A, B, and C are positive integers. Is their product an even number ?
I. A is an even number.
II. The product of A and B is an even number and that of A and C is also an even number.

Give answer (A) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

Give answer (B) if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

Give answer (C) if the data either in statement I alone or in statement II alone are sufficient to answer the question.

Give answer (D) if the data even in both statements I and II together are not sufficient to answer the question

Give answer (E) if the data even in both statement I and II together are necessary to answer the question.