Hi Ryan,

Given that points (−a, b) and (−b,a) are in the same quadrant which means a and b have the same sign.

Case 1: It can be in II quadrant, if a and b are both positive, as (−a,b)=(−,+)=(−b,a)

OR

Case 2: It can be in IV quadrant, in case they are both negative, as (−a,b)=(+,−)=(−b,a)

Now the point (−x,y) will be in the same quadrant if “x” has the same sign as “a” (or which is the same with b) & y has the same sign as a (or which is the same with b). Or in other words if all four: a, b, x, and y have the same sign.

Statement I is insufficient: xy>0.

x and y have the same sign. Nothing about a or b here. So, not sufficient.

Statement II is insufficient: ax>0.

a and x have the same sign. But we know nothing about y, hence not sufficient.

Together I and II sufficient,

x and y have the same sign and  a and x have the same sign.

All four: a, b, x, and y have the same sign.

Hence sufficient.

So, the answer is C.

Hope that helps.

You can also do plugging in based on the above two cases.