If ab does not = 0 and points (-a, b) and (-b, a)

[Guest]

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!!

[GMAT 2007]

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

[Guest]

What does "ve" in your explanation mean?

[GMAT 2007]

+ve = positive
-ve = negative

GMAT 2007

[kannan_m_80]

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

I think you meant to say Quadrant IV...good explanation anyway.

thanks

[RonPurewal]

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

I think you meant to say Quadrant IV...good explanation anyway.

thanks

nice catch