Power prep DS

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If ab is not 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

Please explain the answer

[kajcha]

IMO C

From the question (-a,b) and (-b,a) are in the same quadrant means both a and b are either -ve or +ve

a & b both +ve => (-a,b) and (-b, a) lies in II quadrant
a & b both -ve => (-a,b) and (-b, a) lies in IV quadrant

Stmt 1 - xy > 0 means x<0 and y<0 OR x>0 and y>0

When x<0 & y<0 => (-x,y) lies in IV quadrant
When x>0 & y>0 => (-x,y) lies in II quadrant

However, this stmt does not say anything about a or b so NOT SUFF

Stmt 2 - ax > 0 means x > 0 when a >0 and x <0 when a<0 but y can be +ve or -ve so NOT SUFF

Together, when a<0 => x<0 and y<0 => (-x,y)lies in same quadrant as (-a,b)
when a>0 => x>0 and y>0 => (-x,y) lies in same quadrant as (-a,b)

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Thanks