$$Is\ \ x^2\ y^2>0\ ?$$
$$\left(1\right)\ x^2-y^2>\left(x-y\right)$$
$$\left(2\right)\ x^2-y^2<\left(x+y\right)$$
The OA is E.
I don't have it clear. Please, can any expert explian this DS question? Thanks.
Is x^2-y^2>0?
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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
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