Is the product of two integers \(A\) and \(B\) odd?

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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