Points on a quadrant

[gmatruler]

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

[Patrick_GMATFix]

This question is a bit challenging because it disguises itself as a geometry question when it's really a number properties question.

Two points can be in the same quadrant only if the x coordinates have the same sign and the y coordinates have the same sign. So this question is asking: Is (-x) of the same sign as (-a) and (-b)? Also is y of the same sign as a and b?

For (-x) to have the same sign as (-a) and (-b), x, a and b must have the same sign. Essentially we're asked whether all variables have the same sign.

The correct answer is C.

To better understand, have a look at the video solution. This is GMATPrep question 1043. To practice similar questions, set topic='Geometry, Coordinate' and difficulty='600-700' in the drill generator

-Patrick

[gmatruler]

The OA is C. Thanks Patrick. Explanation and video solution are very helpful.