This question also has some further discussion that can make it more valuable. Can anyone think of a restriction that we could put on x and/or y that would make statement 2 sufficient?

yup - if they do have same sign , in that case condition x = -y is not possible.

Yeah, great responses - I was thinking in my own head of "for positive numbers x and y..." which also precludes x = -y. If both have to be positive, then only x - y could equal 0 and since we know that one of them has to then we've got it.

I love that style of thinking - I was just at lunch with a friend who is studying for the GMAT and was telling her the same thing...if you start to push the parameters of these questions yourself ("how can I make this harder?" or "How can I change the answer with just one word?") you become a real master of the format.

sdas0112 wrote:How about x+y != 0?

I don't know if any factorial can be equal to 0 unless its 0! and I'm not sure if 0! exists (I'm not a mathematician). In any case, if 0! does exist, then x+y must equal to 0. x+y=0 only tells us x and y are on the opposite side of the number line, insufficient to answer the value of x-y.

Nevermind. Didn't see Brian's post before. But the restriction of x+y!=0 is brilliant!

Brian, a basic question: i thought it should be D as in B, I divided both sides by (x+y) and hence x-y=0.I think can be done irrespective of whether x+y is positive of negative.
Thanks,

Bryan: I chose D and hence a related basic question. cant we divide both sides of B by (x+y). wouldn't this be suffice irrespective of whether (x+y) is negative or positive.

Hey, great question guys, about dividing both sides by x + y in statement 2.

Just as a refresher since we're on page 2, statement 2 was:

x^2 - y^2 = 0

Here's why you can't do that - we know, via factoring that:

(x + y)(x - y) = 0

which means that AT LEAST ONE of those two expressions MUST BE 0.

Well, we can't divide by 0 (it's undefined) and so we can't divide by one of them to just assume that the other is 0, because we might well be dividing by the one that is, itself, 0.

For example, say that x = 4 and y = -4, we'd have:

(4 + -4)(4 - (-4)) = 0

0 * 8 = 0

If you were to divide both sides by x + y without accounting for it to potentially be 0, you'd have:

8 = 0

And that's clearly way, way off.

So the catch is that we can't divide by a variable unless we know it's not 0. You'll find that a great many GMAT problems include that caveat (If x does-not-equal-0...) to allow for algebra, but if they don't, particularly in a Data Sufficiency context in which that one unique number changes everything, you have to account for it.