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

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

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02 Mar 2011, 06:10
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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
[Reveal] Spoiler: OA
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Re: Is point A closer to point (1,2) than to point (2,1) ? [#permalink]

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02 Mar 2011, 06:23
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Expert's post
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 3283 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.

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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02 Mar 2011, 06:30
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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02 Mar 2011, 06:41
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.

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

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02 Mar 2011, 06:45
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.

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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19 May 2011, 02:49
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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03 Feb 2013, 13:39
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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03 Feb 2013, 13:42
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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03 Feb 2013, 14:12
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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03 Feb 2013, 16:22
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
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Re: Is point A closer to point (1,2) than to point (2,1) ? [#permalink]

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04 Feb 2013, 04:10
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

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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04 Feb 2013, 21:08
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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17 Sep 2014, 21:01
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Re: Is point A closer to point (1,2) than to point (2,1) ? [#permalink]

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28 Oct 2014, 05:17
Answe: Option A
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Re: Is point A closer to point (1,2) than to point (2,1) ?   [#permalink] 28 Oct 2014, 05:17
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