Question

If A and B are positive integers, is the product AB even?
(1) The sum A $+$ B is odd.
(2) A is even.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

Answer: (B), (D)

The correct options are
B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
D Each statement alone is sufficient.

The sum of odd and even is always odd whereas the product of odd and even or the product of even and even is always even. Thus, each statement alone is sufficient to answer the question.