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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

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

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

Show Tags

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.

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 4768 times ]

As you can see point (2, 1) is the closest to line y=x.

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

Show Tags

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?

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

Show Tags

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.

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

Show Tags

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+

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

Show Tags

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

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.
_________________

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

Show Tags

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

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

Show Tags

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 !

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...

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.
_________________

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

Show Tags

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 !

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...