jitendra wrote:
If ab≠0 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
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 --> SIGNSso ... 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!
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)
Statement (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
Statement (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
**THE ENTIRE POINT OF DATA SUFFICIENCY is to reward test takers who actually focus on the goal of the problem, and to punish those who don't.
if you begin your work thinking "i need to find a specific quadrant", you've already gotten the problem wrong, BEFORE YOU EVEN START WORKING ON IT.this is, in fact, the entire reason why the DS format was invented.
a multiple-choice question can't punish you for finding too much information. (if you can find the information... well, good for you.)
on the other hand, DS problems can... and they do.
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