SOLUTION: If m + n is an odd number when m and n are positive integers, which expression always represents an even number? (A) m - n (B) m^2 + n^2 (C) (m + n )^2 (D) m^2 - n^2 (E)

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: If m + n is an odd number when m and n are positive integers, which expression always represents an even number? (A) m - n (B) m^2 + n^2 (C) (m + n )^2 (D) m^2 - n^2 (E)      Log On


   

Question 307083: If m + n is an odd number when m and n are positive integers, which expression always represents an even number?
(A) m - n
(B) m^2 + n^2
(C) (m + n )^2
(D) m^2 - n^2
(E) (mn)^2
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
If m+n is an odd number, then one of the numbers must be even and the other must be odd. Now, if you take the product of this even and odd number, you ALWAYS get an even number! The square of this even number will always be an even number, so the correct answer is E. All of the other choices will always give you an odd number.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus