Math Multiple Choice
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.
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)