Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 11 May 2008
Posts: 546

On the coordinate plane is point (0, 0) closer to point (u,
[#permalink]
Show Tags
Updated on: 14 May 2014, 00:50
Question Stats:
28% (01:56) correct 72% (02:01) wrong based on 263 sessions
HideShow timer Statistics
On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ? (1) v + u^2 = 1 (2) v < 0 M2211
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by arjtryarjtry on 28 Aug 2008, 09:27.
Last edited by Bunuel on 14 May 2014, 00:50, edited 4 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.



SVP
Joined: 07 Nov 2007
Posts: 1689
Location: New York

Re: wats this mean?
[#permalink]
Show Tags
Updated on: 29 Aug 2008, 06:27
arjtryarjtry wrote: On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
1.v + u^2 = 1 2. v < 0
OA is A. but sorry, i didnt understand this ... Boss don't post OA .. GIVE A CHANCE TO OTHERS. Distance between (0, 0) and (u, v) = \(sqrt {u^2+v^2 }\) Distance between (0, 0) and (u, v+1) = \(sqrt {u^2+v^2 +2v+1}\) 1.v + u^2 = 1 > u^2 = 1v ( u^2 is alwasy positive.. So.. v must be ve and <1) 2v+1 > ve \(sqrt {u^2+v^2 +2v+1}\) is alwasy less than \(sqrt {u^2+v^2 }\)
_________________
Your attitude determines your altitude Smiling wins more friends than frowning
Originally posted by x2suresh on 28 Aug 2008, 09:45.
Last edited by x2suresh on 29 Aug 2008, 06:27, edited 1 time in total.



Senior Manager
Joined: 29 Mar 2008
Posts: 333

Re: wats this mean?
[#permalink]
Show Tags
28 Aug 2008, 11:33
x2suresh wrote: arjtryarjtry wrote: On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
1.v + u^2 = 1 2. v < 0
OA is A. but sorry, i didnt understand this ... Boss don't post OA .. GIVE CHANCE TO OTHERS. Distance between (0, 0) and (u, v) = \(sqrt {u^2+v^2 }\) Distance between (0, 0) and (u, v+1) = \(sqrt {u^2+v^2 +2v+1}\) 1.v + u^2 = 1 > u^2 = 1v ( u^2 is alwasy positive.. So.. v must be ve and <1) 2v+1 > ve \(sqrt {u^2+v^2 +2v+1}\) is alwasy less than \(sqrt {u^2+v^2 }\) Why will S2 not work? What is the OA?
_________________
To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." Edward Bulwer Lytton



SVP
Joined: 07 Nov 2007
Posts: 1689
Location: New York

Re: wats this mean?
[#permalink]
Show Tags
28 Aug 2008, 11:50
leonidas wrote: x2suresh wrote: arjtryarjtry wrote: On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
1.v + u^2 = 1 2. v < 0
OA is A. but sorry, i didnt understand this ... Boss don't post OA .. GIVE CHANCE TO OTHERS. Distance between (0, 0) and (u, v) = \(sqrt {u^2+v^2 }\) Distance between (0, 0) and (u, v+1) = \(sqrt {u^2+v^2 +2v+1}\) 1.v + u^2 = 1 > u^2 = 1v ( u^2 is alwasy positive.. So.. v must be ve and <1) 2v+1 > ve \(sqrt {u^2+v^2 +2v+1}\) is alwasy less than \(sqrt {u^2+v^2 }\) Why will S2 not work? What is the OA? Hey Nemo, 2v+1 > ve or +ve. v<0 v=1/4 2v+1>0 v=2 2v+1<0
_________________
Your attitude determines your altitude Smiling wins more friends than frowning



Senior Manager
Joined: 29 Mar 2008
Posts: 333

Re: wats this mean?
[#permalink]
Show Tags
28 Aug 2008, 13:26
x2suresh wrote: leonidas wrote: Why will S2 not work? What is the OA?
Hey Nemo, 2v+1 > ve or +ve. v<0 v=1/4 2v+1>0 v=2 2v+1<0 Got it, didn't try a fraction Thanks X2Suresh
_________________
To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." Edward Bulwer Lytton



CEO
Joined: 17 Nov 2007
Posts: 3446
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: wats this mean?
[#permalink]
Show Tags
29 Aug 2008, 01:44
Let's consider each statement carefully: a) On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ? First of all, u does not influence on answer. Therefore, we can restate: On the coordinate line is point (0) closer to point (v) than to point (v + 1) ? Now, we can translate it to language of formulas: v<v+1 Eventually, we can write: v>0.5 b) v + u^2 = 1 > v=1u^2 > v<1 Now, we can restate our problem as following: Does v>0.5 ? 1. v<1 2. v<0 Answer is obviously A.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  Limited GMAT/GRE Math tutoring in Chicago



Current Student
Joined: 11 May 2008
Posts: 546

Re: wats this mean?
[#permalink]
Show Tags
29 Aug 2008, 03:44
thanks , but how did u get 2 from 1?? could not quite understand... walker wrote: Let's consider each statement carefully:
a) On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ? First of all, u does not influence on answer. Therefore, we can restate: On the coordinate line is point (0) closer to point (v) than to point (v + 1) ? Now, we can translate it to language of formulas: v<v+1......(1) Eventually, we can write: v>0.5....(2)
b) v + u^2 = 1 > v=1u^2 > v<1
Now, we can restate our problem as following:
Does v>0.5 ? 1. v<1 2. v<0
Answer is obviously A.



CEO
Joined: 17 Nov 2007
Posts: 3446
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: wats this mean?
[#permalink]
Show Tags
29 Aug 2008, 04:13
Full solution: v<v+1 1) v<1: v<v1 > 0<1 > always false 2) 1<=v<=0: v<v+1 > v>0.5 > 0.5<v<=03) v>0: > v<v+1 > 0<1 always true. Therefore, inequality is true when v>0.5Fast solution: large negative v: inequality is false large positive v: inequality is true switch point v=0.5 > v>0.5
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  Limited GMAT/GRE Math tutoring in Chicago



Senior Manager
Joined: 09 Oct 2007
Posts: 447

Re: wats this mean?
[#permalink]
Show Tags
29 Aug 2008, 09:11
Duh! I went for D but after reading your solutions I realized I forgot to test fractions.



Retired Moderator
Joined: 17 Sep 2013
Posts: 352
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: On the coordinate plane is point (0, 0) closer to point (u,
[#permalink]
Show Tags
Updated on: 14 May 2014, 01:58
An even better way to look at this one: Is \sqrt{u^2+v^2} > \sqrt{u^2+ (v+1)^2} \sqrt{u^2+v^2} > \sqrt{u^2+v^2+2v+1} So \sqrt{u^2+v^2} is equal on both sides so the deciding factor is 2v+1 2v+1>0 or v>1/2 then the right side of the inequality is the greater one I sufficiently tells us...u^2= 1  v...As u^2 can never be negative..we have 1. v > 1 2. v = 1..in both the cases we get the same answer..Suff II. V can be between 0 and 1/2..or <1/2 ...Insuff A it is
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..
Originally posted by JusTLucK04 on 13 May 2014, 15:15.
Last edited by JusTLucK04 on 14 May 2014, 01:58, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 49892

Re: On the coordinate plane is point (0, 0) closer to point (u,
[#permalink]
Show Tags
14 May 2014, 00:51
arjtryarjtry wrote: On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
(1) v + u^2 = 1
(2) v < 0
M2211 On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1x_2)^2+(y_1y_2)^2}\). So basically the question asks whether the distance between the points \((0, 0)\) and \((u, v)\) is less than the distance between the points \((0, 0)\) and \((u, v + 1)\): is \(\sqrt{(u0)^2+(v0)^2}<\sqrt{(u0)^2+(v+10)^2}\)? > is \(\sqrt{u^2+v^2}<\sqrt{u^2+(v+1)^2}\)? > is \(u^2+v^2<u^2+v^2+2v+1\)? > is \(v>\frac{1}{2}\)? (1) \(v + u^2 = 1\) > \(v=1u^2\leq{1}\) > so the answer to the question is NO. Sufficient. (2) \(v<0\). Not sufficient. Answer: A.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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. ,11 Mixed Questions, 12 Fresh Meat 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., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 17 Jul 2013
Posts: 82

Re: On the coordinate plane is point (0, 0) closer to point (u,
[#permalink]
Show Tags
24 Jun 2014, 22:49
How we could have represented this equation on graph ..... and solved by using graph technique
Please help



Math Expert
Joined: 02 Sep 2009
Posts: 49892

Re: On the coordinate plane is point (0, 0) closer to point (u,
[#permalink]
Show Tags
25 Jun 2014, 02:44



Intern
Joined: 25 Jan 2014
Posts: 15
Concentration: Technology, General Management
Schools: Kellogg '17, Booth '17, Ross '17, Haas '17, Stern '17, Duke '17, Anderson '17, Tepper '17, KenanFlagler '17, Marshall '17, LBS '17, Oxford, ISB '17, Georgia Tech '17, Merage '17, Schulich '17, NUS '17, UrbanaChampaign '17, NTU '17, SPJ GMBA '17

Re: On the coordinate plane is point (0, 0) closer to point (u,
[#permalink]
Show Tags
04 Dec 2014, 03:27
Bunuel wrote: arjtryarjtry wrote: On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
(1) v + u^2 = 1
(2) v < 0
M2211 On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1x_2)^2+(y_1y_2)^2}\). So basically the question asks whether the distance between the points \((0, 0)\) and \((u, v)\) is less than the distance between the points \((0, 0)\) and \((u, v + 1)\): is \(\sqrt{(u0)^2+(v0)^2}<\sqrt{(u0)^2+(v+10)^2}\)? > is \(\sqrt{u^2+v^2}<\sqrt{u^2+(v+1)^2}\)? > is \(u^2+v^2<u^2+v^2+2v+1\)? > is \(v>\frac{1}{2}\)? (1) \(v + u^2 = 1\) > \(v=1u^2\leq{1}\) > so the answer to the question is NO. Sufficient. (2) \(v<0\). Not sufficient. Answer: A. hi Bunuel, i could not understand the last step. v=1u^2\leq{1} > so the answer to the question is NO. I did not get how did you infer 'v' lesser than 1 from the last equation??



Math Expert
Joined: 02 Sep 2009
Posts: 49892

Re: On the coordinate plane is point (0, 0) closer to point (u,
[#permalink]
Show Tags
04 Dec 2014, 04:40
arshu27 wrote: Bunuel wrote: arjtryarjtry wrote: On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
(1) v + u^2 = 1
(2) v < 0
M2211 On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1x_2)^2+(y_1y_2)^2}\). So basically the question asks whether the distance between the points \((0, 0)\) and \((u, v)\) is less than the distance between the points \((0, 0)\) and \((u, v + 1)\): is \(\sqrt{(u0)^2+(v0)^2}<\sqrt{(u0)^2+(v+10)^2}\)? > is \(\sqrt{u^2+v^2}<\sqrt{u^2+(v+1)^2}\)? > is \(u^2+v^2<u^2+v^2+2v+1\)? > is \(v>\frac{1}{2}\)? (1) \(v + u^2 = 1\) > \(v=1u^2\leq{1}\) > so the answer to the question is NO. Sufficient. (2) \(v<0\). Not sufficient. Answer: A. hi Bunuel, i could not understand the last step. v=1u^2\leq{1} > so the answer to the question is NO. I did not get how did you infer 'v' lesser than 1 from the last equation?? First of all please read Writing Mathematical Formulas on the Forum. As for your question, we need to find whether \(v>\frac{1}{2}\). (1) gives \(v=1u^2\). Since u^2 (the square of a number) must be nonnegative, then we have that \(v=1(nonnegative)\leq{1}\), therefore v is NOT greater than 1/2, so we have a definite NO answer to the question. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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. ,11 Mixed Questions, 12 Fresh Meat 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., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 23 Nov 2016
Posts: 76
Location: United States (MN)
GPA: 3.51

Re: On the coordinate plane is point (0, 0) closer to point (u,
[#permalink]
Show Tags
09 Mar 2017, 20:56
Bunuel wrote: GmatDestroyer2013 wrote: How we could have represented this equation on graph ..... and solved by using graph technique
Please help This question is not a good candidate for graphic approach. Hi Bunuel, What's wrong with graphing this? It worked for me but perhaps I am missing something? Prompt is asking basically asking if v > .5; graphically: are all possible u,v above the blue line? (1) States that the only solutions lie on the red line. Thus, all possible (u,v) are below the blue line. Sufficient. (2) States that all possible values are below the yellow/brown line. So, we can have some values above the blue line, some below the blue line. Insufficient.
Attachments
gmat.JPG [ 20.98 KiB  Viewed 992 times ]



Senior Manager
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 468
Location: India

Re: On the coordinate plane is point (0, 0) closer to point (u,
[#permalink]
Show Tags
10 Mar 2017, 02:55
for positive value of v, (u,v) will be closer and for negative value of v, (u, v+1) will be closer St 1: v+u^2 = 1. since u^ will always be positive, we can say that v is negative. for negative value of v, v+1 will always be closer to x axis as compared to v. ANSWER St 2: v<0. Hence (u,v+1) will be closer. ANSWER Option D
_________________
GMAT Mentors




Re: On the coordinate plane is point (0, 0) closer to point (u, &nbs
[#permalink]
10 Mar 2017, 02:55






