Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 26 Jun 2007
Posts: 75

S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
15 Mar 2008, 00:41
Question Stats:
77% (00:59) correct 23% (01:07) wrong based on 1657 sessions
HideShow timer Statistics
S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices? (1) The number of distinct points in S is 5. (2) No three of the points in S are collinear.
Official Answer and Stats are available only to registered users. Register/ Login.




CEO
Joined: 17 Nov 2007
Posts: 2966
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
15 Mar 2008, 00:49
C1. we cannot create triangles for 5 points of a line but can do that for points that are not collinear. insuff. 2. we don't know the number of points insuff. 1&2 \(C^5_3=\frac{5*4*3*2}{3*2*2}=10\)
_________________
HOT! GMAT Club Forum 2020  GMAT ToolKit 2 (iOS)  The OFFICIAL GMAT CLUB PREP APPs, musthave apps especially if you aim at 700+




Senior Manager
Joined: 10 Mar 2013
Posts: 458
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: S is a set of points in the plane. How many distinct triangles
[#permalink]
Show Tags
Updated on: 23 Sep 2015, 01:02
My observation about such kind of questions  you read it, and have no clue/idea how to solve it  read the options, and in the second option there is a hint about whether the points are collinear. As for me, it helped me to solve this question. Official Explanation (I've used the same logic, but it's just well written here 1) the number of triangles can be 0 (if the points are collinear) and the number of triangles can be greater than 0 (if the points are not all collinear); NOT sufficient. 2) Given that no three points of S are collinear, the number of triangles can be 1 (if S consists of 3 points) and the number of triangles can be 4 (if S consists of 4 points); NOT sufficient. Taking (1) and (2) together, the number of distinct triangles must be 5C3 = 10, which is the number of combinations of 5 points taken 3 at a time Answer (C)
Originally posted by BrainLab on 23 Sep 2015, 00:57.
Last edited by BrainLab on 23 Sep 2015, 01:02, edited 1 time in total.




Senior Manager
Joined: 10 Mar 2013
Posts: 458
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

S is a set of points in the plane. How many distinct triangles
[#permalink]
Show Tags
23 Sep 2015, 00:51
S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices? (1) The number of distinct points in S is 5. (2) No three of the points in S are collinear. Source: OG 2016It's a an interesting question that I've rated it as 700 level, please correct the rating if appropriate.



Manager
Joined: 16 Jan 2013
Posts: 71
Location: Bangladesh
GMAT 1: 490 Q41 V18 GMAT 2: 610 Q45 V28
GPA: 2.75

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
26 May 2016, 00:10
GGUY wrote: S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?
(1) The number of distinct points in S is 5. (2) No three of the points in S are collinear. l got A. What does collinear mean?
_________________
Heading towards perfection>>



Math Expert
Joined: 02 Sep 2009
Posts: 60678

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
26 May 2016, 00:54
ranaazad wrote: GGUY wrote: S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?
(1) The number of distinct points in S is 5. (2) No three of the points in S are collinear. l got A. What does collinear mean? Collinear points are those that lie on the same straight line. BTW the correct answer is C, not A. Check the solutions above and ask if anything remains unclear.
_________________



Manager
Joined: 03 Dec 2014
Posts: 89
Location: India
Concentration: General Management, Leadership
GPA: 1.9
WE: Engineering (Energy and Utilities)

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
27 May 2016, 00:11
walker wrote: C
1. we cannot create triangles for 5 points of a line but can do that for points that are not collinear. insuff. 2. we don't know the number of points insuff.
1&2 \(C^5_3=\frac{5*4*3*2}{3*2*2}=10\) Does distinct pint not mean that points are differently located.? I marked the A assume the above. please make it clear.



Math Expert
Joined: 02 Sep 2009
Posts: 60678

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
27 May 2016, 07:02
robu wrote: walker wrote: C
1. we cannot create triangles for 5 points of a line but can do that for points that are not collinear. insuff. 2. we don't know the number of points insuff.
1&2 \(C^5_3=\frac{5*4*3*2}{3*2*2}=10\) Does distinct pint not mean that points are differently located.? I marked the A assume the above. please make it clear. From (1) the points are distinct but 3 or more from them can be on the same line (collinear), thus they won't form a triangle.
_________________



Manager
Joined: 25 Sep 2015
Posts: 99
Location: United States
GPA: 3.26

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
28 May 2016, 13:02
Bunuel wrote: robu wrote: walker wrote: C
1. we cannot create triangles for 5 points of a line but can do that for points that are not collinear. insuff. 2. we don't know the number of points insuff.
1&2 \(C^5_3=\frac{5*4*3*2}{3*2*2}=10\) Does distinct pint not mean that points are differently located.? I marked the A assume the above. please make it clear. From (1) the points are distinct but 3 or more from them can be on the same line (collinear), thus they won't form a triangle. I marked E... considering how can we be sure of the distances between the points would make valid Triangles?? What am I missing??



Math Expert
Joined: 02 Sep 2009
Posts: 60678

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
29 May 2016, 02:26
rachitshah wrote: Bunuel wrote: robu wrote:
Does distinct pint not mean that points are differently located.? I marked the A assume the above. please make it clear.
From (1) the points are distinct but 3 or more from them can be on the same line (collinear), thus they won't form a triangle. I marked E... considering how can we be sure of the distances between the points would make valid Triangles?? What am I missing?? ANY 3 points on a plane that are not collinear form a triangle.
_________________



Manager
Joined: 25 Sep 2015
Posts: 99
Location: United States
GPA: 3.26

S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
29 May 2016, 05:43
Example: if the distances between the 3 points are 5,6 & 13? Here they won't form a triangle right? Since 5+6 < 13?



Math Expert
Joined: 02 Sep 2009
Posts: 60678

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
30 May 2016, 14:48
rachitshah wrote: Example: if the distances between the 3 points are 5,6 & 13? Here they won't form a triangle right? Since 5+6 < 13? You cannot have this case. If the distance from A to B is 5 and the distance from B to C is 6, then the distance C to A cannot be more than 11.
_________________



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9144
Location: United States (CA)

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
19 Oct 2016, 05:57
GGUY wrote: S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?
(1) The number of distinct points in S is 5. (2) No three of the points in S are collinear. We are given that S is a set of points in the plane and we must determine how many distinct triangles can be drawn with three of the points in S as vertices. So essentially, we must determine how many distinct triangles can be drawn with the points provided. Statement One Alone: The number of distinct points in S is 5. Using the information in statement one, it may be tempting to conclude that the number of triangles that can be drawn is 5C3 = (5 x 4 x 3)/3! = 10 triangles. However, because we do not know the positioning of the points, we cannot actually say that 10 distinct triangles can be created. Let’s say, for instance, that all the points were collinear, which means that they are all located on one line. If that were the case, we would not be able to create any triangles. Thus, statement one is not sufficient to answer the question. We can eliminate answer choices A and D. Note: We were able to determine that 10 triangles could be formed with 5 points if and only if no 3 points are collinear. Only then would the number of triangles be 5C3 = 10. Statement Two Alone: No three of the points in S are collinear. Using the information in statement two, we cannot answer the question because we do not know how many points are in S. We can eliminate answer choice B. Statements One and Two Together: Using the information from statements one and two we know that we have 5 points in the plane and that no three points are collinear. Thus, we can determine that the number of triangles that can be created in the plane is 5C3 = 10. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 08 Jun 2017
Posts: 1

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
22 Jun 2017, 18:08
Bunuel wrote: rachitshah wrote: Example: if the distances between the 3 points are 5,6 & 13? Here they won't form a triangle right? Since 5+6 < 13? You cannot have this case. If the distance from A to B is 5 and the distance from B to C is 6, then the distance C to A cannot be more than 11. I know that this is over a year late but I just want to clarify that if one were to connect 3 points (ABC) with the distances of 5(AB), 6(BC), and 13(AC), the only possible way is to make all 3 points collinear. Which would thus not form a triangle.



Manager
Joined: 17 Feb 2016
Posts: 89
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.12
WE: Education (Internet and New Media)

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
22 Jun 2017, 21:33
GGUY wrote: S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?
(1) The number of distinct points in S is 5. (2) No three of the points in S are collinear. St1: the position of the distinct points are not discussed If all the five points lie in a straight line, then no triangle can be formed NS St 2 : No of points are not discussed NS 1+2 Collinear ( Not straight line)and 5 points sufficient C total triangles can be obtained by using combination 5C3=10 #5C3= selecting 3 points from total 5 points
_________________
Never stop fighting until you arrive at your destined place  that is, the unique you. Have an aim in life, continuously acquire knowledge, work hard, and have the perseverance to realise the great life. A. P. J. Abdul Kalam



Manager
Joined: 21 Jul 2014
Posts: 60
GMAT Date: 07302015

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
09 Jul 2017, 00:03
Could you please explain how did you derive the PNc form. I am bit rusty in PNc so I am still not being able to understand how to arrive at this solution. Eventhough I don't need to solve in a DS. walker wrote: C
1. we cannot create triangles for 5 points of a line but can do that for points that are not collinear. insuff. 2. we don't know the number of points insuff.
1&2 \(C^5_3=\frac{5*4*3*2}{3*2*2}=10\)



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10020
Location: Pune, India

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
14 Nov 2017, 21:53
GGUY wrote: S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?
(1) The number of distinct points in S is 5. (2) No three of the points in S are collinear. Responding to a pm: S is a set of points. To make a triangle, we need 3 distinct points such that the 3 do not lie in a straight line (i.e. are not collinear). When you join 3 points which are in a straight line, you get a line, not a triangle. (1) The number of distinct points in S is 5. We know that we have 5 points. but what if all 5 are in a straight line? We won't be able to make any triangles. If they are not in a straight line, we will be able to make triangles. Hence, this statement alone is not sufficient. (2) No three of the points in S are collinear. We know that the points are not collinear but how many points do we have? The more the number of points, the more the number of triangles. Using both statements, we know that we have 5 points, no 3 of which are collinear. So we can select any 3 points out of 5 and make a triangle out of them. No of triangles we can make = 5C3 = 10 triangles.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 02 Jul 2018
Posts: 4

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
14 Jul 2018, 14:14
KarishmaB wrote: GGUY wrote: S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?
(1) The number of distinct points in S is 5. (2) No three of the points in S are collinear. Responding to a pm: S is a set of points. To make a triangle, we need 3 distinct points such that the 3 do not lie in a straight line (i.e. are not collinear). When you join 3 points which are in a straight line, you get a line, not a triangle. (1) The number of distinct points in S is 5. We know that we have 5 points. but what if all 5 are in a straight line? We won't be able to make any triangles. If they are not in a straight line, we will be able to make triangles. Hence, this statement alone is not sufficient. (2) No three of the points in S are collinear. We know that the points are not collinear but how many points do we have? The more the number of points, the more the number of triangles. Using both statements, we know that we have 5 points, no 3 of which are collinear. So we can select any 3 points out of 5 and make a triangle out of them. No of triangles we can make = 5C3 = 10 triangles. What does the C in 5C3 = 10 triangles stand for?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10020
Location: Pune, India

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
16 Jul 2018, 05:33
cheyconnors wrote: KarishmaB wrote: GGUY wrote: S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?
(1) The number of distinct points in S is 5. (2) No three of the points in S are collinear. Responding to a pm: S is a set of points. To make a triangle, we need 3 distinct points such that the 3 do not lie in a straight line (i.e. are not collinear). When you join 3 points which are in a straight line, you get a line, not a triangle. (1) The number of distinct points in S is 5. We know that we have 5 points. but what if all 5 are in a straight line? We won't be able to make any triangles. If they are not in a straight line, we will be able to make triangles. Hence, this statement alone is not sufficient. (2) No three of the points in S are collinear. We know that the points are not collinear but how many points do we have? The more the number of points, the more the number of triangles. Using both statements, we know that we have 5 points, no 3 of which are collinear. So we can select any 3 points out of 5 and make a triangle out of them. No of triangles we can make = 5C3 = 10 triangles. What does the C in 5C3 = 10 triangles stand for? This is the combinations formula. \(nCr = \frac{n!}{r! * (nr)!}\) You use this formula when you need to choose r items from n distinct items without repetition. Learn more about this formula in this post I wrote for Veritas Prep: https://www.veritasprep.com/blog/2011/1 ... binations/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 16 Nov 2016
Posts: 267
WE: Advertising (Advertising and PR)

Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
Show Tags
23 Jul 2018, 21:54
what does 'no three of the points in S are collinear' mean? Also is this really a sub 600 level question? Shouldn't it be at least 600700 level?




Re: S is a set of points in the plane. How many distinct triangles can be
[#permalink]
23 Jul 2018, 21:54



Go to page
1 2
Next
[ 30 posts ]



