Ankitaverma wrote: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.
Patrick's approach is fantastic.
Here's another (backup approach):
It may be useful to find the prime factorization of 400
400 = (2)(2)(2)(2)(5)(5)
Now let's examine answer choice E.
If n is ODD, there are only a few possible values for n.
n = 1, in which case k = 400 (in which case, k is EVEN)
n = 5, in which case k = 80 (in which case, k is EVEN)
n = 25, in which case k = 16 (in which case, k is EVEN)
n = -1, in which case k = -400 (in which case, k is EVEN)
n = -5, in which case k = -80 (in which case, k is EVEN)
n = -25, in which case k = -16 (in which case, k is EVEN)
So, for every possible ODD value of n,
k is always EVEN
So, answer choice
E must be true.
Cheers,
Brent
