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If x and y are positive integers . . .

This topic has 1 expert reply and 0 member replies

If x and y are positive integers . . .

Post Mon Nov 06, 2017 6:49 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If x and y are positive integers, what is the remainder when y^x is divided by 2?

    (1) y^2 is an odd integer.
    (2) xy is an even integer.

    The OA is A.

    Why is A the correct? I don't know how to prove that statement 1 is sufficient.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Mon Nov 06, 2017 12:34 pm
    Hi M7MBA,

    We're told that X and Y are positive integers. We're asked for the remainder when Y^X is divided by 2.

    This question can be solved by TESTing VALUES and/or by using Number Properties. It's worth noting that when dividing an integer by 2, the only possible remainders are 0 and 1.

    1) Y^2 is an ODD integer.

    Fact 1 tells us that Y^2 is an ODD integer - and we already know that X and Y are both POSITIVE INTEGERS.

    (Even)^2 = Even
    (Odd)^2 = Odd

    This means that Y MUST be ODD. By extension, an ODD number raised to an INTEGER power will ALWAYS be ODD. Fact 1 essentially tells us that Y^X will ALWAYS be an ODD number. Dividing ANY odd number by 2 will ALWAYS give us a remainder of 1.
    Fact 1 is SUFFICIENT

    2) XY is an EVEN integer.

    The information in Fact 2 means that one - or both - of the two integers are EVEN.

    IF....
    X=2, Y=1, then Y^X = 1 and the answer to the question is 1.
    X=1, Y=2, then Y^X = 2 and the answer to the question is 0.
    Fact 2 is INSUFFICIENT

    Final Answer: A

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: M7MBA

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