Orange08 wrote:

If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?

I. ab is even

II. ab > 0

III. c is even

A. I only

B. II only

C. I and II

D. I and III

E. I, II, and III

We are given that (a*b^2)/c is a positive even integer. Therefore, a*b^2 must be even. (If a*b^2 is odd, (a*b^2)/c can’t ever be even.)

Now recall that the product of an even number and any integer is even, so either a or b, or both, must be even. Thus we see that ab must be an even integer. However, ab DOES NOT have to be greater than zero, since a could be -2 and b could be 1. Finally, we see that c does not have to be even, since a could be -2, b could be 1, and c = -1. Thus, only Roman numeral I must be true.

Answer: A

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