SOLUTION: 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.

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Question 165478: 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.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


(A) n + k > 0

You didn't say the integers had to be positive.
so (-400)x(-1) = 400, yet (-400)+(-1)=-401 which is not
greater than zero.  So that is not true.  It would have
been if the problem had stated "positive integers".

(B) n ≠ k 

That is not true since 20x20 = 400

(C) Either n or k is a multiple of 10. 

That is not true since 16*25 = 400, yet neither
16 nor 25 is a multiple of 10. 

(D) If n is even, then k is odd. 

That is not true since 2*200 = 400.  
Both 2 and 200 are even.

(E) If n is odd, then k is even. 

That is true since the product of two odd numbers 
is odd. If both n and k were odd, their product 
would be odd, not 400.

So the only correct choice is (E).

Edwin