Data Sufficiency

Can anyone tell me the explanation for this problem.

Thank you

OA: C

Explanation given in my earlier reply to ur thread.

Anyways here it goes again
Original explanation by only4me -
From the main statement we deduce that a and b are either both positive or both negative. Only in this case (-a;b) and (-b;a) can be in one quadrant – in II or in IV

(1)
xy>0
x and y can both negative and positive
(x positive)(y positive)>0 will be in the same quadrant
(x negative)(y negative)>0 will NOT be in the same quadrant
It is INSUFFICIENT

(2)
ax>0
a and x can both negative and positive
(a positive)(x positive)>0
(a negative)(x negative)>0
But we don know is a positive or negative!
It is INSUFFICIENT

(1) and (2)
This means that a, b, x and y are either ALL positive or all negative.
Here I substituted positive and negative meanings and found that taking (1) and (2) I can answer that (-a;b), (-b;a) and (-x;y) will always be in the same quadrant.
ANSWER - C

thank you rishi235