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# M24#34

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Senior Manager
Joined: 20 Feb 2008
Posts: 295
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross

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29 Nov 2008, 00:19
Point $$(1, 0)$$ is closest to which of the following lines?

(A) $$y = x$$
(B) $$y = 1$$
(C) $$y + x = 3$$
(D) $$x = 2$$
(E) $$x + y = -1$$

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions
Intern
Joined: 06 May 2010
Posts: 8

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06 May 2010, 15:42
3
KUDOS
Here is the formula

The shortest distance from (X1,Y1) to the line ax+by+c=0 is

mod(aX1+bY1+c)/\sqrt{(a$$2+b2$$)}

Mod(aX1+bY1+c)/sqrt(a^2+b^2).
Senior Manager
Joined: 21 Dec 2009
Posts: 264
Location: India

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20 May 2010, 07:28
3
KUDOS

The distance from a point (m, n) to the line Ax + By + C = 0 is given by:
Attachments

Image21-summary2.jpg [ 5.39 KiB | Viewed 7828 times ]

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Cheers,
SD

SVP
Joined: 29 Aug 2007
Posts: 2473

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29 Nov 2008, 12:40
1
KUDOS
ventivish wrote:
Point $$(1, 0)$$ is closest to which of the following lines?

(C) 2008 GMAT Club - m24#34

* $$y = x$$
* $$y = 1$$
* $$y + x = 3$$
* $$x = 2$$
* $$x + y = -1$$

Agree with A.
The shortest distance between point (1, 0) and the equation y = x is 1/sqrt(2).

Any of the equation other than y = x has distance more than 1/sqrt(2). A drawing of graph would have much clear visualization.
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Manager
Joined: 18 Nov 2008
Posts: 116

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29 Nov 2008, 05:48
A

We can get this answer by drawing the lines of equations given in answer choices and visually comparing the distances.

But can anyone find the algebraic way to solve this kind of questions? Of course, if it won't take 18 min, to calculate
Manager
Joined: 12 Aug 2008
Posts: 61

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05 Sep 2009, 22:37
My brain is fried.

Stupid question: How to draw the graphs of these lines?
Manager
Joined: 27 Feb 2010
Posts: 105
Location: Denver

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06 May 2010, 06:11
sid3699 you will have to substitue values for X and Y and point those values on the X and Y graph.

example
for A) i.e y = x

X Y
0 0
1 1
2 2
-1 -1
-2 -2

For B, Y =1 the line is parallel to X axis at y = 1
Manager
Joined: 04 Dec 2009
Posts: 70
Location: INDIA

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06 May 2010, 20:13
Ans:A draw line for each option is fastest way to solve.
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Manager
Joined: 23 Nov 2009
Posts: 89
Schools: Wharton..:)

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07 May 2010, 01:30
if u want to do this question by elimination see x=1 and y =1 give the same answers , so both gets eliminated ..ofcourse A is the ans ..
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Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 229
Schools: Johnson '15

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14 May 2012, 06:13
ventivish wrote:
Point $$(1, 0)$$ is closest to which of the following lines?

(A) $$y = x$$
(B) $$y = 1$$
(C) $$y + x = 3$$
(D) $$x = 2$$
(E) $$x + y = -1$$

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

i got the ANSWER by drawing the lines in a sheet and then finding out...is there any other easier way plz... i want to lessen the number of calculations i do...help required from the SMEs here
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Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

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Math Expert
Joined: 02 Sep 2009
Posts: 39702

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15 May 2013, 08:41
ventivish wrote:
Point $$(1, 0)$$ is closest to which of the following lines?

(A) $$y = x$$
(B) $$y = 1$$
(C) $$y + x = 3$$
(D) $$x = 2$$
(E) $$x + y = -1$$

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

Point (1,0) is closest to which of the following lines?

A. y=x
B. y=1
C. y+x=3
D. x=2
E. x+y=−1

Look at the diagram below:
Attachment:

Untitled.png [ 15.99 KiB | Viewed 2235 times ]
As you can see point (1,0) is closest to line y=x.

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Intern
Joined: 04 Jul 2012
Posts: 6

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15 May 2013, 12:33
Just try to eliminate the answers ...

for x = 1 , the distance is 1 , so with y =1 so both of these are not answers and rest two line equations except y=x are far from the point (1,0). so left with option y=x.

may need to calculate the distance in other examples.
Manager
Joined: 20 Oct 2013
Posts: 66

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30 Apr 2014, 02:26
HI Bunnel

when the equation is y=1 then why is your line on the graph passing through y=2... also when we have x=2... the distance between y=x line and dst between x=2 line are same.
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Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21

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30 Apr 2014, 03:27
nandinigaur wrote:
HI Bunnel

when the equation is y=1 then why is your line on the graph passing through y=2... also when we have x=2... the distance between y=x line and dst between x=2 line are same.

Hi,

The question asks out of all the lines in the option A to E, Which is closest to Point (1,0).

Yes, the line should pass through Y=1. The distance between the point (1,0) and line Y=X and between Point (1,0) and line X=2 can be same so this tells you surely these 2 options are not the answers. You can eliminate these answer choices

Also Distance of Point (x1,y1) from a line $$ax+by+c=0$$ can be found using the formulae

|$$(ax1+by1+c)/$$$$\sqrt{a^2+b^2}$$ |
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Manager
Joined: 20 Oct 2013
Posts: 66

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30 Apr 2014, 03:33
but the answer is A (y=x)... I am again confused.
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Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21

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30 Apr 2014, 04:54
nandinigaur wrote:
but the answer is A (y=x)... I am again confused.

Refer to the figure below. Pt(1,0) is closest to Blue line which is y=x and hence ans is A. The distance from line x=2 is more as can be seen in the graph.
Attachments

m 1.png [ 11.39 KiB | Viewed 2792 times ]

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Manager
Joined: 20 Oct 2013
Posts: 66

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30 Apr 2014, 06:34
Thanks.... i got it...I guess I am so stressed that i am not even getting the easy explanations
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Math Expert
Joined: 02 Sep 2009
Posts: 39702

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01 May 2014, 09:27
nandinigaur wrote:
HI Bunnel

when the equation is y=1 then why is your line on the graph passing through y=2... also when we have x=2... the distance between y=x line and dst between x=2 line are same.

Edited the graph of y=1.
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Manager
Joined: 20 Oct 2013
Posts: 66

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01 May 2014, 11:07
Thanks Bunnel. I understood!.
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Intern
Joined: 22 Jun 2013
Posts: 42

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01 May 2014, 22:09
Here is how i did this Question without using the Distance formula

After drawing all the lines
We can see tht there is a close call between
(A) $$y = x$$
(B) $$y = 1$$
(D) $$x = 2$$

Rest 2 could be eliminated just by seeing that their distance would be greater than the above 3 lines.

As for
(B) $$y = 1$$
(D) $$x = 2$$

Both have Perpendicular Distance =1 from the point $$(1, 0)$$
Now we can guess that since we have to find the shortest distance & no 2 options can have the minimum value & be the answer
Thus $$y = x$$ will be the answer
Re: M24#34   [#permalink] 01 May 2014, 22:09
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# M24#34

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