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# M10-27

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:42
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Difficulty:

65% (hard)

Question Stats:

51% (01:13) correct 49% (01:16) wrong based on 104 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 $$y = -x$$

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15 Sep 2014, 23:42
Official Solution:

See the diagram below.

(1) Point $$A$$ lies on the line $$y = x$$. You can see that no matter where on blue line point A is, it will always be equidistant from the given points. Sufficient.

(2) Point $$A$$ lies on the line $$y = -x$$. If A is on the red line we cannot say whether it's closer to point (1, 2) than to point (2, 1). Not sufficient.

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24 May 2016, 04:48
I read somewhere (don't remember the exact source, but must be some GMAT Prep Book) that in GMAT Data Sufficiency the statements can never be contradictory or can never provide conflicting information. That is, it's not possible to have a statement that says X = 0 (or say, X is Odd) while the another statement says X = 1 (or say, X is even).
Just wanted to check that for this particular problem, can the statements be considered contradictory or conflicting?
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24 May 2016, 05:55
jusjmkol740 wrote:
I read somewhere (don't remember the exact source, but must be some GMAT Prep Book) that in GMAT Data Sufficiency the statements can never be contradictory or can never provide conflicting information. That is, it's not possible to have a statement that says X = 0 (or say, X is Odd) while the another statement says X = 1 (or say, X is even).
Just wanted to check that for this particular problem, can the statements be considered contradictory or conflicting?

Hi,
the statements here are NOT contradictory..
Both give you equation of line on which point A lies..
clearly point A is the intersection of these lines which is the origin (0,0)...

Its ONLY that statement (2) does not give you a clear answer as the answer will depend on the place of A....
However in statement (1), the line y=x and both are in the same quadrant and we do not require exact location of A as any point in the line y=x will give you same answer..

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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24 May 2016, 06:32
Thanks Chetan. Got it now.
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Joined: 06 Jul 2014
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20 Jun 2017, 01:56
As per my opinion st 2 is also true.
As per the perpendicular distance between line Ax+By+C =0 and point (m,n) is given by the formula d=∣Am+Bn+C∣ /sq rt (A^2 + B^2)

So as per this both points gives the same distance.
​​
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20 Jun 2017, 02:14
sudheersandu wrote:
As per my opinion st 2 is also true.
As per the perpendicular distance between line Ax+By+C =0 and point (m,n) is given by the formula d=∣Am+Bn+C∣ /sq rt (A^2 + B^2)

So as per this both points gives the same distance.
​​

The solution above, shows the graph, which clearly shows that (2) is not sufficient. Point A can be anywhere on the red graph (y = -x). Different positions of A give different answer to the question.
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02 May 2018, 23:37
1
sudheersandu wrote:
As per my opinion st 2 is also true.
As per the perpendicular distance between line Ax+By+C =0 and point (m,n) is given by the formula d=∣Am+Bn+C∣ /sq rt (A^2 + B^2)

So as per this both points gives the same distance.
​​

just to elaborate more on statement 1 .
Here we have x=y meaning that the coordinate values of x and y are equal and the point (1,2) and (2,1) are mirror images of each other .One point to here is that point A can lie anywhere on the line but its distance will remain same from both the given points as point A will always form an isosceles triangle with the other two points.

Problem with statement is that Point A is not fixed and these two points are not mirror images with respect to the new line hence we have to know the coordinate of point A to determine the distance .Hence this statement is of no value to us .

Hope its clear now .
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11 Jul 2018, 19:16
Bunuel 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 $$y = -x$$

Hi Bunuel,

I have a small doubt here.
Is point $$A$$ closer to point $$(1, 2)$$ than to point $$(2, 1)$$?
Actually per the question which is YES-NO question we will have answer as
YES-A is closer to (1,2) than to (1,2)
NO-A is not closer to (1,2) than to (1,2)=> A is closer to (2,1) than to (1,2)

In solving the question we get to know that A is at same distant from both points but per question it asks A is closer to which point and we got another scenario i.e, A is at same distance.
Pls Explain I did not get the solution is answering the question(Is point $$A$$ closer to point $$(1, 2)$$ than to point $$(2, 1)$$?).
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11 Jul 2018, 19:58
tejyr wrote:
Bunuel 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 $$y = -x$$

Hi Bunuel,

I have a small doubt here.
Is point $$A$$ closer to point $$(1, 2)$$ than to point $$(2, 1)$$?
Actually per the question which is YES-NO question we will have answer as
YES-A is closer to (1,2) than to (1,2)
NO-A is not closer to (1,2) than to (1,2)=> A is closer to (2,1) than to (1,2)

In solving the question we get to know that A is at same distant from both points but per question it asks A is closer to which point and we got another scenario i.e, A is at same distance.
Pls Explain I did not get the solution is answering the question(Is point $$A$$ closer to point $$(1, 2)$$ than to point $$(2, 1)$$?).

(1) gives that A is equidistant from the given two points, which is a NO answer to the question: the point (1, 2) is NOT closer to A than A is to the point (2, 1).
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22 Nov 2018, 06:06
The reflection of (1,2) across the line y=x is the point (2,1)
A is sufficient. Point A is equidistant from Both the given points.
Re: M10-27 &nbs [#permalink] 22 Nov 2018, 06:06
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# M10-27

Moderators: chetan2u, Bunuel

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