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first from the stem it seems that points are either in II or in IV quadrant cause (-a;b) and (-b;a) are in the same quadrant, or they should have similar signs.
From stmnt 1) X and Y are either both + or both - so the point is in II or IV quadrant so 1 is suff.
From stmnt 2- gives nothing abt Y-insuff.
So A) IMO

a,-b and b,-a are in the same quard and ab != o that means

a and b both has same sign. they can be both positive or they can be both negative.

statement 1) says xy >0 that mean x and y both have the same sign. but in order for -x,y to be in the same quard as a,-b x,y needs to have the same sign as a and b. but from this statement we don't know whether x and y are both positive or negative, at the same time we don't know whether a, b are both positive or negative

statement 2) ax > 0 that nells a and x has the same sign. statement 2 alone is not sufficient because x and y need to have the same sign as well in order to be in the quard.

but if we take both the statement, we can solve the problem

a,-b and b,-a are in the same quard and ab != o that means

a and b both has same sign. they can be both positive or they can be both negative.

statement 1) says xy >0 that mean x and y both have the same sign. but in order for -x,y to be in the same quard as a,-b x,y needs to have the same sign as a and b. but from this statement we don't know whether x and y are both positive or negative, at the same time we don't know whether a, b are both positive or negative

statement 2) ax > 0 that nells a and x has the same sign. statement 2 alone is not sufficient because x and y need to have the same sign as well in order to be in the quard.

but if we take both the statement, we can solve the problem

So, C it is!

Very good explanation. Thanks. _________________

Whether you think you can or think you can't. You're right! - Henry Ford (1863 - 1947)

This is an question.. May be there is a simpler solution..

Pick some values and it can be seen that (-a,b) and (-b,a) can be in the same quadrant only if a & b are of the same sign..
Eg. a = 1, b =2 => (-1,2) & (-2,1) .. lie in 2nd quadrant..
a = -1, b = -2 => (1,-2) & (2,-1) ... lie in 4th quadrant.
a = -1, b = 2 => (1,2) & (-2, -1) --- don't lie in the same quadrant.
Similarly for a +ve and b -ve ... not possible.

So both a & b are both +ve or both -ve. For (-x,y) to be in the same quadrant as that of (-a,b) we need:
a). x & y need to be both +ve or both -ve.
b). x or y should have the same sign as a or b

From (1) => x*y > 0 => x & y have same sign. Still we don't know if (-a,b) and (-b,a) lie in 2nd or 4th quadrant.. INSUFF

From (2) ax > 0 => a and x have same sign. we don't know the sign of y .. INSUFF.

1) & 2)
x, y, and a are of same sign. SUFF to say that (-x,y) and (-a,b) are in same quadrant. _________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

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