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In the rectangular coordinate system, are the points (r,s) [#permalink]
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03 Sep 2009, 03:04
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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 OPEN DISCUSSION OF THIS QUESTION IS HERE: intherectangularcoordinatesystemarethepointsrs92823.html== Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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03 Sep 2009, 03:13
Most discussed GPrep Q you need to prove r^2 + s^2 = u^2 + v^2 hence you need both the (1) and (2) CasperMonday wrote:
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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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03 Sep 2009, 03:17
My solution is:
the distance of the first point from the origin is \(r^2+s^2\) the distance of the second point is \(u^2+v^2\) the question is actually asking is \(r^2+s^2=u^2+v^2\)?
(1) \(r+s=1\) apparently, insufficient. we know nothing about \(u\) and \(v\)
(2) \(u=1r\) and \(v=1s\) might be sufficient but we should check by substituting for \(u\), \(v\) in the original equation: \(r^2+s^2=(1r)^2+(1s)^2\) by simplifying the equation we get: \(r^2+s^2=r^2+s^22(r+s)+2\) this doesn't allow us to make any conclusions. hence, insufficient
by combining (1) and (2), we get that \((1s)^2+s^2=((1s)^2+s^22((1s)+s)+2\) simplifying, \(12s+2s^2=12s+2s^2\)
final answer is C.
but i am wondering if there are other approaches to this problem. thank for contributions.



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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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03 Sep 2009, 03:19
nitya34 wrote: Most discussed GPrep Q
you need to prove
r^2 + s^2 = u^2 + v^2
hence you need both the (1) and (2)
i was typing my answer right when you posted yours. as i said i am interested in other methods to solve the prob.))



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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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03 Sep 2009, 03:40
same strategy as yours with slight modification we need to prove r^2+s^2=u^2+v^2 now r^2+s^2=(1u)^2 + (1v)^2= 22(u+v)+(u^2+v^2) Now from (1) and (2) u+v=1+1(r+s) = 21=1hence r^2+s^2=u^2+v^2
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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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01 Oct 2009, 13:17
How can you say \(r^2+s^2\). it must be sqrt of (\(r^2+s^2\))........thank god I got it after lot of efforts CasperMonday wrote: My solution is:
the distance of the first point from the origin is \(r^2+s^2\) the distance of the second point is \(u^2+v^2\) the question is actually asking is \(r^2+s^2=u^2+v^2\)?
(1) \(r+s=1\) apparently, insufficient. we know nothing about \(u\) and \(v\)
(2) \(u=1r\) and \(v=1s\) might be sufficient but we should check by substituting for \(u\), \(v\) in the original equation: \(r^2+s^2=(1r)^2+(1s)^2\) by simplifying the equation we get: \(r^2+s^2=r^2+s^22(r+s)+2\) this doesn't allow us to make any conclusions. hence, insufficient
by combining (1) and (2), we get that \((1s)^2+s^2=((1s)^2+s^22((1s)+s)+2\) simplifying, \(12s+2s^2=12s+2s^2\)
final answer is C.
but i am wondering if there are other approaches to this problem. thank for contributions.



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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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02 Oct 2009, 08:13



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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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07 Sep 2010, 06:51
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mrsmarthi wrote: Hey guyz I am not master of quant either verbal:) but i did this question really quick.Maybe lucky. a) R+S=1 (no info about U and V then insufficient) b) u+r=1, v+s=1 not sufficent Together U+R= R+S U=S and V+S=R+S V=R if U=S and V=R they are equidistant from the orgin. PS: I did like that cuz i couldnt remember the main formula however it is more quick
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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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07 Sep 2010, 07:09
C.
Find the distance of U,V from origin. Substitute U = 1R and V = 1S. You will notice that when R+S=1 this distance equals the distance of R,S from origin.



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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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07 Sep 2010, 07:36
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CasperMonday wrote: OA 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 Distance between the point A (x,y) and the origin can be found by the formula: \(D=\sqrt{x^2+y^2}\). Basically the question asks is \(\sqrt{r^2+s^2}=\sqrt{u^2+v^2}\) OR is \(r^2+s^2=u^2+v^2\)? (1) \(r+s=1\), no info about \(u\) and \(v\); (2) \(u=1r\) and \(v=1s\) > substitute \(u\) and \(v\) and express RHS using \(r\) and \(s\) to see what we get: \(RHS=u^2+v^2=(1r)^2+(1s)^2=22(r+s)+ r^2+s^2\). So we have that \(RHS=u^2+v^2=22(r+s)+ r^2+s^2\) and thus the question becomes: is \(r^2+s^2=22(r+s)+ r^2+s^2\)? > is \(r+s=1\)? We don't know that, so this statement is not sufficient. (1)+(2) From (2) question became: is \(r+s=1\)? And (1) says that this is true. Thus taken together statements are sufficient to answer the question. Answer: C. Hope it helps.
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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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10 Sep 2010, 15:09
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We need to check whether r^2 + s^2 = u^2 + v^2=> is \((ru)* (r+u) = (vs)* (v+s)\) A Statement 1: Apparently Insufficient as no information about u and v Statement 2: Given \(u = 1  r\) and \(v = 1  s\) B => \(r+u =1\) and \(v+s = 1\)C Using equations A and C we need to check if \(ur = sv\) if \(u+v = r+s\) if \(u+v = r+s = 1r + 1s\) if \(r+s = 1\) D Not Sufficient. combine statement 1 and equations D , we can prove the distance is same.
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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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21 Oct 2010, 23:53
Was about to post this. I'm glad I checked before I did. Thanks for the explanations!
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Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
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