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Source: — Data Sufficiency |
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by Frankenstein » Sat May 21, 2011 3:14 am
for points (r,s)&(u,v) to be equidistant from origin, we need to check whether sqrt(r^2 + s^2)=sqrt(u^2 + v^2)
from(1): we know nothing about u and v.
Insufficient
from (2) : r+u=1,v+s=1
Is (r^2 + s^2) = (u^2+v^2) ?
=> is r^2-u^2 = v^2-s^2?
=> is (r-u)(r+u) = (v-s)(v+s)?
=> is (r-u)(1) = (v-s)(1)?
=> is r-u = v-s ?
=> is r+s = v+u ?
Insufficient
Using (1) and (2)
r+s=1 and u+v=(1-r)+(1-s) =>u+v = 2-(r+s) =2-1 =1
so r+s = v+u
Sufficient

Hence C
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by GMATGuruNY » Sat May 21, 2011 3:25 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
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.
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