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

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Manager
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In the rectangular coordinate system, are the points (r,s) [#permalink]

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03 Aug 2007, 19:48
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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

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Director
Joined: 12 Jun 2006
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03 Aug 2007, 21:12
abhi_ferrari 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

Is the origin always (0,0)? if so, I say B is sufficient. r,s and u,v can never be equidistant assuming B is true

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Senior Manager
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03 Aug 2007, 22:04
1
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abhi_ferrari 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

It has to be C.

RS = (r^2+s^2)^(1/2)
UV = (u^2+v^2)^(1/2)

Assuming of course that the origin is at (0,0).

Stmt 1: insufficient.

Stmt 2: UV = [(1-r)^2 + (1-s)^2]^(1/2)
or, UV = [r^2 + s^2 - 2(r+s) + 2]^(1/2)
insufficient as we do not know (r+s).

Both together are sufficient.

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GMAT Club Legend
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04 Aug 2007, 00:32
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St1:
No information about u and v, out.

St2:
(u,v) = (1-r,1-s)

If (r,s) = (10,4) then (u,v) = (-9,-3) -> different distance
If (r,s) = (1,1) then (u,v) = (0,0) -> different distance
If (r,s) = (1/4, 3/4) then (u,v) = (3/4, 1/4) -> same distacnce

Insufficiet.

Using both st1 and st2:
If (r,s) = (1/2,1/2) then (u,v) = (1/2, 1/2) -> same distance
If (r,s) = (4,-3) then (u,v) = (-3,4) -> same distance
Insufficient.

Ans B

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Manager
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04 Aug 2007, 10:40
Thanks, Sumande and ywilfred. OA is C.

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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]

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03 Jul 2017, 08:51
Hello from the GMAT Club BumpBot!

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Re: In the rectangular coordinate system, are the points (r,s)   [#permalink] 03 Jul 2017, 08:51
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