If n and k are integers whose product is 400, which of the

Note that the question is: "whcih of the following must be true?"

Given: \(nk=400\)

For the product of two integers to be even at least one integer must be even.

D says: If n is even, then k is odd --> not necessarily true, n can be even and k be even too --> \(nk=20*20=400\);
E says: If n is odd, then k is even --> this must be true, if one of the factors is odd (n) the second one (k) must be even for their product to be even.

Other choices:

A. n+k>0 --> not necessarily true: \(nk=(-20)*(-20)=400\);
B. n does not equal k --> not necessarily true: \(nk=20*20=400\);
C. Either n or k is a multiple of 10 --> not necessarily true: \(nk=16*25=400\).

Answer: E.

Hope it's clear.