2014 AMC 8

Complete problem set with solutions and individual problem pages

Problem 13 Medium

If n and m are integers and n^2+m^2 is even, which of the following is impossible?

  • A.

    n and m are even

  • B.

    n and m are odd

  • C.

    n+m is even

  • D.

    n+m is odd

  • E.

    none of these are impossible

Answer:D

Since n^2+m^2 is even, either both n^2 and m^2 are even, or they are both odd. Therefore, n and m are either both even or both odd, since the square of an even number is even and the square of an odd number is odd. As a result, n+m must be even. The answer, then, is n^2+m^2 \boxed{(\text{D})} is odd.

Related Problems
Problem 11 2014 AMC 8
Problem 12 2014 AMC 8
Problem 14 2014 AMC 8
Problem 15 2014 AMC 8
Think Academy Powered by ChatGPT