It is currently 19 Feb 2018, 00:00

### 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

# There are 15 points in a given plane, no three of which are

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Jun 2012
Posts: 140
There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

18 Sep 2012, 00:24
1
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

50% (01:01) correct 50% (01:16) wrong based on 308 sessions

### HideShow timer Statistics

There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?

A. 91
B. 105
C. 182
D. 210
E. 455
[Reveal] Spoiler: OA

_________________

Please give Kudos if you like the post

Last edited by Bunuel on 18 Sep 2012, 00:32, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 43804
Re: There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

18 Sep 2012, 00:36
6
KUDOS
Expert's post
4
This post was
BOOKMARKED
summer101 wrote:
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?

A. 91
B. 105
C. 182
D. 210
E. 455

Any 2 points out 14 points will create triangle with third point A, so the answer is $$C^2_{14}=91$$.

Similar question to practice:
if-4-points-are-indicated-on-a-line-and-5-points-are-132677.html

_________________
Manager
Joined: 25 Jun 2012
Posts: 67
Location: India
WE: General Management (Energy and Utilities)
Re: There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

18 Sep 2012, 02:40
Fist point is A which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2
I m confused, where am I wrong
Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)
Re: There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

18 Sep 2012, 03:27
2
KUDOS
bhavinshah5685 wrote:
Fist point is A which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2
I m confused, where am I wrong

Order of choosing the two other points doesn't matter: ABC and ACB is the same triangle.
Therefore, you should divide 182 by 2, because you counted each triangle twice.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Joined: 13 Aug 2012
Posts: 456
Concentration: Marketing, Finance
GPA: 3.23
Re: There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

05 Jan 2013, 00:43
summer101 wrote:
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?

A. 91
B. 105
C. 182
D. 210
E. 455

$$=\frac{14!}{2!12!} = 91$$
Note: The question specified that no three points lie on the same line. If that is true, the number of triangles would be less. But luckily, no such three points will form a line so rest assured, all will become triangles.
_________________

Impossible is nothing to God.

Non-Human User
Joined: 09 Sep 2013
Posts: 13832
Re: There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

29 Oct 2014, 09:33
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13832
Re: There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

10 Dec 2015, 07:49
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13832
Re: There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

27 Aug 2017, 18:47
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.
_________________
Intern
Joined: 26 Mar 2017
Posts: 29
GMAT 1: 720 Q50 V38
Re: There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

29 Aug 2017, 08:02
summer101 wrote:
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?

A. 91
B. 105
C. 182
D. 210
E. 455

Hi summer101,
Do you think you can change the wording "that contain the point A" to "that has A as one of its vertices" ? Otherwise the problem becomes a bit complex and confusing. The current wording says the formed triangle will contain the point A either on its perimeter or inside it.

Thanks
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1975
Re: There are 15 points in a given plane, no three of which are [#permalink]

### Show Tags

31 Aug 2017, 09:23
summer101 wrote:
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?

A. 91
B. 105
C. 182
D. 210
E. 455

A triangle has 3 vertices. However, since 1 of the 3 vertices has been predetermined to be A, we have to choose 2 points from the remaining 14 points as the remaining 2 vertices of the triangle. Thus, the number of triangles that can be created with A as 1 of the vertices is:

14C2 = 14!/[2!(14-2)!] = 14!/(2!12!) = (14 x 13)/2! = 7 x 13 = 91

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: There are 15 points in a given plane, no three of which are   [#permalink] 31 Aug 2017, 09:23
Display posts from previous: Sort by