GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 28 Jan 2020, 03:33 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Is point A closer to point (1,2) than to point (2,1) ?

Author Message
TAGS:

### Hide Tags

Manager  Joined: 06 Apr 2010
Posts: 101
Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

2
4 00:00

Difficulty:   65% (hard)

Question Stats: 53% (01:40) correct 47% (01:45) wrong based on 161 sessions

### HideShow timer Statistics

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: 60701
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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 4877 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
_________________
Retired Moderator Joined: 20 Dec 2010
Posts: 1532
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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"
Retired Moderator Joined: 20 Dec 2010
Posts: 1532
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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?
Math Expert V
Joined: 02 Sep 2009
Posts: 60701
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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).
_________________
Director  Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 779
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

point on y=x

mirror image line this is. distance will be always equal.
Director  Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 826
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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
Director  Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 826
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 60701
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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.
_________________
Director  Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 826
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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
Math Expert V
Joined: 02 Sep 2009
Posts: 60701
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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.
_________________
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10023
Location: Pune, India
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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.
_________________
Karishma
Veritas Prep GMAT Instructor

CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3066
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

Answe: Option A
Attachments 1.jpg [ 207.93 KiB | Viewed 2020 times ]

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern  B
Joined: 04 Feb 2018
Posts: 6
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.5
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3066
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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.
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Non-Human User Joined: 09 Sep 2013
Posts: 14004
Re: Is point A closer to point (1,2) than to point (2,1) ?  [#permalink]

### Show Tags

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.
_________________ Re: Is point A closer to point (1,2) than to point (2,1) ?   [#permalink] 27 Nov 2019, 21:42
Display posts from previous: Sort by

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