GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Nov 2018, 04:46

ISB R1 results on Nov 15:

Join Chat Room for Live Updates


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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2631
Location: New York City
Which of the following points is closest to line y=x?  [#permalink]

Show Tags

New post Updated on: 01 Jul 2012, 06:55
5
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

64% (00:46) correct 36% (00:41) wrong based on 433 sessions

HideShow timer Statistics

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

Originally posted by bmwhype2 on 21 Nov 2007, 07:14.
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: 365
  [#permalink]

Show Tags

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: 552
Re: PS closest point  [#permalink]

Show Tags

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: 805
Schools: University of Chicago, Wharton School
Re: PS closest point  [#permalink]

Show Tags

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
Re: PS closest point  [#permalink]

Show Tags

New post 22 Nov 2007, 00:25
1
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: 112
Re: Which of the following points is closest to line y=x? (2,  [#permalink]

Show Tags

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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50608
Re: Which of the following points is closest to line y=x? (2,  [#permalink]

Show Tags

New post 01 Jul 2012, 06:58
4
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 6083 times ]
As you can see point (2, 1) is the closest to line y=x.

Answer: D.

Hope it helps.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 13 May 2010
Posts: 112
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

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?
Manager
Manager
avatar
Joined: 25 Jun 2012
Posts: 62
Location: India
WE: General Management (Energy and Utilities)
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

New post 04 Jul 2012, 02:41
4
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: 112
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

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.
Manager
Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 198
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

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+

Senior Manager
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 473
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: Which of the following points is closest to line y=x? (2,  [#permalink]

Show Tags

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50608
Re: Which of the following points is closest to line y=x? (2,  [#permalink]

Show Tags

New post 11 Sep 2012, 02:05
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 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?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 431
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

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.

Manager
Manager
avatar
Joined: 23 Jan 2013
Posts: 145
Concentration: Technology, Other
Schools: Berkeley Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

New post 30 Apr 2013, 21:48
1
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: 1745
Concentration: Finance
GMAT ToolKit User
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

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 :)
Director
Director
User avatar
B
Joined: 10 Mar 2013
Posts: 513
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

New post 20 Jul 2015, 07:29
Hi all, why do we consider only a line passing through Quadrants III and I, and not also a line passing through quadrants II and IV (X=-1, Y=-1 etc) ? In this case the answer would be C...
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50608
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

New post 20 Jul 2015, 07:33
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2635
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Which of the following points is closest to line y=x?  [#permalink]

Show Tags

New post 20 Jul 2015, 07:39
BrainLab wrote:
Hi all, why do we consider only a line passing through Quadrants III and I, and not also a line passing through quadrants II and IV (X=-1, Y=-1 etc) ? In this case the answer would be C...


This is as per the question. It talks about y=x and this only passes through I and III quadrants. y=-x will be the line passing through II and IV quadrants.
Director
Director
User avatar
B
Joined: 10 Mar 2013
Posts: 513
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Which of the following points is closest to line y=x?  [#permalink]

Show Tags

New post 20 Jul 2015, 07:43
Engr2012 wrote:
BrainLab wrote:
Hi all, why do we consider only a line passing through Quadrants III and I, and not also a line passing through quadrants II and IV (X=-1, Y=-1 etc) ? In this case the answer would be C...


This is as per the question. It talks about y=x and this only passes through I and III quadrants. y=-x will be the line passing through II and IV quadrants.


Thanks, was a silly mistake... we can not get values (-1,1) in th equiatoin y=x, was just to fast in drawing symmetrical fihures ))...
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

GMAT Club Bot
Which of the following points is closest to line y=x? &nbs [#permalink] 20 Jul 2015, 07:43

Go to page    1   2    Next  [ 21 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.