If ab does not equal zero

[guest612]

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?

[Sudhan]

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

[RonPurewal]

If ab does not equal zero and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane,

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!

9 is point (-x,y) in the same quadrant?

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)

1. xy>0

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

2. ax>0

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

[guest612]

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

[rfernandez]

Glad it makes sense.

[loshko]

Very nice explanation. Thanks, Ron!

[sudaif]

homerun explanation!

[RonPurewal]

thanks guys

[rahul9395]

Ron great explanation

[RonPurewal]

Ron great explanation

thx

[sukhvinder.mech]

Thanks Ron!

Great explanation

[RonPurewal]

Thanks Ron!

Great explanation

glad it helped

[aagar2003]

OMG this is too tough! Can't think of cracking it in real GMAT in time pressure and that too with so many combinations?
Anybody knows if the source of this problem is official GMAT?

[RonPurewal]

OMG this is too tough! Can't think of cracking it in real GMAT in time pressure and that too with so many combinations?
Anybody knows if the source of this problem is official GMAT?

every problem in this folder is from the GMAT PREP official software; GMAC states that these problems previously appeared on the official test.

[aps_asks]

Very Good Explanation !