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Math Help - If x and y are both odd numbers, which of the following numbers must be an even numb

  1. #1
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    If x and y are both odd numbers, which of the following numbers must be an even numb

    If x and y are both odd numbers, which of the following numbers must be an even number?
    xy
    xy + 2
    x + y
    2x + y
    x + y + 1
    None of the above
    I don't know
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  2. #2
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    Re: If x and y are both odd numbers, which of the following numbers must be an even n

    Try an example. In this particular problem, one example is sufficient because for each expression f(x,y) (i.e., f(x,y) = xy, f(x,y) = xy + 2, etc.), f(x,y) is either always even or always odd under the assumption that x and y are odd.

    However, you should also be able to prove the correct answer. Since x is odd, x can be represented as 2x' + 1 for some integer x'. For example, 7 = 2 * 3 + 1 and -7 = 2 * (-4) + 1. Similarly, y = 2y' + 1 for some integer y'. What do you get when you multiply x and y and simplify the result?
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  3. #3
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    Re: If x and y are both odd numbers, which of the following numbers must be an even n

    Any odd number can be written in the form 2n+1 where n is a an integer so let first number=2m+1 2nd number =2n+1 and you will be able to answer the questions.
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