Find all School-related info fast with the new School-Specific MBA Forum

It is currently 02 Sep 2014, 09:44

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Which of the following points is closest to line y=x?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2770
Location: New York City
Followers: 6

Kudos [?]: 220 [0], given: 4

GMAT Tests User
Which of the following points is closest to line y=x? [#permalink] New post 21 Nov 2007, 07:14
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

58% (01:45) correct 42% (00:24) wrong based on 198 sessions
Which of the following points is closest to line y=x?

A. (2, -1)
B. (2, 4)
C. (-1, 1)
D. (2, 1)
E. (-2, 0)

M12-20
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Jul 2012, 06:55, edited 1 time in total.
Edited the question and added the OA.
Current Student
User avatar
Joined: 31 Aug 2007
Posts: 370
Followers: 1

Kudos [?]: 39 [0], given: 1

GMAT Tests User
 [#permalink] New post 21 Nov 2007, 08:20
looks like (2,1)...just closest to 1:1 ratio...whats the OA?
Director
Director
User avatar
Joined: 08 Jun 2007
Posts: 583
Followers: 1

Kudos [?]: 68 [0], given: 0

GMAT Tests User
Re: PS closest point [#permalink] New post 21 Nov 2007, 20:24
bmwhype2 wrote:
Which of the following points is closest to line y=x?

(2, -1)
(2, 4)
(-1, 1)
(2, 1)
(-2, 0)

How can i solve this with a mathematical approach rather than drawing it out?


Well I am still struggling to find a gmat solution ( nice and easy ) for this. Kept waiting that some one will solve.

Here's my take

Drop a perpendicular from the point to the line y=x. Slope will be -1 for all the perps which are dropped on this line

The point where it hits will be have same x and y coordinates. Assume its a
So a - (-1) / a - 2 = -1 => a + 1 = 2 -a => a = 1 .
Now we can calculate the distance by
sqrt [ ( a - 2 ) ^ 2 + ( a + 1 ) ^2 ] ...no need to take square root , the smallest of the values .
Again few points can be ignored by just viewing on a rough sketch.
Director
Director
User avatar
Joined: 03 May 2007
Posts: 899
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 44 [0], given: 6

GMAT Tests User
Re: PS closest point [#permalink] New post 22 Nov 2007, 00:02
bmwhype2 wrote:
Which of the following points is closest to line y=x?

(2, -1)
(2, 4)
(-1, 1)
(2, 1)
(-2, 0)

How can i solve this with a mathematical approach rather than drawing it out?


D. can be solved by finding the length between each answer option and x=y point.

Also can be found drawing a rough sketch and pointing the points in answer choices.
Intern
Intern
avatar
Joined: 21 Nov 2007
Posts: 11
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: PS closest point [#permalink] New post 22 Nov 2007, 00:25
bmwhype2 wrote:
Which of the following points is closest to line y=x?

(2, -1)
(2, 4)
(-1, 1)
(2, 1)
(-2, 0)

How can i solve this with a mathematical approach rather than drawing it out?


Here is a formula which can be use to canculate the distance between a point (m,n) and a general line L : aX+bY+C=0

d=abs(am+bn+c)/sqrt(a^2+b^2)

Take this question for instance :
L x-y=0 ---> a=1, b=-1
then you can get the distance for the first choice 2*1+(-1)*(-1)+0/sqrt[1^2+(-1)^2)]
Actually for this question you dont need nessisarily to work the distance out to get the smallest one
Manager
Manager
avatar
Joined: 13 May 2010
Posts: 124
Followers: 0

Kudos [?]: 6 [0], given: 4

GMAT Tests User
Re: Which of the following points is closest to line y=x? (2, [#permalink] New post 01 Jul 2012, 06:50
can someone please explain me how you guys solved this question using graphical approach? If someone can post the actual graphic solution, that will be helpful.
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25253
Followers: 3432

Kudos [?]: 25270 [2] , given: 2702

Re: Which of the following points is closest to line y=x? (2, [#permalink] New post 01 Jul 2012, 06:58
2
This post received
KUDOS
Expert's post
teal wrote:
can someone please explain me how you guys solved this question using graphical approach? If someone can post the actual graphic solution, that will be helpful.


Which of the following points is closest to line y=x?

A. (2, -1)
B. (2, 4)
C. (-1, 1)
D. (2, 1)
E. (-2, 0)


Look at the diagram below:
Attachment:
m12-20.png
m12-20.png [ 12.86 KiB | Viewed 2874 times ]
As you can see point (2, 1) is the closest to line y=x.

Answer: D.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 13 May 2010
Posts: 124
Followers: 0

Kudos [?]: 6 [0], given: 4

GMAT Tests User
Re: Which of the following points is closest to line y=x? [#permalink] New post 01 Jul 2012, 07:45
Thanks a lot for getting back. Distance of points from the line (that we need to consider) is the length of the perpendicular dropped on the line from each point? Please confirm. Also, how to get such a good image (with an almost accurate estimate) on the exam scratch pad?
1 KUDOS received
Current Student
avatar
Joined: 25 Jun 2012
Posts: 71
Location: India
WE: General Management (Energy and Utilities)
Followers: 2

Kudos [?]: 38 [1] , given: 15

Re: Which of the following points is closest to line y=x? [#permalink] New post 04 Jul 2012, 02:41
1
This post received
KUDOS
I solved like this :

y=x line is given
=> x-y = 0

now for all the option choice do X-Y operation
1. 2-(-1)=3
2. 2 -4 =-2
3. -1-1=-2
4. 2-1 = 1
5. -2-0 = -2

Clearly option 4 is nearest to 0 which is our equation x=y...

Am I right on this approach?
Manager
Manager
avatar
Joined: 13 May 2010
Posts: 124
Followers: 0

Kudos [?]: 6 [0], given: 4

GMAT Tests User
Re: Which of the following points is closest to line y=x? [#permalink] New post 05 Jul 2012, 19:55
Bunnel, please confirm if Bhavin's approach will always work?

Visual approach worked out fine this time for me, I drew the figure on my pad just like the one Bunnel has drwan......I utilized the square grid of my pad for drawing the graph, it worked out...now I am glad I will not lose this question. Thanks, Bunnel.
Senior Manager
Senior Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 278
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 20 [0], given: 282

Re: Which of the following points is closest to line y=x? [#permalink] New post 07 Aug 2012, 22:04
I think bunuel's approach is the right one for this. I do not know if you can substitute for x and y with the points given as per Bhavinshah's approach!
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Director
Director
avatar
Joined: 24 Aug 2009
Posts: 509
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 9

Kudos [?]: 367 [0], given: 241

Re: Which of the following points is closest to line y=x? (2, [#permalink] New post 10 Sep 2012, 08:13
Bunuel wrote:
teal wrote:
can someone please explain me how you guys solved this question using graphical approach? If someone can post the actual graphic solution, that will be helpful.


Which of the following points is closest to line y=x?

A. (2, -1)
B. (2, 4)
C. (-1, 1)
D. (2, 1)
E. (-2, 0)


Look at the diagram below:
Attachment:
m12-20.png
As you can see point (2, 1) is the closest to line y=x.

Answer: D.

Hope it helps.


Hi bunuel,

Is there any other way to solve this problem apart from drawing perpendicular to the respective points or graphs

Waiting for your response
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25253
Followers: 3432

Kudos [?]: 25270 [0], given: 2702

Re: Which of the following points is closest to line y=x? (2, [#permalink] New post 11 Sep 2012, 02:05
Expert's post
fameatop wrote:
Bunuel wrote:
teal wrote:
can someone please explain me how you guys solved this question using graphical approach? If someone can post the actual graphic solution, that will be helpful.


Which of the following points is closest to line y=x?

A. (2, -1)
B. (2, 4)
C. (-1, 1)
D. (2, 1)
E. (-2, 0)


Look at the diagram below:
Attachment:
m12-20.png
As you can see point (2, 1) is the closest to line y=x.

Answer: D.

Hope it helps.


Hi bunuel,

Is there any other way to solve this problem apart from drawing perpendicular to the respective points or graphs

Waiting for your response


From my point of view the best way to solve this question in to make a diagram as in my post above.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 14

Kudos [?]: 192 [0], given: 11

GMAT ToolKit User GMAT Tests User
Re: Which of the following points is closest to line y=x? [#permalink] New post 05 Jan 2013, 00:33
bmwhype2 wrote:
Which of the following points is closest to line y=x?

A. (2, -1)
B. (2, 4)
C. (-1, 1)
D. (2, 1)
E. (-2, 0)

M12-20


My approach is to draw the points and then the x=y line.

(2,-1) is 3 units away to the right and to the bottom of the line
(2,4) is 2 units away to the top of the line
(-1,1) is 2 units to the left of the line
(2,1) is 1 unit to the bottom and to the right of the line
(-2,0) is 2 units to the right of the lne

Answer: D
_________________

Impossible is nothing to God.

1 KUDOS received
Manager
Manager
avatar
Joined: 23 Jan 2013
Posts: 81
Concentration: Technology, Other
Followers: 1

Kudos [?]: 5 [1] , given: 13

GMAT ToolKit User CAT Tests
Re: Which of the following points is closest to line y=x? [#permalink] New post 30 Apr 2013, 21:48
1
This post received
KUDOS
If the line is ax+by+c =0 and Point ( x1, y1)

Distance = | ax1+ by1 + c | / sqrt( a^2 + b^2 )

Using this formulae one can easily plug in and find out the least distance :)
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1630
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 157 [0], given: 256

GMAT ToolKit User
Re: Which of the following points is closest to line y=x? [#permalink] New post 28 Dec 2013, 07:24
shelrod007 wrote:
If the line is ax+by+c =0 and Point ( x1, y1)

Distance = | ax1+ by1 + c | / sqrt( a^2 + b^2 )

Using this formulae one can easily plug in and find out the least distance :)


I think it is much easier just to draw the points than to apply this formula under real GMAT conditions

Hope you consider it

PS. Is bhavinshah5685 approach valid anyone? Looks nice too

Cheers!
J :)
Re: Which of the following points is closest to line y=x?   [#permalink] 28 Dec 2013, 07:24
    Similar topics Author Replies Last post
Similar
Topics:
Of the following integers, which is the closest divanshuj 2 28 Feb 2010, 09:28
7 Experts publish their posts in the topic Point (1,0) is closest to which of the following lines? A. arvs212 6 11 Aug 2009, 20:24
Point (1, 0) is closest to which of the following lines? y = arjtryarjtry 11 26 Aug 2008, 09:54
Point (1,0) is closest to which of the following lines? y=x bmwhype2 2 01 Nov 2007, 12:28
Which of the following is the closest approximation of pi? GMATT73 5 09 Sep 2006, 05:03
Display posts from previous: Sort by

Which of the following points is closest to line y=x?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.