|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 21 Jan 2010
Posts: 234
Followers: 3
Kudos [?]:
44
[1] , given: 38
|
In the rectangular coordinate system, are the points (r,s) [#permalink]
 17 Apr 2010, 06:57
1
This post received
KUDOS
Question Stats:
69% (02:14) correct
30% (01:11) wrong based on 8 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
Last edited by Bunuel on 16 Feb 2012, 21:22, edited 1 time in total.
Added the OA
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11583
Followers: 1797
Kudos [?]:
9581
[6] , given: 826
|
Re: GPrep - Coordinate [#permalink]
17 Apr 2010, 07:31
6
This post received
KUDOS
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. Answer: C. Hope it helps.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11583
Followers: 1797
Kudos [?]:
9581
[1] , given: 826
|
Re: GPrep - Coordinate [#permalink]
01 Sep 2010, 19:48
1
This post received
KUDOS
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 = (1-r)^2 + (1-s)^2So, 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=1-r and v=1-s. 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=(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. 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.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11583
Followers: 1797
Kudos [?]:
9581
[1] , given: 826
|
Re: GPrep - Coordinate [#permalink]
21 Jan 2013, 05:09
1
This post received
KUDOS
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=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.
Answer: C.
Hope it helps. So the formula used here is different from the distance formula of square root of (x2-x1)^2 + (y2-y1)^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_1-x_2)^2+(y_1-y_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.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 21 Jan 2010
Posts: 234
Followers: 3
Kudos [?]:
44
[0], given: 38
|
Re: GPrep - Coordinate [#permalink]
19 Apr 2010, 02:48
Awesome. Thanks a bunch 
|
|
|
|
|
|
SVP
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1756
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 50
Kudos [?]:
145
[0], given: 108
|
Re: GPrep - Coordinate [#permalink]
01 Sep 2010, 19:20
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 = (1-r)^2 + (1-s)^2So, 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: my-ir-logbook-diary-133264.html
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 558
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 8
Kudos [?]:
63
[0], given: 212
|
Rectangular co-ordinate system [#permalink]
16 Feb 2012, 17:26
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 As the OA is not provided I think the answer should be C. I got this by substituting the values of r and s from statement 1 into statement 2. Any thoughts guys please?
_________________
Best Regards,
E.
MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
|
|
|
|
|
|
Director
Status:
Joined: 24 Jul 2011
Posts: 504
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 37
Kudos [?]:
162
[0], given: 9
|
Re: Rectangular co-ordinate system [#permalink]
16 Feb 2012, 21:22
(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 = 1-r and v=1-s => r^2 + s^2 = (1-r)^2 + (1-s)^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.
_________________
Free profile evaluation by top b-school alumni: email us at info@gyanone.com
B-school application service http://www.gyanone.com/appone.html
[b]Visit our blog: www.gyanone.com/blog
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11583
Followers: 1797
Kudos [?]:
9581
[0], given: 826
|
Re: Rectangular co-ordinate system [#permalink]
16 Feb 2012, 21:24
|
|
|
|
|
|
Intern
Joined: 22 Jan 2012
Posts: 6
Followers: 0
Kudos [?]:
0
[0], given: 1
|
Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
02 Mar 2012, 00:52
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.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11583
Followers: 1797
Kudos [?]:
9581
[0], given: 826
|
Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
02 Mar 2012, 03:29
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=1-r and v=1-s have infinitely many solutions for r, s, u and v.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 28 Apr 2011
Posts: 188
Followers: 0
Kudos [?]:
3
[0], given: 6
|
Re: In the rectangular coordinate system, are the points (r,s) [#permalink]
31 Mar 2012, 10:21
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 
|
|
|
|
|
|
Senior Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 271
Location: Pakistan
Concentration: Strategy, Marketing
GMAT 1: 680 Q46 V37
GMAT 2: Q V
Followers: 13
Kudos [?]:
459
[0], given: 48
|
rectangular coordinate system [#permalink]
01 Apr 2012, 09:26
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=1-r and from (2) u=1-r. so, s=ulikewise, from (1) s=1-r and from (2) s=1-v. so, r=vans: C
_________________
press +1 Kudos to appreciate posts
Download Valuable Collection of Percentage Questions (PS/DS)
|
|
|
|
|
|
Senior Manager
Joined: 29 Nov 2012
Posts: 294
Followers: 1
Kudos [?]:
12
[0], given: 248
|
Re: GPrep - Coordinate [#permalink]
21 Jan 2013, 05:03
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=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.
Answer: C.
Hope it helps. So the formula used here is different from the distance formula of square root of (x2-x1)^2 + (y2-y1)^2
|
|
|
|
|
|
|
Re: GPrep - Coordinate
[#permalink]
21 Jan 2013, 05:03
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
In the rectangular coordinate system, are the points (r,s)
|
ceg2002 |
1 |
24 Aug 2004, 15:27 |
|
|
|
|
In the rectangular coordinate system, are the points (r,s)
|
ellisje22 |
3 |
04 Jan 2006, 19:00 |
|
|
|
|
In the rectangular coordinate system, are the points (r,s)
|
mrmikec |
6 |
15 Jun 2006, 01:12 |
|
|
|
|
in the rectangular coordinate system, are the points (r,s)
|
el1981 |
1 |
17 Feb 2008, 17:21 |
|
|
|
|
In the rectangular coordinate system, are the points (r,s)
|
japped187 |
4 |
04 May 2008, 21:33 |
|
|
|
|
|
|
close
