Problem Solving

If n and k are integers whose product is 400, which of the following statements must be true?

(A) n + k > 0
(B) n≠k
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E) If n is odd, then k is even.

Ans is E

But I am not sure how to test different values to make sure what really holds true. I got confused, any ideas?

I don't see how D and E are different. k and n could be either or.

I think the answer is E

because the factors of 400 are 2^4 5^2.

So if n is odd
N = 5 or n = 25

Therefore k has to be even multiple of 2

In the case of D

N could be odd and K could still be even
Ex: n = 1 , k = 400

Comments Welcome

Sorry for the typo in the previous post

in choice D, If n is even then k cannot be odd

ex: n = 2 then k = 200

llewellyn27 wrote:Sorry for the typo in the previous post

in choice D, If n is even then k cannot be odd

ex: n = 2 then k = 200

n could be 5 and k = 80, this is wicked

400 is an even number. To get an even product, we can multiply either:

(1) an odd by an even; or

(2) an even by an even.

So, if one of the numbers is even, the other could be even or odd.

However, if one of the numbers is odd, the other MUST be even: choose (E).