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If m and p are positive integers and (m + p) x m is even, which of the following must be true?

• (A) If m  is odd, then p  is odd.    CORRECT ANSWER
• (B) If m  is odd, then p  is even.
• (C) If m  is even, then p  is even.
• (D) If m  is even, then p  is odd.
• (E) m  must be even.

Explanation:

If m is even, then the expression (m + p) x m will always be even and it cannot be determined whether p is even or odd. This eliminates choices (C) and (D). If m is odd, then (m + p) x m will be even only when m + p is even and m + p will be even only when p is odd. The correct answer is (A) since the truth of statement (A) also eliminates choices (B) and (E).

(from the October 18, 1997 test)