If positive integer $N=A-B,$ where $A$ is a positive integer and $B$ is a prime number, is $N$ odd?

If positive integer $N=A-B,$ where $A$ is a positive integer and $B$ is a prime number, is $N$ odd?

(1) $B$ and $X$ are the only prime factors of $A$, and $B-X=4$

(2) $A$ is divisible by 9 numbers in total, one of which is $B^2$

Answer: A

Source: e-GMAT

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