The question is attached.

The answer is C.

Is there a formulaic way to approach problems like this one?

What underlying concept is this testing?

Thanks!!

Guest,

This problem tests the knowledge of quadrants. Specifically the key in this question is to identify for which values (+ve, -ve) the points (-a,b) & (-b,a) and finally (-x,y) lie in same quadrants.

If you rephrase the information given in the question - It tells (-a,b) & (-b,a) lie in same quadrants, it means a & b has to have same sign. Either both +ve or both -ve.

For ex a =1, b =2 then points will be (-1,2) & (-2,1)---both lie in II quadrant
Similarly if a = -2, b =-3 then points will be (2,-3) and (3,-2) - both lie in II quadrant

Now the question is whether (-x,y) lie in the same quadrant too? If x & y also carry the same sign as that of a & b, then (-x,y) will also lie in same quadrant as that of (-a,b) & (-b,a).

statement (1)

xy>0, gives the information about x & y, and that is they both are either +ve or -ve. We don't know if they carry the same signs as a & b. Hence, Insufficient

statement (2)

ax>0, this gives information about a & x, but doesn't give any information about relation between x & y. So, Insufficient.

If you combine both (1) & (2)

We know a,b, x & y - all are either +ve or -ve. So this is sufficient.

GMAT 2007

What does "ve" in your explanation mean?

+ve = positive
-ve = negative

GMAT 2007