I am not Ian or Stuart, but will add my $0.02 anyways...

First of all wrong sub-forum for this post, it should be in PS forum.

As for your question,
Realize that there are four quadrants and each quadrant has a specific sign attached to its X & Y coordinates.
Quadrant 1- X is +ve and Y is +ve
Quadrant 2- X is -ve and Y is +ve
Quadrant 3- X is -ve and Y is -ve
Quadrant 4- X is +ve and Y is -ve.

So, from the question you have to figure out if what is the relation between the signs of a, b, x, y.
From the data given in the question, we can see that the signs of a and b must be the same, i.e. a,b can be -ve -ve or +ve, +ve.
For (-x,y) to be in the same quadrant, it also has to have the same sign as (a, b) and obviously not lie on the axes or origin.

Once you have deduced this, rest should be easy.

Dear Kapssi,
Thanks a ton. The explanation given is well understood, but why it cant be D? Need to know how to solve such questions under 1.5-2 mins.
This question may seem silly for most, but was looking for some quick tips from experts for such questions. Therefore addressed to them.
This qustion is a DS and its in the right forum .

Rgds
sumit

This is how I came to the conclusion, please correct me if I am wrong

1. xy>0...so x and y both should either be +ve or negative Insufficient
2. ax>0...nothing has been told about y...so insufficient

Both together..... ax > 0 is given....a is positive(since signs is only to represent the quadrant)...so x should be positive..
therefore y should also be +ve....

Hence (-x,y) lies in the same quadrant. Sufficient

Please let me know if the assumption that I made that 'a' is positive is wrong

First of all, I must admit, its a good quest, and may take more than 2 mins.

Anyhow, here's the explanation:
With Q stem we dont know abt the signs of a,b, x, y.
We know this much but that a and b have to be of same sign, either +ve or -ve, if (-a,b) and (-b,a) have to be in same quad.

Stmt I:
xy>0
Doesn't tell us anything more than both x and y are of same sign.
So, if both positive: (-x,y) is in II quad.
If both negative, (-x,y) is in IV quad.
Lets c about a & b.
If both a & b +ve, II quad.
If both a & b -ve, IV quad.

But the missing link is how we be sure when both x,y are +ve, a & b are also +ve, and similarly for -ve.

Not sufficient.

Stmt II:

ax>0
Either both a & x are +ve, or both are -ve.
No help either

Let's combine both.
So, if ax>0, either both are +ve or both -ve.
In case when both are +ve.
then b & y are also positive.
So, (-a,b),(-b,a) and (-x,y) lie in same quad i.e II quad.

If both a & x are -ve, then b and y are also -ve.
So, (-a,b),(-b,a) and (-x,y) still lie in same quad i.e IV quad.

Hence combining both answers the ques.
Hence, C

Phew..