M10: Q27 - DS

balboa · **Posted:** Fri Aug 22, 2008 2:42 pm

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

A

Source: GMAT Club Tests - hardest GMAT questions

Bunuel · **Posted:** Tue Sep 07, 2010 5:33 am

balboa 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

[Reveal] Spoiler: OA

A

Source: GMAT Club Tests - hardest GMAT questions

See the graph below:

Attachment:

graph.php.png [ 17.76 KiB | Viewed 2340 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.

Bunuel · **Posted:** Tue Sep 07, 2010 7:52 pm

varun2410 wrote:

why ans is not D,from both equ. ans is NO .

For (2): point A is on the red line. Now, if point A is in the II quadrant then it will be closer to point (1, 2) than to point (2, 1), so answer wold be YES BUT if point A is in the IV quadrant (or at the origin) then it won't be closer to point (1, 2) than to point (2, 1), so answer wold be NO. Two different answers. Not sufficient.

Bunuel · **Posted:** Tue Sep 14, 2010 10:22 am

supernth wrote:

I thought it was that in DS the statements will never contradict each other...and in this case the only time that does not happen is if the point is at the origin..am i not understanding this problem correctly?

Yes, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Now, if we consider 2 statements together we'll get that as point A lies on both blue and red lines then it must be at the origin (intersection point of these 2 lines).

dk94588 · **Posted:** Fri Aug 22, 2008 3:02 pm

E because even though you can tell that the point is within a line, there is no way of telling where the point is exactly; ant he line itself is not on either side of the points, it is directly in the middle and equidistant from both points. therefore it is impossible to tell how far it would be to either other point.

dk94588 · **Posted:** Sat Aug 23, 2008 9:27 am

Act maybe A, because if A is on y=x then A must be equidistant from both points, which does answer the question in an outside the box way, someone else please put in your input.

GMAT2010 · **Posted:** Fri Sep 05, 2008 11:19 am

I say C because if x=y and -x=y, only possible point is the origin. Therefore, they're both equal distance from the origin and sufficient to answer the question.

any thoughts?

dk94588 · **Posted:** Sat Sep 06, 2008 1:29 pm

good one

Dauren · **Posted:** Wed Dec 03, 2008 12:46 pm

A is sufficient, since the point will always be equdistanat, to the qustion : Is A closer (2,1) than to (1,2) we can answer NO.

kalrac · **Posted:** Tue Sep 07, 2010 4:18 am

good one.

abarasia · **Posted:** Tue Sep 07, 2010 5:13 am

Guys the answer is A)...

soumanag · **Posted:** Tue Sep 07, 2010 6:07 am

stm1. point A lies on the line y=x
Solution is 0,0/1,1 / 2,2 / 3,3 / ....................... -1,-1/ -2,-2
either both X&Y are positive with same value / X&Y are negative with same value. distance between A(X,Y) and point (1,2) = A(X,Y)and point (2,1).
Sufficient
stm1. point A lies on the line y=-x
Solution is 0,0 / 1,-1 / 2,-2 .................... -1,1 / -2,2

Taking A(0,0) distance between A and both the given points is \sqrt{5} - equidistant
taking A(-1,1) distance between A & (1,2) = \sqrt{5}
Distance between A & (2,1)= 3
Not equidistant.
Insufficient.

Answer: A

varun2410 · **Posted:** Tue Sep 07, 2010 7:43 pm

why ans is not D,from both equ. ans is NO .

rahuljaiswal · **Posted:** Tue Sep 07, 2010 9:33 pm

Bunuel wrote:

balboa 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

[Reveal] Spoiler: OA

A

Source: GMAT Club Tests - hardest GMAT questions

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.

Nice Explanantion...I got my approach right by drawing the diagram..Since y=x was equidistant from the given points, therefore got down to ans options A & D...though i missed drawing the y=-x line in the 2nd Quadrant, thus thought the ans to be D....that opened my eyes!! :D

Kudos + 1, atta boy!!

prabu · **Posted:** Tue Sep 07, 2010 10:38 pm

Its A.. we are sure when y=x the point a is always equi-distance..
But in case of option:2 -- its not possible

/Prabu

BlitzHN · **Posted:** Tue Sep 07, 2010 11:56 pm

ans is A. I also followed Bunuel's method.

dkverma · **Posted:** Wed Sep 08, 2010 2:16 am

A is sufficient.

gtr022001 · **Posted:** Wed Sep 08, 2010 9:36 pm

Bunuel wrote:

balboa 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

[Reveal] Spoiler: OA

A

Source: GMAT Club Tests - hardest GMAT questions

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.

Nice approach, my graph didn't look as neat as Bunuel's, so i didn't visualize it correctly...

samark · **Posted:** Sat Sep 11, 2010 7:05 am

Bunuel, you are a champ in quant. I salute u!

sahilkhurana06 · **Posted:** Sat Sep 11, 2010 6:20 pm

A line is a collection of points joined together.So how can you guys be so sure about the exact location of point A.It can be anywhere on the line x=y and x=-y.In both cases,the distance will vary accordingly.

But if we combine the two fact statements,we can only get one value A(0,0) and thus we can have a unique solution that point (1,2) is closer than point (2,1).

Hence the correct answer should be C.

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