{11}\) is added to \(A,\) the sum is an odd number.
Answer: A
Source: e-GMAT