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Senior Manager
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Question Stats:
65% (01:52) correct
34% (01:00) wrong based on 73 sessions
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 = -1Source: GMAT Club Tests - hardest GMAT questions
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Manager
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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 
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CEO
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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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Director
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A.
I guess, the fastest way is to draw line for each and visualise.
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Manager
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My brain is fried.
Stupid question: How to draw the graphs of these lines?
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Manager
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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
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Manager
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I will go with option A.
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Intern
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I think that Option A is correct.
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Intern
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Here is the formula
The shortest distance from (X1,Y1) to the line ax+by+c=0 is
mod(aX1+bY1+c)/\sqrt{(a2+b2)}
Mod(aX1+bY1+c)/sqrt(a^2+b^2).
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Manager
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Ans:A draw line for each option is fastest way to solve.
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Manager
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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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Senior Manager
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Answer is A. 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 4077 times ]
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Manager
Status: I will not stop until i realise my goal which is my dream too
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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 = -1Source: 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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Bunuel wrote: 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 = -1Source: GMAT Club Tests - hardest GMAT questions A. y=x B. y=1 C. y+x=3 D. x=2 E. x+y=−1 Look at the diagram below: Attachment: m24-34.png As you can see point (1,0) is closest to line y=x. Answer: A. Thanks, Bunuel. A couple things: first, did you graph line B correctly? I see that line A would still be correct. Second, is there any other way to solve this? Maybe something that doesn't involve graphing?
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Intern
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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.
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close
