Is point A closer to point (1,2) than to point (2,1) ? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 01:38

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

CEO
Joined: 21 Jan 2007
Posts: 2756
Location: New York City
Followers: 11

Kudos [?]: 860 [0], given: 4

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

### Show Tags

15 Dec 2007, 13:48
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

46% (01:55) correct 54% (01:13) wrong based on 80 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Is there an algebraic/formula approach to this

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-point-a-closer-to-point-1-2-than-to-point-110262.html
[Reveal] Spoiler: OA
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 550

Kudos [?]: 3565 [0], given: 360

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

### Show Tags

15 Dec 2007, 14:22
(incorrect. Sorry guys, I misread the question. Perhaps, I'm too sleepy )
D

The geometrical approach is easer and faster for me.
a pure algebraic approach seems to be too unwieldy.

some simpler algebraic approach.

1. y=x.

we try to shift line to the a new place that a new line goes through our points.

point (1,2): y=x+1, shift is equal 1 to right
point (2,1): y=x-1, shift is equal 1 to left
so, points are equidistant.
SUFF.

2. y=-x

we try to make the same procedure with shifts.

point (1,2): y=-x+3, shift is equal 3 to right
point (2,1): y=-x+3, shift is equal 3 to right
so, points are equidistant.
SUFF.

Last edited by walker on 15 Dec 2007, 14:30, edited 1 time in total.
Intern
Joined: 12 Nov 2007
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 0

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

### Show Tags

15 Dec 2007, 14:24
Answer A is right.

The best way to approach this is to draw the points and the lines in a cartesian plane.
With condition 1, each point on the line is equally distant from both the points, therefore it is SUFFICIENT to answer NO

With condition 2, it is simplt to visualize the some points on the line are closer to (1,2) and other points are closer to (2,1)
SVP
Joined: 29 Aug 2007
Posts: 2492
Followers: 68

Kudos [?]: 736 [1] , given: 19

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

### Show Tags

29 May 2009, 08:39
1
KUDOS
bmwhype2 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

Is there an algebraic/formula approach to this

A should be it.

1. If point A lies on the line y=x, any point on this line has equal value for x and y and both are either positive or negative. Lets say point A lies on (4, 4).

i. The distance between A and (1, 2 ) = Sqrt {(4-1)^2 + (4-2)^2} = Sqrt {9 + 4 } = Sqrt (13)
ii. The distance between A and (2, 1 ) = Sqrt {(4-2)^2 + (4-1)^2} = Sqrt {4 + 9} = Sqrt (13)
Both are same.

If point A lies on (-3, -3).

i. The distance between A and (1, 2 ) = Sqrt {(-3-1)^2 + (-3-2)^2} = Sqrt (41)
ii. The distance between A and (2, 1 ) = Sqrt {(-3-2)^2 + (-3-1)^2} = Sqrt (41)

Both are equidistance. Suff..

2. If point A lies on the line y=-x, any point other than (0, 0) on this line has different values for x and y i.e. if x is +ve, y is -ve and vice versa. So any point on the line y = -x is not equidistance from point (1,2) and (2,1).

Lets say point A lies on (4, -4).

i. The distance between A and (1, 2 ) = Sqrt {(4-1)^2 + (-4-2)^2} = Sqrt {9 + 36 } = Sqrt (45)
ii. The distance between A and (2, 1 ) = Sqrt {(4-2)^2 + (-4-1)^2} = Sqrt {4 + 25} = Sqrt (29)

So these two points are not equidistance from A. NSF. Hence only A is correct.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Senior Manager
Joined: 27 Aug 2007
Posts: 253
Followers: 1

Kudos [?]: 12 [0], given: 0

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

### Show Tags

30 May 2009, 07:10
Clearly A.

Totally agree, it is hard to look up even simple tricks when you sleepy.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13535
Followers: 577

Kudos [?]: 163 [0], given: 0

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

### Show Tags

17 Sep 2014, 02:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36624
Followers: 7103

Kudos [?]: 93604 [0], given: 10582

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

### Show Tags

17 Sep 2014, 02:32
bmwhype2 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

Is there an algebraic/formula approach to this

See the graph below:

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-point-a-closer-to-point-1-2-than-to-point-110262.html
_________________
Re: Is point A closer to point (1,2) than to point (2,1) ?   [#permalink] 17 Sep 2014, 02:32
Similar topics Replies Last post
Similar
Topics:
2 N and P are points on the number line below 20. Is P closer to 10 than 2 29 Jul 2016, 09:33
3 Points A, B, and C are points on a circle with a radius of 6. Point D 4 08 Jun 2016, 11:09
3 Is point A closer to point (1,2) than to point (2,1) ? 13 02 Mar 2011, 05:10
6 On the coordinate plane, is point (u,v) closer to point 18 21 Nov 2009, 07:25
9 On the coordinate plane is point (0, 0) closer to point (u, 16 28 Aug 2008, 08:27
Display posts from previous: Sort by

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.