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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
