Let * denote a mathematical operation. Is it true that x * y = y * x for all x and y?

(1) x * y = 1/x + 1/y
(2) x * y = x - y


Any suggestions?

Is (D) the answer?

Looks like 2 contradicting statements.

Statement (1) x * y = y * x for the given definition.
Statement (2) x * y is not equal to y * x as per the given definition.

So from both statements we can determine whether x * y = y * x.

I am not sure whether I am missing anything.

I agree that statement 1 is sufficient, but what if X = Y, then statement 2 proves that X*Y=Y*X. But if X and Y are distinctive, then statement 2 proves that X*Y doesn't = Y*X...

Can it be the case?

I went with (A) myself, but the source says (D) is answer, without further explanation. Maybe it's an error.

Since the question asks for if X * Y = Y * X for "all x and y", we need to consider all possibilities of x and y. As you mentioned Statement(2) will be true only if x = y. So we cannot say x * y = y * x for all x and y. Hence SUFFICIENT.

Just an FYI - you haven't gotten a response from an instructor on this one because you haven't cited the source - we can't respond unless the source has been cited. Please remember to cite the source in future! :)