Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 18:00

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

CEO
Joined: 21 Jan 2007
Posts: 2745
Location: New York City
Followers: 11

Kudos [?]: 942 [0], given: 4

Which of the following points is closest to line y=x? [#permalink]

### Show Tags

21 Nov 2007, 08:14
3
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

64% (01:45) correct 36% (00:38) wrong based on 373 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Jul 2012, 07:55, edited 1 time in total.
Edited the question and added the OA.
Current Student
Joined: 31 Aug 2007
Posts: 369
Followers: 1

Kudos [?]: 143 [0], given: 1

### Show Tags

21 Nov 2007, 09:20
looks like (2,1)...just closest to 1:1 ratio...whats the OA?
Director
Joined: 08 Jun 2007
Posts: 578
Followers: 2

Kudos [?]: 98 [0], given: 0

### Show Tags

21 Nov 2007, 21:24
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
Joined: 03 May 2007
Posts: 875
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 209 [0], given: 7

### Show Tags

22 Nov 2007, 01:02
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
Joined: 21 Nov 2007
Posts: 11
Followers: 0

Kudos [?]: 7 [0], given: 0

### Show Tags

22 Nov 2007, 01:25
1
This post was
BOOKMARKED
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
Joined: 13 May 2010
Posts: 122
Followers: 0

Kudos [?]: 17 [0], given: 4

Re: Which of the following points is closest to line y=x? (2, [#permalink]

### Show Tags

01 Jul 2012, 07:50
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
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106248 [2] , given: 11618

Re: Which of the following points is closest to line y=x? (2, [#permalink]

### Show Tags

01 Jul 2012, 07:58
2
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 [ 12.86 KiB | Viewed 4886 times ]
As you can see point (2, 1) is the closest to line y=x.

Hope it helps.
_________________
Manager
Joined: 13 May 2010
Posts: 122
Followers: 0

Kudos [?]: 17 [0], given: 4

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

01 Jul 2012, 08:45
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
Joined: 25 Jun 2012
Posts: 71
Location: India
WE: General Management (Energy and Utilities)
Followers: 4

Kudos [?]: 119 [3] , given: 17

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

04 Jul 2012, 03:41
3
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
Joined: 13 May 2010
Posts: 122
Followers: 0

Kudos [?]: 17 [0], given: 4

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

05 Jul 2012, 20:55
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
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 260
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 97 [0], given: 282

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

07 Aug 2012, 23:04
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
Joined: 24 Aug 2009
Posts: 504
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 19

Kudos [?]: 735 [0], given: 276

Re: Which of the following points is closest to line y=x? (2, [#permalink]

### Show Tags

10 Sep 2012, 09:13
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.

Hope it helps.

Hi bunuel,

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

_________________

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
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106248 [0], given: 11618

Re: Which of the following points is closest to line y=x? (2, [#permalink]

### Show Tags

11 Sep 2012, 03:05
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.

Hope it helps.

Hi bunuel,

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

From my point of view the best way to solve this question in to make a diagram as in my post above.
_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23
Followers: 26

Kudos [?]: 467 [0], given: 11

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

05 Jan 2013, 01:33
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

_________________

Impossible is nothing to God.

Manager
Joined: 23 Jan 2013
Posts: 172
Concentration: Technology, Other
Schools: Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 48 [1] , given: 41

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

30 Apr 2013, 22:48
1
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
Current Student
Joined: 06 Sep 2013
Posts: 2005
Concentration: Finance
Followers: 68

Kudos [?]: 643 [0], given: 355

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

28 Dec 2013, 08:24
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
Joined: 10 Mar 2013
Posts: 597
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 17

Kudos [?]: 356 [0], given: 200

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

20 Jul 2015, 08:29
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.

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

Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106248 [0], given: 11618

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

20 Jul 2015, 08:33
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...

Have you checked this:

_________________
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2644
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 128

Kudos [?]: 1475 [0], given: 789

Re: Which of the following points is closest to line y=x? [#permalink]

### Show Tags

20 Jul 2015, 08:39
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.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Director
Joined: 10 Mar 2013
Posts: 597
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 17

Kudos [?]: 356 [0], given: 200

Which of the following points is closest to line y=x? [#permalink]

### Show Tags

20 Jul 2015, 08:43
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.

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

Which of the following points is closest to line y=x?   [#permalink] 20 Jul 2015, 08:43
Similar topics Replies Last post
Similar
Topics:
Which of the following points reflect to y=-x at (-3,2)? 2 21 May 2017, 18:00
Which of the following values is closest to 4 18 Mar 2017, 10:34
3 Which of the following points is reflect to y=-x at (-2,1)? 4 20 Feb 2017, 19:23
4 Which of the following points is symmetric with y=x at (-1,-2)? 3 27 Aug 2016, 15:31
17 Point (1,0) is closest to which of the following lines? A. 8 16 Oct 2016, 10:11
Display posts from previous: Sort by