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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. _________________

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