Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 21 Jan 2010
Posts: 120

In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
Updated on: 06 Feb 2019, 03:09
Question Stats:
59% (01:57) correct 41% (02:01) wrong based on 942 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by calvinhobbes on 17 Apr 2010, 05:57.
Last edited by Bunuel on 06 Feb 2019, 03:09, edited 2 times in total.
Renamed the topic.




Math Expert
Joined: 02 Sep 2009
Posts: 64314

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
17 Apr 2010, 06:31
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.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 64314

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
01 Sep 2010, 18:48
metallicafan wrote: Bunuel, I have a question: How did you know that you had to express the equation in that way? For example, I expressed (based on clue # 2) in this way: \(r^2 + s^2 = (1r)^2 + (1s)^2\) So, I obtain: r + s = 1 The same as clue # 1. How did you know that you had to do in the other way? Thanks! Not sure I understand your question. But here is how I solved it: The question asks: is \(r^2+s^2=u^2+v^2\)? Then (2) says: \(u=1r\) and \(v=1s\). So now we can 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. When combining: 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. Hope it's clear.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 64314

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
21 Jan 2013, 04:09
fozzzy wrote: Bunuel 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
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. So the formula used here is different from the distance formula of square root of (x2x1)^2 + (y2y1)^2 No it's not. The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1x_2)^2+(y_1y_2)^2}\). Now, if one point is origin, coordinates (0, 0), then the formula can be simplified to: \(D=\sqrt{x^2+y^2}\). Hope it's clear.
_________________



Manager
Joined: 09 Mar 2018
Posts: 55
Location: India

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
06 Jun 2019, 10:08
chetan2u Bunuel VeritasKarishmaGreetings Experts, while trying to figure out a shorter approach for this question, I noticed  St 1. r + s = 1 > r = 1  s OR s = 1  r St 2. u = 1  r and v = 1  sfrom the above statements, we can deduce > u = s and v = rHence, the points will definitely be equidistant. Please correct me if I am wrong.



Math Expert
Joined: 02 Aug 2009
Posts: 8623

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
06 Jun 2019, 23:04
sakshamchhabra wrote: chetan2u Bunuel VeritasKarishmaGreetings Experts, while trying to figure out a shorter approach for this question, I noticed  St 1. r + s = 1 > r = 1  s OR s = 1  r St 2. u = 1  r and v = 1  sfrom the above statements, we can deduce > u = s and v = rHence, the points will definitely be equidistant. Please correct me if I am wrong. Yes, you are correct in the present state.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10506
Location: Pune, India

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
07 Jun 2019, 01:01
sakshamchhabra wrote: chetan2u Bunuel VeritasKarishmaGreetings Experts, while trying to figure out a shorter approach for this question, I noticed  St 1. r + s = 1 > r = 1  s OR s = 1  r St 2. u = 1  r and v = 1  sfrom the above statements, we can deduce > u = s and v = rHence, the points will definitely be equidistant. Please correct me if I am wrong. Yes, your logic works and it's great! Note that r = 1  s AND s = 1  r Since r and s add up to 1, whatever the value of r, value of s will be complementary to that. So r will be 1  s and s will be 1  r.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 21 Jan 2010
Posts: 120

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
19 Apr 2010, 01:48
Awesome. Thanks a bunch



Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 873
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
01 Sep 2010, 18:20
Bunuel, I have a question: How did you know that you had to express the equation in that way? For example, I expressed (based on clue # 2) in this way: \(r^2 + s^2 = (1r)^2 + (1s)^2\) So, I obtain: r + s = 1 The same as clue # 1. How did you know that you had to do in the other way? Thanks!
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html GMAT Club Premium Membership  big benefits and savings



SVP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 2052

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
16 Feb 2012, 20:22
(r,s) and (u,v) will be equidistant from the origin when r^2 + s^2 = u^2 + v^2 Using statement (1), r+s=1 gives us no information about u and v and so is insufficient. Using statement (2), u = 1r and v=1s => r^2 + s^2 = (1r)^2 + (1s)^2 => 2r + 2s  2 = 0 or r + s = 1, which may or may not be true. Insufficient. Combining (1) and (2) is clearly sufficient. (C) is the answer.
_________________
GyanOne [www.gyanone.com] Premium MBA and MiM Admissions Consulting
Awesome Work  Honest Advise  Outstanding Results Reach Out, Lets chat!Email: info at gyanone dot com  +91 98998 31738  Skype: gyanone.services



Intern
Joined: 22 Jan 2012
Posts: 5

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
01 Mar 2012, 23:52
I think it is a simple way to pick up values to solve this question because it is clear that each statement is not sufficient. For example;
for r=2, s=1 we have u=1, v=2 or for r=1, s=0 we have u=0, v=1 and so on. Therefore only if we know both statements, we can talk about the distance. So, the answer is C.



Math Expert
Joined: 02 Sep 2009
Posts: 64314

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
02 Mar 2012, 02:29
ustureci wrote: I think it is a simple way to pick up values to solve this question because it is clear that each statement is not sufficient. For example;
for r=2, s=1 we have u=1, v=2 or for r=1, s=0 we have u=0, v=1 and so on. Therefore only if we know both statements, we can talk about the distance. So, the answer is C. This is not a good question for number picking. Notice that variables are not restricted to integers only, so r+s=1, u=1r and v=1s have infinitely many solutions for r, s, u and v.
_________________



Manager
Joined: 28 Apr 2011
Posts: 83

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
31 Mar 2012, 09:21
best approch is imagine point to be on circumference of same circle. Now radius of circle = use distance formula so use equations in this logic. and get C



Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 179

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
01 Apr 2012, 08:26
question: \(r^2+s^2=u^2+v^2?\)
(a) insufficient because there's no info about u,v. (b) insufficient. plug in numbers to see if it holds: find a 'yes' and then find a 'no'.
\((r,s)=(u,v)=(\frac{1}{2},\frac{1}{2})\) > 'yes' points are equidistant \((r,s)=(0,0\), then \((u,v)=(1,1)\) > 'no' points are not equidistant
(c) together we can even prove it algebraically. from (1) \(s=1r\) and from (2) \(u=1r\). so, \(s=u\) likewise, from (1) \(s=1r\) and from (2) \(s=1v\). so, \(r=v\)
ans: C



Director
Joined: 29 Nov 2012
Posts: 673

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
21 Jan 2013, 04:03
Bunuel 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
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. So the formula used here is different from the distance formula of square root of (x2x1)^2 + (y2y1)^2



Intern
Joined: 02 Mar 2010
Posts: 18

Re: In the rectangular coordinate system, are the points (r,s) and (u,v)
[#permalink]
Show Tags
17 Sep 2014, 14:23
1) Not Suff as no info about u & v. 2) Not suff as 4 variables and 2 equations.
(1) and (2) combined: From Statement (1), r =(1s) = v by definition given in statement (2); and similarly s=(1r)=u by definition given in statement (2). Therefore s=u and r=v. Hence (r,s) and (u,v) represent same point and so have the same distance from origin. SUFF. Correct answer = C.



NonHuman User
Joined: 09 Sep 2013
Posts: 15088

Re: In the rectangular coordinate system, are the points (r,s)
[#permalink]
Show Tags
18 Oct 2019, 04:25
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.
_________________




Re: In the rectangular coordinate system, are the points (r,s)
[#permalink]
18 Oct 2019, 04:25




