Error Check--More than 1 possible answer??

Here is the problem:

If x and y are positive integers, and (xy + x) is even, which of the following must be true?

A. If x is odd, then y is odd.

B. If x is odd, then y is even.

C. If x is even, then y is odd.

D. If x is even, then y is even.

E. x cannot be odd.

The answer given is A, but isn't there more than 1 answer for this problem??

Re: Error Check--More than 1 possible answer??

Hi

Let's check each of the conditions.

A)-If x is odd and xy+x is even, that means that x*(y+1) is even. For it to be even, at least one, x or y+1, must be even, and because it isn't x, it must be y+1. And, if y+1 is even, then y is certainly odd.

B)-This is not true if x=3 and y=1. 3*1+3=6 is even and the statement "If x is odd, then y is even" isn't true. And if it isn't true for one value of x and y, then the statement is false.

C)-This one is not true for x=2 and y=4.

D)-This one isn't true for x=2 and y=3.

E)-This one isn't true for x=1 and y=3.

So, we have that only A is **always** correct.

If you didn't understand some part of my post, feel free to ask.