In the rectangular coordinate system, are the points (r, s) and (u, v) equidistant from the origin?
1. r+s = 1
2. u = 1-r and v = 1-s
Statement 1: r+s = 1.
No information about (u,v).
Insufficient.
Statement 2: u = 1-r and v = 1-s.
Let r=1, u = 1-1 = 0.
Let s=1, v = 1-1 = 0.
Then (r,s) = (1,1) and (u,v) = (0,0).
Are (1,1) and (0,0) equidistant from the origin? No.
Let r=1, u = 1-1 = 0.
Let s=0, v = 1-0 = 1.
Then (r,s) = (1,0) and (u,v) = (0,1).
Are (1,0) and (0,1) equidistant from the origin? Yes.
Since in the first case the answer is No and in the second case the answer is Yes, insufficient.
Statements 1 and 2 combined:
Statement 1: r+s = 1.
Statement 2: r+u = 1.
Thus, r+s = r+u.
Thus, s=u.
Statement 1: r+s = 1.
Statement 2: v+s = 1.
Thus, r+s = v+s.
Thus, r=v.
Thus, (r,s) = (v,u), indicating that the two points will be equidistant from the origin.
Sufficient.
The correct answer is
C.
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
