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Manager  Joined: 06 Apr 2010
Posts: 112
Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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1 00:00

Difficulty:   65% (hard)

Question Stats: 53% (01:39) correct 47% (01:45) wrong based on 192 sessions

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Is point A closer to point (1,2) than to point (2,1) ?

(1) Point A lies on the line y = x
(2) Point A lies on the line y = -x
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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1
udaymathapati wrote:
Is point A closer to point (1,2) than to point (2,1) ?
1.Point A lies on the line y=x
2.Point A lies on the line y= -x

This is question from GMAT club test. Can anyone explain it with picture please?

See the graph below:
Attachment: graph.php.png [ 17.76 KiB | Viewed 4550 times ]

You can see that no matter where on blue line point A is, it will always be equidistant from the given points. So statement (1) is sufficient.

But if A is on the red line we can not say whether it's closer to point (1, 2) than to point (2, 1). Not sufficient.

Answer: A.

Also discussed here: m10-q27-ds-69234.html
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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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1
Is point A closer to point (1,2) than to point (2,1) ?
1.Point A lies on the line y=x
2.Point A lies on the line y= -x

Equation of a line passing through two points (1,2) and (2,1)

$$\frac{1-2}{2-1}=\frac{y-2}{x-1}$$

$$y = -x + 3$$

Slope =-1

1. y=x;
Slope = 1
Thus this line is perpendicular to the line (y = -x+3)

Not only this is perpendicular, but also it bisects the line in two equal parts.

Thus, all points on this line will be equidistant from both points (1,2) and (2,1).

Sufficient.

How to be sure that it is perpendicular bisector;

Let us find the midpoint of (1,2) and (2,1)

(2+1)/2, (1+2)/2

3/2, 3/2

Does this point satisfy the equation y=x; indeed it does.

2. y = -x

This line passes through the origin and goes at 45 degrees in 2nd and 4th quadrant.

So; if we visualize, when x=2, y=-2;
Point 2,1 will be closer

if x=-2, y=2
Point 1,2 will be closer.

Not sufficient.

Ans: "A"
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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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Bunuel wrote:
udaymathapati wrote:
Is point A closer to point (1,2) than to point (2,1) ?
1.Point A lies on the line y=x
2.Point A lies on the line y= -x

This is question from GMAT club test. Can anyone explain it with picture please?

See the graph below:
Attachment:
graph.php.png

You can see that no matter where on blue line point A is, it will always be equidistant from the given points. So statement (1) is sufficient.

But if A is on the red line we can not say whether it's closer to point (1, 2) than to point (2, 1). Not sufficient.

Answer: A.

Also discussed here: m10-q27-ds-69234.html

Bunuel, may I ask how to draw such fine graphical/geometrical figures and attach them? Is there any post where it is discussed in length?
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Posts: 55228
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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fluke wrote:
Bunuel wrote:
udaymathapati wrote:
Is point A closer to point (1,2) than to point (2,1) ?
1.Point A lies on the line y=x
2.Point A lies on the line y= -x

This is question from GMAT club test. Can anyone explain it with picture please?

See the graph below:
Attachment:
graph.php.png

You can see that no matter where on blue line point A is, it will always be equidistant from the given points. So statement (1) is sufficient.

But if A is on the red line we can not say whether it's closer to point (1, 2) than to point (2, 1). Not sufficient.

Answer: A.

Also discussed here: m10-q27-ds-69234.html

Bunuel, may I ask how to draw such fine graphical/geometrical figures and attach them? Is there any post where it is discussed in length?

Usually I use these two online plotters: http://graph-plotter.cours-de-math.eu/ and http://www.wolframalpha.com/

Then save the image and attach to the post (Choose file --> Add the file).
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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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point on y=x

mirror image line this is. distance will be always equal.
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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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Is point A closer to point (1,2) than to point (2,1)?

(1) Point A lies on the line y=x

(2) Point A lies on the line y=−x
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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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My doubt is The answer to above question is A, but I am not convinced.
consider a point on Y = X
(1,1)
Its distance from (1,2) is 1 unit
its distance from (2,1) is 1 unit

For the answer to be A , statement 1 should specifically answer that it is either closer to one of the two points.

Pls corrcct me if i am wrong.
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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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Archit143 wrote:
Is point A closer to point (1,2) than to point (2,1)?

(1) Point A lies on the line y=x

(2) Point A lies on the line y=−x

Please refer to the solutions above.
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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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Hi bunuel
I have checked the post prior to posting the question, but it does not addresses my doubt...can you pls help me with the doubt its posted above.

Regards
Archit
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Posts: 55228
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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Archit143 wrote:
Hi bunuel
I have checked the post prior to posting the question, but it does not addresses my doubt...can you pls help me with the doubt its posted above.

Regards
Archit

First of all, please post your doubts/questions in the thread which already exists.

As for your question:
Archit143 wrote:
My doubt is The answer to above question is A, but I am not convinced.
consider a point on Y = X
(1,1)
Its distance from (1,2) is 1 unit
its distance from (2,1) is 1 unit

For the answer to be A , statement 1 should specifically answer that it is either closer to one of the two points.

Pls corrcct me if i am wrong.

Yes, you are wrong. The question asks whether point A is closer to point (1,2) than to point (2,1). From (1) we have that ANY point on y=x is equidistant from the given points, so the answer to the question is NO.

Hope it's clear.
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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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Archit143 wrote:
My doubt is The answer to above question is A, but I am not convinced.
consider a point on Y = X
(1,1)
Its distance from (1,2) is 1 unit
its distance from (2,1) is 1 unit

For the answer to be A , statement 1 should specifically answer that it is either closer to one of the two points.

Pls corrcct me if i am wrong.

DS questions of this type are often a source of confusion.

There are two types of DS questions:
1. What is the value of x? Here you need to answer the question with one unique value. If you do, the statement(s) is(are) sufficient. Otherwise not.
2. Is x = 4? Here you need to answer the question with either a 'Yes' or a 'No'. Either is acceptable as long as you can take a stand. You could have found that x must be 4 or you could have found that x cannot be 4. If you say 'may be' or 'cannot say', that's when the statement is not sufficient to answer this question.

If you can say that the point will be equidistant from (2, 1) and (1, 2), you can say that 'no, it is not closer to (1, 2)' which is a perfectly acceptable reply. When you say that may be it is closer, may be it is not, that's when the statement is not sufficient.
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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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Answe: Option A
Attachments 1.jpg [ 207.93 KiB | Viewed 1789 times ]

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Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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But why can't we apply the formula of "distance of line from a point" in equation of the line is given!!!!

Posted from my mobile device
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Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

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dipankar0890 wrote:
But why can't we apply the formula of "distance of line from a point" in equation of the line is given!!!!

Posted from my mobile device

dipankar0890
Distance of a point from a line is always the perpendicular distance (Shortest distance) whereas the question doesn't talk about the shortest distance in question.

When the question says that point A is on the line then it never mentions that Points is on the line at shortest distance from given points, therefore point A remains variable anywhere on th eline hence the distance can't be predicted.

I hope this explains your doubt.
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