BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

OG 164 DS

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 273
Joined: Thu Sep 08, 2011 6:50 am
Thanked: 5 times
Followed by:3 members

OG 164 DS

by fangtray » Sun Mar 25, 2012 1:44 am
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


Please help with this question. I have rephrased the question to ask:

Is r^2+s^2 = u^2+v^2?

statement one does not help.
statement 2, states that U does not equal R. and V does not equal S. Hence it seems to me as if it would be sufficient, but C is actually the OA. Could someone please clarify?
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Mar 25, 2012 2:28 am
fangtray wrote: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


Please help with this question. I have rephrased the question to ask:

Is r^2+s^2 = u^2+v^2?

statement one does not help.
statement 2, states that U does not equal R. and V does not equal S. Hence it seems to me as if it would be sufficient, but C is actually the OA. Could someone please clarify?
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
Top
Post new topic Post Reply
• Page 1 of 1