Data Sufficiency

4meonly wrote:(x-1)(y-1)=1 ?
xy-x-y+1=1
xy=1-1+x+y
xy=x+y

So, the question can be rephrased in
Does xy=x+y ?

(1) Directly gives you the answer

(2) x=y
sustitute yy=y+y
y^2 = 2y
y = 2
2*2 = 2+2 or (2-1)(2-1)=1
According to xy>0? 2*2 > 0

Answer D

You are doing the math correctly, but you're answering a different question from the one that's being asked here. The question is:

Is (x-1)(y-1) = 1 ?

As you've done, you can rephrase the question:

Is xy = x + y ?

Still, that's the question. It's not a fact. Do not assume the answer to the question is 'yes', and use it as if it were a fact. This is crucially important, and it's a common trap people fall into when they first start doing DS questions.

So, you aren't trying to find x or y here; you are trying to decide, from Statement 2, whether xy = x+y must be true. If we know statement 2, we know that x = y, so we need to know whether x*x = x+x, that is whether x^2 = 2x. Well, x could be 2, and then x^2 = 2x, or x could be 3, and x^2 does not equal 2x. So we can't answer the question by only using 2) alone. As demonstrated above, Statement 1) is sufficient.

sumithshah wrote:I agree with your explanation IAN but if an equation is simplified and found to be true, shouldlnt the un simplified equation be true also?

Yes, but I'm afraid I don't see the relevance of that to this question. We can rewrite or simplify the equation in the question all we want; using Statement 2 alone, we can't prove that it's true.