Hi Anand,

Statement 1:
Your reasoning is correct, as statement one is sufficient due to commutative property of addition.

Statement 2 can be analysed putting value X=5,Y=3
X-Y=2
Y-X=-2

So here x#y not = y#x for all X and Y.
Hence it answers the question( Is it true that x#y = y#x for all x and y?)Answer is No.
Remember this is Yes-No question of data sufficiency.You only need to definitively answers yes or no without doubt.


So answer is D(both statements are sufficient alone)

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Manpreet

Right. So my question is: what if x=y=0? Then the (2)becomes inconsistent, doesn't it?

anand108 wrote:Right. So my question is: what if x=y=0? Then the (2)becomes inconsistent, doesn't it?

The question that is asked is: Is it true that x#y = y#x for all x and y?
If x#y=x-y, then does x#y = y#x for all x and y?

manpreet singh is correct...we can answer definitively that it is not true for all x and y. It doesn't matter whether it's true for x=y=0. We want to know whether it is true for all x and y, and it is not.

I came back and edited this answer after I saw how it was written.
The red text above is written ambiguously. The opposite of 'x#y = y#x is true for all x and y' is 'there exists x and y that x#y = y#x is false'.