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Positive/Negative: If x, y, and z are positive integers, is

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Positive/Negative: If x, y, and z are positive integers, is Post Sun Apr 13, 2008 3:16 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If x, y, and z are positive integers, is x-y odd ?

    (1) x = z^2
    (2) y = (z - 1)^2

    Thanks.



    Last edited by II on Mon May 05, 2008 1:41 am; edited 1 time in total

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    Post Sun Apr 13, 2008 5:14 am
    II wrote:
    If x, y, and z are positive integeres, is x-y odd ?

    (1) x = z^2
    (2) y = (z - 1)^2

    Thanks.
    Interesting question II.

    This is the very essence of Data Sufficiency. Within 10-20 seconds you should be able to eliminte A / B and D as possible answers.

    Why?

    Since the relationship being tested requires us to look for the outcome of X - Y, it becomes obvious that Statement 1 and Statement 2 by themselves are not going to pull it off (they only have X and Z, and Y and Z respectively.

    If on test-da your time is running out (or even if it is not), something like this is really going to help you.

    Now to decide between C and E:

    Together:
    X - Y = Z^2 - (Z-1)^2.................(This is the classic difference of squares rule)

    Therfore, X- Y = ( Z - (Z-1)) ( Z+(Z+1))
    which is then = (Z - Z +1) (2Z+1)
    which simplifies as = (1) (2Z +1) = 2Z +1

    The odd number kingdom is defined as 2(integer) + 1 OR 2(Integer) - 1.

    Since Z is an integer, 2Z+1 MUST be odd. This answers the question with an ALWAYS YES, and hence sufficiency.

    C is the answer.

    _________________
    For love, not money.

    Post Sun Apr 13, 2008 8:19 am
    I will go with C, too.

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