Author 
Message 
TAGS:

Hide Tags

MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 5666
Location: India
City: Pune
GPA: 3.4
WE: Business Development (Manufacturing)

On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
13 May 2013, 09:16
Question Stats:
46% (01:38) correct 54% (01:44) wrong based on 176 sessions
HideShow timer Statistics
Question Source : My own questionOn the x y plane, there are 8 points of which 4 are collinear. How many straight lines can be formed by joining any 2 points from the 8 points ? A) 28 B) 22 C) 20 D) 23 E) 56 OA and OE after some discussion. +1 Kudo for Each correct and Detailed explanationRegards Narenn
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Chances of Getting Admitted After an Interview [Data Crunch]
Must Read Forum Topics Before You Kick Off Your MBA Application
New GMAT Club Decision Tracker  Real Time Decision Updates



Manager
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 122
Location: India
Concentration: General Management, Technology
GPA: 3.5
WE: Web Development (Computer Software)

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
13 May 2013, 09:47
Narenn wrote: Question Source : My own question
On the x y plane, there are 8 points of which 4 are collinear. How many straight lines can be formed by joining any 2 points from the 8 points ?
A) 28 B) 22 C) 20 D) 23 E) 56
OA and OE after some discussion. +1 Kudo for Each correct and Detailed explanation
Regards
Narenn I believe the answer should be 23 lines i.e [D]The approach taken by me would be simple counting: 1. We can always say that one line is to pass though the collinear points, let the names be A, B, C and D. 2. The other four points are scattered under the xy plane. Hence Each point can form 4 lines with the A,B,C and D. Hence, the total lines would be 16. 3. Finally, the total number of lines between the 4 noncollinear points would be the same as the 4C2 i.e 6. I am assuming here the rest of points are noncollinear and no line can also be drawn among any 3 of them. Hence the total comes to be 23. Hope I am correct! Regards, Arpan
_________________
Feed me some KUDOS! *always hungry*
My Thread : Recommendation Letters



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1076
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
13 May 2013, 09:53
Each line is defined by two points. 4 points are collinear => 1 line passes through those. Now each of those points form 5 line => 4 lines with the "out" points and 1 line is the common one but this is counted (the common) so we just add 4(point)*4(lines)=16 to the sum. Finally the 4 points "out" of the common line form 4C2 = 6 different lines 1+16+6=23 totals
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
13 May 2013, 11:23
My answer is A 28.(quite skeptical).
Let the 4 collinear points be A,B,C,D. then I can join AB as 1 line, BC as 1 line,CD as 1 line. AC as 1 line. AD as 1, BC,CD as 2 more. Giving a total of 6 lines.(1) My reasoning here is question says the number of line that CAN be formed by joining any 2 points. So all the above lines can be treated as different lines between 2 points. Like line AD passes through points B and C but in essence it is a different line to BC or CD.
Next each non collinear point will have 1 passing through A,B,C and D..hence all 4 non collinear pints will in total have 16 lines.(2)
And between the 4 non collinear we can for 6 lines.(4C2) or you can visualise these 4 points to be the corners of a square so you will have 4 sides and 2 diagonals. total 6 lines.(3)
hence total number of lines are (1)+(2)+(3) = 6+16+6=28.



Manager
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 122
Location: India
Concentration: General Management, Technology
GPA: 3.5
WE: Web Development (Computer Software)

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
13 May 2013, 11:27
mdbharadwaj wrote: My answer is A 28.(quite skeptical).
Let the 4 collinear points be A,B,C,D. then I can join AB as 1 line, BC as 1 line,CD as 1 line. AC as 1 line. AD as 1, BC,CD as 2 more. Giving a total of 6 lines.(1) My reasoning here is question says the number of line that CAN be formed by joining any 2 points. So all the above lines can be treated as different lines between 2 points. Like line AD passes through points B and C but in essence it is a different line to BC or CD.
Next each non collinear point will have 1 passing through A,B,C and D..hence all 4 non collinear pints will in total have 16 lines.(2)
And between the 4 non collinear we can for 6 lines.(4C2) or you can visualise these 4 points to be the corners of a square so you will have 4 sides and 2 diagonals. total 6 lines.(3)
hence total number of lines are (1)+(2)+(3) = 6+16+6=28. Umm mdbharadwaj don't you think the 6 linesegments joining the collinear points can actually considered to be one unique line. If we are not considering unique lines, then the number is bound to increase significantly. Regards, Arpan
_________________
Feed me some KUDOS! *always hungry*
My Thread : Recommendation Letters



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
13 May 2013, 11:41
arpanpatnaik wrote: mdbharadwaj wrote: My answer is A 28.(quite skeptical).
Let the 4 collinear points be A,B,C,D. then I can join AB as 1 line, BC as 1 line,CD as 1 line. AC as 1 line. AD as 1, BC,CD as 2 more. Giving a total of 6 lines.(1) My reasoning here is question says the number of line that CAN be formed by joining any 2 points. So all the above lines can be treated as different lines between 2 points. Like line AD passes through points B and C but in essence it is a different line to BC or CD.
Next each non collinear point will have 1 passing through A,B,C and D..hence all 4 non collinear pints will in total have 16 lines.(2)
And between the 4 non collinear we can for 6 lines.(4C2) or you can visualise these 4 points to be the corners of a square so you will have 4 sides and 2 diagonals. total 6 lines.(3)
hence total number of lines are (1)+(2)+(3) = 6+16+6=28. Umm mdbharadwaj don't you think the 6 linesegments joining the collinear points can actually considered to be one unique line. If we are not considering unique lines, then the number is bound to increase significantly. Regards, Arpan I thought of that, however the questions asks for the number of line segments that can be formed between any 2 points. Consider numbers 1,2,3,4 on the number line. So line 12 is different from line 34. 12 is an unique line between points 1 and 2 so is 34. And the number doesn't increase significantly , as there will be a maximum of 28 lines. Because if we consider the line joining the 4 collinear points to be 1 single line or to be 6 different lines, the number of lines between the the non collinear points themselves and the collinear points will not change. there will be 16+6 = 22 lines only. Hope I got my point across.



Manager
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 122
Location: India
Concentration: General Management, Technology
GPA: 3.5
WE: Web Development (Computer Software)

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
13 May 2013, 12:00
mdbharadwaj wrote: I thought of that, however the questions asks for the number of line segments that can be formed between any 2 points. Consider numbers 1,2,3,4 on the number line. So line 12 is different from line 34. 12 is an unique line between points 1 and 2 so is 34. And the number doesn't increase significantly , as there will be a maximum of 28 lines. Because if we consider the line joining the 4 collinear points to be 1 single line or to be 6 different lines, the number of lines between the the non collinear points themselves and the collinear points will not change. there will be 16+6 = 22 lines only. Hope I got my point across. Lemme just clarify my idea over this. Please refer to my *supremely sloppy* paintwork attached (Apologize for that ). You can see, that A, B and C lie on the line L. Now As the question states: Quote: How many straight lines can be formed by joining any 2 points from the 8 points ? Now, If I am to consider a straight line passing through A and B, it would be L. Again if I am to consider a straight line passing through B and C, it would be L. Same is the case for A and C as well. The AB, BC and CA are segments. L is the only unique straight line passing through the collinear points. Getting back to the question, you are spoton for the 16 and 6 values. After adding the one line that passes through the collinear points, I believe you have the answer! Hope I am correct! Mods please verify! Regards, Arpan **edited for a typo! sorry!
Attachments
image.png [ 4.66 KiB  Viewed 9572 times ]
_________________
Feed me some KUDOS! *always hungry*
My Thread : Recommendation Letters



Intern
Joined: 05 Mar 2013
Posts: 44
Location: India
Concentration: Entrepreneurship, Marketing
GMAT Date: 06052013
GPA: 3.2

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
13 May 2013, 16:48
Narenn wrote: Question Source : My own question
On the x y plane, there are 8 points of which 4 are collinear. How many straight lines can be formed by joining any 2 points from the 8 points ?
A) 28 B) 22 C) 20 D) 23 E) 56
OA and OE after some discussion. +1 Kudo for Each correct and Detailed explanation
Regards
Narenn Number of ways two points can be selected from the 8 points is 8C2. Number of lines that can be formed by the collinear points if they were non collinear is 4C2. Therefore total number of lines is 8C2  4C2 + 1(one for the line which is formed by the collinear points)
_________________
"Kudos" will help me a lot!!!!!!Please donate some!!!
Completed Official Quant Review OG  Quant
In Progress Official Verbal Review OG 13th ed MGMAT IR AWA Structure
Yet to do 100 700+ SC questions MR Verbal MR Quant
Verbal is a ghost. Cant find head and tail of it.



MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 5666
Location: India
City: Pune
GPA: 3.4
WE: Business Development (Manufacturing)

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
14 May 2013, 12:16
Dear Responders,Thank you all for participating in this quiz, coming with your detailed solutions, and having a thoughtful debate here. I would also like to congratulate all interns as well for being the part of this glorious community. At first I would like to inform you that this question and its logic is based on the question given in Indian school text book (CBSE / Class XI / Volume II / Chapter 35  Combinations / Page 35.13 / Author  Shri R. D. Sharma). The snapshot of this reference question is also given herewith for your clear understanding. We have 8 points on x y plane of which 4 are collinear. We should know that the 4 collinear points can not form any other line among them except for 1 that will connect two extremes. (We are discussing here about a line and not about a line segment) Connecting any two points from 8 points is similar to choose 2 things from 8. This can be done in 8C2 ways. Note these 8C2 combinations also include the combination of fictitious lines that can be formed from 4 collinear points. This we can calculate as 4C2 We also have to include 1 line (formed by connection collinear extremes) in above combinations. Hence Total Number of Combinations will be 8C2  4C2 + 1 > 28  6 + 1 = 23 = Choice D. This logic we can take further in triangle case Number of triangles = 8C3  4C3 (Here collinear extremes will not form any triangle, so no need to add 1 in this case) mdbharadwaj wrote: I thought of that, however the questions asks for the number of line segments that can be formed between any 2 points.
Question indeed asks for number of lines and not for number of line segments. Those who gave correct solution have been awarded Kudos. In exceptional case, Kudos has also been awarded to 'mdbharadwaj' for his honest fight and to encourage him/her for further contribution. Thank You,
Regards,
Narenn
Attachments
CBSE P&C.png [ 286.58 KiB  Viewed 9493 times ]
lines combinations.png [ 25.48 KiB  Viewed 9453 times ]
_________________
Chances of Getting Admitted After an Interview [Data Crunch]
Must Read Forum Topics Before You Kick Off Your MBA Application
New GMAT Club Decision Tracker  Real Time Decision Updates



Intern
Joined: 14 May 2013
Posts: 7
Location: United States
Concentration: Entrepreneurship, General Management

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
14 May 2013, 13:00
Narenn wrote: Question Source : My own question
On the x y plane, there are 8 points of which 4 are collinear. How many straight lines can be formed by joining any 2 points from the 8 points ?
A) 28 B) 22 C) 20 D) 23 E) 56
OA and OE after some discussion. +1 Kudo for Each correct and Detailed explanation
Regards
Narenn 8 points total  4 are collinear (lie along a straight line) and 4 are noncollinear. a) All the collinear points lie on a straight line  1 line can be drawn through them. b) Use combinations for the remaining 4 noncollinear points. We use combinations because, the order of the points along a line do not matter. We have 4 total points to choose from, and we can choose only 2 points to draw a line through. Hence, it is 4C2. 4C2 = 4!/(2!*2!) = 6. Thus, 6 lines can be drawn here. c) Each noncollinear point can draw a unique line through each collinear point. That is, 4 noncollinear points * 4 collinear points = 16 possible lines. Thus there are 1+6+16=23 possible lines that can be drawn. The correct answer should be D.



Math Expert
Joined: 02 Sep 2009
Posts: 50000

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
15 May 2013, 04:18



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12673
Location: United States (CA)

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
21 Feb 2018, 21:57
Hi All, Another way to think about this setup is to 'map out' the options (without physically drawing them all). I'm going to call the first 4 points A, B, C, and D and the 4 collinear points E, F, G, and H Point A can form a line with any of the other 7 points = 7 lines Point B can also form a line with any point (but already formed a line with point A, so we can't count that line twice) = 6 lines Point C already formed lines with Point A and Point B.....= 5 lines Point D = 4 lines + 1 more line formed by EFGH.... 7+6+5+4+1 = 23 lines Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Intern
Joined: 12 Jul 2017
Posts: 32

Re: On the x y plane, there are 8 points of which 4 are collinea
[#permalink]
Show Tags
18 Mar 2018, 10:15
Another way would be the following: total number of formations is 8C2=28 number of lines that can be formed by 4 points is 4C2=6 (so 1 line has 5 duplicates) thus total is 285=23




Re: On the x y plane, there are 8 points of which 4 are collinea &nbs
[#permalink]
18 Mar 2018, 10:15






