A student of mine just emailed me about this question, so I thought I'd post my reply. First, the question so that you can take a look:
What is the value of x - y?
(1) x - y = y - x
(2) x - y = x^2 - y^2
Looking at statement 1, we see a great example of a common Data Sufficiency Algebra principle - the GMAT usually gives you information in an inconvenient form, and you can manipulate the algebra to make it useful. If we add y to both sides and add x to both sides, we get:
2x = 2y
x = y
So, x - y is the same as x - x, or 0. Therefore, statement 1 is sufficient.
Looking at statement 2, we can apply the same technique - manipulate the algebra to either solve for the variables or streamline the expression:
x - y = x^2 - y^2
Using Difference of Squares: x - y = (x+y)(x-y)
We can try to divide both sides by (x-y) and we'd get:
x + y = 1
This isn't a complete solution, however, as if x - y is 0 (which we know it can be based on statement 1) we wouldn't be able to divide by it, so we really don't entirely know that. We do know that either x + y = 1 or x - y = 0. Outside of that, we don't know much else - we can't break apart just the (x - y) term, so we have to conclude that this statement is not sufficient, and therefore the answer is B.