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Is x^2-y^2>0?

This topic has 1 expert reply and 0 member replies

Is x^2-y^2>0?

Post Sat Nov 04, 2017 7:14 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    $$Is\ \ x^2\ y^2>0\ ?$$

    $$\left(1\right)\ x^2-y^2>\left(x-y\right)$$
    $$\left(2\right)\ x^2-y^2<\left(x+y\right)$$

    The OA is E.

    I don't have it clear. Please, can any expert explian this DS question? Thanks.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Thu Nov 09, 2017 11:38 am
    Hi swerve,

    The 'title' of this post doesn't match the question that's in it, but I'm going to assume that we're meant to answer the question "Is X^2 times Y^2 greater than 0?" This is a YES/ NO question. We can answer it by TESTing VALUES. It's worth noting that since a 'squared' term can only be 0 or positive, the ONLY time that (X^2)(Y^2) would not be greater than 0 is if one (or both) of the variables equaled 0.

    Before we get to work, it's worth noting that BOTH Facts involve the same 'component' (X^2 - Y^2). In these situations, it can sometimes be useful to think about both Facts at the same time (so that you can find sets of numbers that 'fit' both Facts.

    1) X^2 - Y^2 > (X - Y)

    IF....
    X=0 and Y= 1/2, then the answer to the question is NO
    X=1 and Y= 1/2, then the answer to the question is YES
    Fact 1 is INSUFFICIENT

    2) X^2 - Y^2 < (X + Y)

    IF...
    X=0 and Y= 1/2, then the answer to the question is NO
    X=1 and Y= 1/2, then the answer to the question is YES
    Fact 2 is INSUFFICIENT

    Combined, we already have two pairs of values that produce different answers to the given question.
    Combined, INSUFFICIENT

    Final Answer: E

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

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