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Math Help - Error Check--More than 1 possible answer??

  1. #1
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    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??
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  2. #2
    Member anonimnystefy's Avatar
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    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.
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