# 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**CORRECT ANSWER*m*is odd, then*p*is odd. - (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)