x/y will be <0 when x and y will have different sign
From 1
x=y..i.e x and y have same sign..hence x/y<0 is not true...sufficient

From 2
-x=-(-y)
-x=y i.e x and y are of opposite sign..x/y<0 is true..sufficient

IMO Ans option D

From the stem we know that x & y both are non zero.
The question x/y < zero ? is the same as : is of them positive and another negative?

1) x = y. This is sufficient. Because both are same, either negative or positive. So x/y will always be > 0.
2) -x = -(-y). => x = -y. Again this is also sufficient. This clearly indicates that both of them have a different sign. Hence x/y is negative, x/y < 0.
Hence answer is D.

The two answers contradict each other. This will never be the case in the official gmat. I seem to remember this question from the OG. I think option 1) was "x = -y"

Bertys: Yes, you are absolutely right. This would never be an official GMAT question, because the two statements of a DS question are ALWAYS TRUE and NEVER CONTRADICT ONE ANOTHER.

Vishalranka: Are you sure you copied the problem correctly? If not, please clarify what the question states as printed. Or, if this is how the question was printed originally, then it is not a legitimate question.