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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]  03 Aug 2007, 18:48
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Difficulty:

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Question Stats:

56% (02:40) correct 44% (01:23) wrong based on 11 sessions
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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Re: DS GMAT PREP [#permalink]  03 Aug 2007, 20:12
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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Re: DS GMAT PREP [#permalink]  03 Aug 2007, 21:04
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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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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Thanks, Sumande and ywilfred. OA is C.

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