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Geometry

by tapanmittal » Fri Jul 03, 2015 9:34 pm
If rs not equal to zero and the points (-r,s) and (s,-r) lie in same quadrant of the coordinate plane,is the point (a,b) in this same quadrant?
1. ab<0
2. sb>0

OA is A
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by theCEO » Fri Jul 03, 2015 9:59 pm
tapanmittal wrote:If rs not equal to zero and the points (-r,s) and (s,-r) lie in same quadrant of the coordinate plane,is the point (a,b) in this same quadrant?
1. ab<0
2. sb>0

OA is A
Create columns for all signs of r and s
If points are in the same quadrant, it means the points have the same sign for the x coodinate
In the table below, -r and s have the same signs, when r is negative and s is positive
r s -r -s
+ + - -
+ - - +
- - + +
- + + -

(-r,s) and (s,-r) are in the 1 quadrants, positive x and positive y

1. ab < 0
this means a is negative and b is positive or
this means b is negative and a is positive
Regardless of which, this point will not be in quad1 because its x and y points are not positive
sufficent

2. sb>0
We know s is positive, therefore b is positive
However we arent told anything about "a", therefore we cannot say if a is positive or negative
insufficient

ans = a
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by GMATGuruNY » Sat Jul 04, 2015 5:42 am
tapanmittal wrote:If rs not equal to zero and the points (-r,s) and (s,-r) lie in same quadrant of the coordinate plane,is the point (a,b) in this same quadrant?
1. ab<0
2. sb>0
Case 1: r=1 and s=2
(-r, s) = (-1, 2), (s, -r) = (2, -1)
Case 2: r=-1, s=2
(-r, s) = (1, 2), (s, -r) = (2, 1)
Case 3: r=-1, s=-2
(-r, s) = (1, -2), (s, -r) = (-2, 1)
Case 4: r=1, s=-2
(-r, s) = (-1, -2), (s, -r) = (-2, -1)

Only Cases 2 and 4 satisfy the constraint that (-r, s) and (s, -r) lie in the same quadrant.
In Case 2, (-r, s) and (s, -r) lie in Quadrant I.
In Case 4, (-r, s) and (s, -r) lie in Quadrant III.

For (a, b) also to lie in Quadrant I or III, a and b must have the SAME SIGN.

Statement 1: ab<0
Implication:
a and b do NOT have the same sign.
SUFFICIENT.

Statement 2: sb > 0
Here, it's possible that (-r, s) = (1, 2) -- as in Case 2 above -- and that b=1.
In Case 2, (-r, s) and (s, -r) lie in Quadrant I.
If a=1, then (a, b) = (1, 1), which also lies in Quadrant I.
If a=-1, then (a, b) = (-1, 1), which does NOT also lie in Quadrant I.
INSUFFICIENT.

The correct answer is A.
Last edited by GMATGuruNY on Mon Jul 06, 2015 6:35 am, edited 1 time in total.
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by nikhilgmat31 » Mon Jul 06, 2015 4:10 am
I got the solution for Statement 1.


Please explain solution by Statement 2 in more detail.
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