NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 01:27 It is currently 25 Apr 2024, 01:27
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

On the coordinate plane is point (0, 0) closer to point (u,

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
arjtryarjtry
Current Student
Joined: 11 May 2008
Posts: 377
Own Kudos [?]: 1029 [29]
Given Kudos: 0
Concentration: General
 Q50  V34
Send PM
On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   Updated on: 05 May 2023, 12:14
29
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

34% (02:00) correct 66% (02:03) wrong based on 431 sessions
Hide Show timer Statistics
In the coordinate plane, is the point \((0, 0)\) closer to the point \((u, v)\) than to the point \((u, v + 1)\)?


(1) \(v + u^2 = -1\)

(2) \(v < 0\)

M22-11

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
A

Originally posted by arjtryarjtry on 28 Aug 2008, 09:27.
Last edited by Bunuel on 05 May 2023, 12:14, edited 5 times in total.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92904
Own Kudos [?]: 618875 [9]
Given Kudos: 81594
Send PM
CAT Tests Forum Quiz Mode
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   14 May 2014, 00:51
8
Kudos
1
Bookmarks
Expert Reply
In the coordinate plane, is the point \((0, 0)\) closer to the point \((u, v)\) than to the point \((u, v + 1)\)?

The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).

Essentially, 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 \(\sqrt{(u-0)^2+(v-0)^2} \lt \sqrt{(u-0)^2+(v+1-0)^2}\)?

Is \(\sqrt{u^2+v^2} \lt \sqrt{u^2+(v+1)^2}\)?

Is \(u^2+v^2 \lt u^2+v^2+2v+1\)?

Is \(v \gt -\frac{1}{2}\)?

(1) \(v + u^2 = -1\).

Rearrange: \(v=-1-u^2\). Now, since \(u^2 \ge 0 \), then \(v=-1-u^2 \le -1\), so the answer to the question is NO. Sufficient.

(2) \(v < 0\). Not sufficient.


Answer: A
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10036 [5]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   29 Aug 2008, 01:44
4
Kudos
1
Bookmarks
Expert Reply
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=-1-u^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.
General Discussion
User avatar
x2suresh
Director
Director
Joined: 07 Nov 2007
Posts: 718
Own Kudos [?]: 3077 [4]
Given Kudos: 5
Location: New York
Send PM
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   Updated on: 29 Aug 2008, 06:27
2
Kudos
1
Bookmarks
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 = -1-v ( 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 \(sqrt {u^2+v^2 }\)

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.
User avatar
arjtryarjtry
Current Student
Joined: 11 May 2008
Posts: 377
Own Kudos [?]: 1029 [0]
Given Kudos: 0
Concentration: General
 Q50  V34
Send PM
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   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=-1-u^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.
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10036 [0]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   29 Aug 2008, 04:13
Expert Reply
Full solution:

|v|<|v+1|

1) v<-1: -v<-v-1 --> 0<-1 --> always false
2) -1<=v<=0: -v<v+1 --> v>-0.5 --> -0.5<v<=0
3) v>0: --> v<v+1 --> 0<1 always true.

Therefore, inequality is true when v>-0.5

Fast solution:

large negative v: inequality is false
large positive v: inequality is true
switch point v=-0.5 --> v>-0.5
User avatar
jade3
Manager
Manager
Joined: 19 Nov 2007
Posts: 97
Own Kudos [?]: 801 [2]
Given Kudos: 1
Send PM
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   22 Nov 2009, 05:05
1
Kudos
1
Bookmarks
The question is asking whether u^2+v^2<u^2+ (v+1)^2 => u^2+v^2<u^2+v^2+1+2v

For this happen 1+2v<0

From stem 1 V=-1-u^2; As u^2>0, V<-1 => 1+2V is less than zero. Hence Suff

From stem 2 V<0; but for 1+2V<0 V should be less than -1/2. Hence inSuff

Hence A
User avatar
sriharimurthy
Manager
Manager
Joined: 29 Oct 2009
Posts: 126
Own Kudos [?]: 2860 [2]
Given Kudos: 18
GMAT 1: 750 Q50 V42
Send PM
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   Updated on: 22 Nov 2009, 15:51
2
Kudos
Quote:
I don't know I encountered this question on gmat club test and OA given there was A. Even I reached D.


Question Stem : Which is greater between \(\sqrt{u^2+v^2}\) and \(\sqrt{u^2+v^2+1+2v}\)

St. (1) : \(u^2 = - v - 1\)
Applying this to the question stem we get --> Which is greater between \(\sqrt{v^2 - v - 1}\) and \(\sqrt{v^2+v}\)
It is obvious that \(\sqrt{v^2-v-1}\) will always be greater and therefore always be further away from the origin.
Hence Sufficient.

St. (2) : \(v<0\)
This just tells us that v is negative. However, it is not mentioned that v is an integer. It can be a fraction as well.
Thus, we will get different solutions for v < -0.5, v = -0.5 and v > -0.5. (\(\sqrt{u^2+v^2}\) will be greater than, equal to and less than \(\sqrt{u^2+v^2+1+2v}\) respectively).
Hence Insufficient.

Answer : A

Thus Statement is insufficient.

Originally posted by sriharimurthy on 22 Nov 2009, 05:14.
Last edited by sriharimurthy on 22 Nov 2009, 15:51, edited 1 time in total.
avatar
GmatDestroyer2013
Manager
Manager
Joined: 17 Jul 2013
Posts: 59
Own Kudos [?]: 40 [0]
Given Kudos: 67
Schools: Krannert '17 (S) Smith '17 Weatherhead '17 (II) Katz '17 Rutgers '17 Merage
Send PM
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   24 Jun 2014, 22:49
How we could have represented this equation on graph ..... and solved by using graph technique

Please help
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92904
Own Kudos [?]: 618875 [0]
Given Kudos: 81594
Send PM
CAT Tests Forum Quiz Mode
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   25 Jun 2014, 02:44
Expert Reply
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.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32662
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink] New post   20 Aug 2023, 00:35
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.
GMAT Club Bot
gmatclubot
Re: On the coordinate plane is point (0, 0) closer to point (u, [#permalink]
20 Aug 2023, 00:35
Moderator:
Bunuel
Math Expert
92904 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions