If m and n are integers such that mn=500, which of the following statements must be true?

a) m+n>0
b)either m or n is a multiple of 10
c)m+n is odd
d)if m is odd, then n is even
e)if n is odd, then m is even

^Found this on KaplinGMAT's youtube account.
https://www.youtube.com/watch?v=h4psEqWO ... re=related

skip to the 4 min mark to see the question and explanation.

The correct answer as explained in the video is d. But wouldn't e be fine as well? m and n should interchangeable, no? Am I just an idiot and missing something here?