Data Sufficiency

It's possible to answer a question like this by adding inequalities, but I think it's a difficult way to solve this type of problem. Neither Statement is sufficient alone (though you need to consider a negative value for x to see that Statement 2 is not sufficient). Using both Statements, we know:

16x > 15y
29x > 35y

If we just add these inequalities immediately, we find 45x > 50y, or 9x > 10y. That is true here, but the problem is it's just not very useful - it doesn't answer our question. But if we multiply the first inequality by 6 on both sides first, and then add the inequalities:

96x > 90y
29x > 35y

we find 125x > 125y, and x > y, which is what we wanted to know. I chose to multiply by 6 because the numbers 29 and 35 differ by 6, but the numbers 16 and 15 differ by only 1. We need to make that difference 6 so we'll get the same numbers in front of x and y after adding the inequalities.

That's not a method most test takers will find intuitive, I don't think (I just wanted to show that adding inequalities is still correct in this situation). Instead, you might notice that, using both Statements, we have

x > (15/16)y
x > (35/29)y

If y > 0, then it is always true that

(15/16)y < y < (35/29)y

so if y > 0, then because x > (35/29)y, it must be true that x > y. And if y < 0, it is always true that

(35/29)y < y < (15/16)y.

so if y < 0, then because x > (15/16)y, it must be true that x > y.

So in either case, x > y is true (and x > y is also true if y = 0), so the answer is C.