If ab does not equal zero and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in the same quadrant?
1. xy>0
2. ax>0

Asnwer C.

Can I assume from statements 1 and 2 and x, y, and a all have the same signs? and thus, do not share the same quadrant as the a/b coordinates b/c they hvae opposite signs?

If ab does not equal zero and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in the same quadrant?
1. xy>0
2. ax>0

From (1),
Xy>0, both x & y should be positive or negative to satisfy the condition xy>0. Hence (-x,-y) or (x,y). But from this info we cannot arrive at the conclusion if (-x,y) is in the same quadrant. Hence INSUFF

From (2),
ax>0, both a& x should be positive or negative to satisfy the condition ax>0. But nothing mentioned about y. Hence Insuff.

Using 1 and 2, we can assume that x,y, a all carry the same sign.
Hence, C is sufficient to answer if point(-x,y) is in the same quadrant.

Thanks

here's how to interpret this:
you should immediately make the following association: QUADRANTS --> SIGNS
so ... the x- and y-coordinates of both points have to have the same signs.
this means that
-a and -b have the same sign (from the x coordinates)
and
b and a have the same sign (from the y coordinates)
these are of course the same statement; both are equivalent to saying that a and b have the same sign.

therefore, that's all we know from the problem statement: a and b are nonzero and have the same sign.
note that we do not know which sign that is!



we need to know two things:
(1) whether -x has the same sign as both -a and -b --> whether x has the same sign as a and b (from the first coordinate)
(2) whether y has the same sign as a and b (from the second coordinate)



this means x and y have the same sign as EACH OTHER, but we don't know how it relates to a or b.
insufficient



this means x has the same sign as a (and therefore b), but we don't have any information about y.
insufficient

together: x has the right sign, and y has the same sign as x does. therefore, both of them have the correct sign!

answer = c

sweetness

fantastic. i was interpreting it all wrong. thank you!

Glad it makes sense.