I just wrote a post about this exact question on another forum, so I'll just paste a link if you're interested:

http://www.beatthegmat.com/gmat-scoring ... 98484.html




I think you've missed part of the question here - I think the question says:

If (-a, b) and (-b, a) are in the same quadrant, is the point (-x, y) in the same quadrant as (-a, b)?
1) xy > 0
2) ax > 0


If two points are in the same quadrant, then their x-coordinates have the same sign, and their y-coordinates have the same sign. So from the information that (-a, b) and (-b, a) are in the same quadrant, we learn that a and b have the same sign (either by looking at x-coordinates or at y-coordinates). So we know that a and b are either both positive or both negative, and that the point (-a, b) thus has one negative coordinate and one positive coordinate. The problem is we don't know which coordinate is positive, and which negative; it could be (+, -) or it could be (-, +).

From Statement 1, we learn that x and y have the same sign. Thus the point (-x, y) has coordinates of opposite signs. This point could be (+, -) or (-, +), so we don't know if it's in the same quadrant as (-a, b).

Statement 2 doesn't mention y at all, so cannot be sufficient, since we need to know about the sign of y.

Combining the two statements we know a and b have the same sign (from the stem), a and x have the same sign (from Statement 2) and x and y have the same sign (from Statement 1). So a, b, x and y all have the same sign. Thus the x-coordinates of (-a, b) and (-x, y) have the same sign, as do their y-coordinates, and the two points must be in the same quadrant. The answer is C.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

(-a, b) and (-b, a) are in the same quadrant.
Is the point (-x, y) in the same quadrant as point (-a, b)?

(1) xy > 0
(2) ax > 0

From the information that (-a, b) and (-b, a) are in the same quadrant, it can be determined that
(-a, b) is in either quadrant II or quadrant IV. If (x, y) and (a, b) are in the same exact quadrant, they will have the same sign and (-x, y) will be in the same quadrant as (-a, b)'s.

(1) xy > 0

(x, y) is in quadrant I or quadrant III.
(-x, y) is in quadrant II or quadrant IV.
No further information is provided about (-a, b).

(2) ax > 0

Point x in (x, y) has the same sign as does point a in (a, b). Since a and b have the same sign, x, a and b have the same sign.

But the sign of point x could be different from, or the same as, the sign of point y. The condition that (x, y) and (a, b) have the same sign, and therefore that (-x, y) and (-a, b) are in the same quadrant, is possible but uncertain.

Combined analysis:

x has the same sign as y
x has the same sign as a and b
x, y, a and b all have the same sign.

This means (x, y) and (a, b) are in the same quadrant. (-x, y) and (-a, b) are in the same quadrant.


[xyab+xdj]