VIGNESHWARR wrote:If ab<>0 and points (-a,b) and (-b,a) are in the same quadrant of the xy plane,is point (-x,y) in this same quadrant?
1.xy>0
2.ax>0
Only two cases satisfy the constraint that (-a,b) and (-b,a) are in the same quadrant.
Case 1: Both a and b are positive
Let a=2, b=3.
Then (-a,b) = (-2,3) and (-b,a) = (-3,2).
Both points are in quadrant II.
Case 2: Both a and b are negative
Let a=-2, b=-3.
Then (-a,b) = (2,-3) and (-b,a) = (3,-2).
Both points are in quadrant IV.
Thus, for (-a,b) and (-b,a) to be in the same quadrant, a and b must have the same sign.
Implication:
For (-x,y) to be in the same quadrant as (-a,b) and (-b,a), x and y must have the SAME SIGN as a and b.
Question rephrased:
Do x and y have the same sign as a and b?
Statement 1: xy > 0.
Here, x and y have the same sign.
No way to determine whether this sign is the same as that of a and b.
INSUFFICIENT.
Statement 2: ax>0.
Here, a and x have the same sign.
No information about y.
INSUFFICIENT.
Statements 1 and 2 combined:
Since x and y have the same sign, and a and x have the same sign, x, y, and a -- and thus b -- all have the same sign.
SUFFICIENT.
The correct answer is
C.
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