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# In the rectangular coordinate system, are the points (r,s)

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Manager
Joined: 13 Dec 2005
Posts: 64
In the rectangular coordinate system, are the points (r,s) [#permalink]

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04 Jan 2006, 19:00
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

Statement (1) r+s=1
Statement (2) u=1-r and v=1-s

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT SUFFICIENT
Senior Manager
Joined: 08 Sep 2004
Posts: 257
Location: New York City, USA

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04 Jan 2006, 19:28
For (r,s) to be equidistance from origin as (u,v) -
r^2 + s^2 = u^2 + v^2

stmt1: r+s = 1. Does not say anything about (u,v). Not sufficient.

stmt2: u=1-r and v=1-s
u^2 + v^2 = 1 + r^2 - 2r + 1 + s^2 - 2s
= 2 - 2(r+s) + r^2 + s^2. Not suffcient.

Combining 1 & 2:

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

Ans: C

- Vipin
Senior Manager
Joined: 15 Apr 2005
Posts: 415
Location: India, Chennai

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05 Jan 2006, 00:08
ellisje22 wrote:
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

Statement (1) r+s=1
Statement (2) u=1-r and v=1-s

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT SUFFICIENT

The distance between (0,0) and (r,s) should be same as distance between (0,0) and (u,v)
Distance between (r,s) and (0,0) = sqrt(r^2+S^2)
Distance between (u,v) and (0,0) = sqrt(u^2+V^2)

Stmt 1 is obviously not suff.
From stmt 2 we get sqrt(2+r^2+s^2-2(r+s)) not suff.
Combing we get Sqrt(r^2+s^2) = SQRT(R^2+S^2)
Hence Suff. So C.
Director
Joined: 04 Oct 2005
Posts: 582
Location: Chicago

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07 Jan 2006, 00:49
I got C by plugging in values..but it took a long time 5 min
07 Jan 2006, 00:49
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