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MBA Section Director Joined: 21 Feb 2012 Affiliations: GMAT Club Posts: 8205 City: Pune
On the x y plane, there are 8 points of which 4 are collinea
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Hide Show timer StatisticsQuestion 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 _________________ Manager Joined: 25 Feb 2013 Status:*Lost and found* Posts: 106 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
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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 OA and OE after some discussion. Regards Narenn I believe the answer should be 23 lines i.e [D] The approach taken by me would be simple counting: Hence the total comes to be 23. Hope I am correct! Regards, Director Joined: 02 Sep 2012 Status:Far, far away! Posts: 891 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8
Re: On the x y plane, there are 8 points of which 4 are
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Each line is defined by two points. 4 points are collinear => 1 line passes through those. 1+16+6=23 totals Intern Joined: 26 Feb 2013 Posts: 39 Concentration: Strategy, General Management WE:Consulting (Telecommunications) Re: On the x y plane, there are 8 points of which 4 are collinea
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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. 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 Joined: 25 Feb 2013 Status:*Lost and found* Posts: 106 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]
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. 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 line-segments 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, Intern Joined: 26 Feb 2013 Posts: 39 Concentration: Strategy, General Management WE:Consulting (Telecommunications) Re: On the x y plane, there are 8 points of which 4 are collinea [#permalink]
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. 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 line-segments 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, I thought of that, however the questions asks for the number of line segments that can be formed between any 2 points. Hope I got my point across. Manager Joined: 25 Feb 2013 Status:*Lost and found* Posts: 106 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
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mdbharadwaj wrote: I thought of that, however the questions asks for the number of line segments that can be formed between
any 2 points. Hope I got my point across. Lemme just clarify my idea over this. Please refer to my *supremely sloppy* paint-work attached (Apologize for that 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 A-B, B-C and C-A are segments. L is the only unique straight line passing through the collinear points. Getting back to the question, you are spot-on for the 16 and 6 values. After adding the one line that passes through the collinear points, I believe you have the answer! Regards, **edited for a typo! sorry! Attachments
Intern Joined: 05 Mar 2013 Posts: 34 Location: India Concentration: Entrepreneurship, Marketing GMAT Date: 06-05-2013 GPA: 3.2 Re: On the x y plane, there are 8 points of which 4 are collinea
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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 OA and OE after some discussion. Regards Narenn Number of ways two points can be selected from the 8 points is 8C2. MBA Section Director Joined: 21 Feb 2012 Affiliations: GMAT Club Posts: 8205 City: Pune
Re: On the x y plane, there are 8 points of which 4 are collinea [#permalink]
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. 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 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
_________________ Intern Joined: 14 May 2013 Posts: 6 Location: United States Concentration: Entrepreneurship, General Management
Re: On the x y plane, there are 8 points of which 4 are collinea
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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 OA and OE after some discussion. Regards Narenn 8 points total - 4 are collinear (lie along a straight line) and 4 are non-collinear. a) All the collinear points lie on a straight line - 1 line can be drawn through them. Thus there are 1+6+16=23 possible lines that
can be drawn. Math Expert Joined: 02 Sep 2009 Posts: 87761 Re: On the x y plane, there are 8 points of which 4 are collinea [#permalink]
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 OA and OE after some discussion. Regards Narenn Thank you for the question, Narenn. Similar questions to
practice: Hope it helps. EMPOWERgmat Instructor Joined: 19 Dec 2014 Status:GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Posts: 21108 Location: United States (CA)
Re: On the x y plane, there are 8 points of which 4 are collinea [#permalink]
Hi All, Another way to think about this set-up 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 + 1 more line formed by EFGH.... 7+6+5+4+1 = 23 lines Final Answer: GMAT assassins
aren't born, they're made, Intern Joined: 12 Jul 2017 Posts: 30 Re: On the x y plane, there are 8 points of which 4 are collinea
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Another way would be the following: Non-Human User Joined: 09 Sep 2013 Posts: 25311 Re: On the x y plane, there are 8 points of which 4 are collinea
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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: On the x y plane, there are 8 points of which 4 are collinea [#permalink] 08 Aug 2019, 07:53 Moderators: Senior Moderator - Masters Forum 3098 posts How many triangles can be formed using 8 non collinear points on a plane?The number of triangles that can be drawn by joining these points = 8C3 = 56.
How many straight lines are determined by 8 points?Number of straight lines can be drawn from 8 non collinear points = 8C2 = 28.
How many line segments can you form from 8 collinear points?Answer 28. You can draw 7 lines from the first point.
How many straight lines can be formed from 12 points non collinear points?=6C1×6C1+6C2+1=52.
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