Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

03 Sep 2009, 02:17

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) \(u=1-r\) and \(v=1-s\) might be sufficient but we should check by substituting for \(u\), \(v\) in the original equation: \(r^2+s^2=(1-r)^2+(1-s)^2\) by simplifying the equation we get: \(r^2+s^2=r^2+s^2-2(r+s)+2\) this doesn't allow us to make any conclusions. hence, insufficient

by combining (1) and (2), we get that \((1-s)^2+s^2=((1-s)^2+s^2-2((1-s)+s)+2\) simplifying, \(1-2s+2s^2=1-2s+2s^2\)

final answer is C.

but i am wondering if there are other approaches to this problem. thank for contributions.

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

Show Tags

01 Oct 2009, 12:17

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) \(u=1-r\) and \(v=1-s\) might be sufficient but we should check by substituting for \(u\), \(v\) in the original equation: \(r^2+s^2=(1-r)^2+(1-s)^2\) by simplifying the equation we get: \(r^2+s^2=r^2+s^2-2(r+s)+2\) this doesn't allow us to make any conclusions. hence, insufficient

by combining (1) and (2), we get that \((1-s)^2+s^2=((1-s)^2+s^2-2((1-s)+s)+2\) simplifying, \(1-2s+2s^2=1-2s+2s^2\)

final answer is C.

but i am wondering if there are other approaches to this problem. thank for contributions.

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

Show Tags

07 Sep 2010, 06:09

C.

Find the distance of U,V from origin. Substitute U = 1-R and V = 1-S. You will notice that when R+S=1 this distance equals the distance of R,S from origin.

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) \(u=1-r\) and \(v=1-s\) --> substitute \(u\) and \(v\) and express RHS using \(r\) and \(s\) to see what we get: \(RHS=u^2+v^2=(1-r)^2+(1-s)^2=2-2(r+s)+ r^2+s^2\). So we have that \(RHS=u^2+v^2=2-2(r+s)+ r^2+s^2\) and thus the question becomes: is \(r^2+s^2=2-2(r+s)+ r^2+s^2\)? --> 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.

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

Show Tags

09 May 2017, 18:57

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________