If ab not equal to 0, and points (-a, b) and (-b,a) are in the same quadrant of the xy plane, is point (-x, y) in this same quadrant?

(1) XY >O
(2) AX > O

The question stem:

The only way for (-a, b) and (-b, a) to be in the same quadrant, a and b must have the same sign. In the case that a>0 and b>0, the points are both in quadrant II. In the case that a<0 and b<0, the points are both in quadrant IV. (Try some values to confirm this.)

To answer the question, we need data to tell us whether x and y have the same sign, and if this same sign matches the sign of a and b.

(1) xy>0
This tells us that x and y have the same sign, but we do not know whether this sign matches the sign of a and b. INSUFFICIENT.

(2) ax>0
This tells us that x and a (and b) have the same sign, but we do not know whether y has the same sign as x, a, and b. INSUFFICIENT.

(1&2)
Putting these together, we know that all four variables a, b, x, and y have the same sign. SUFFICIENT.