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 Your Progress
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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
What people who reach the high 700's do differently? We're going to share insights, tips, and strategies from data we collected on over 50,000 students who used examPAL. Save your spot today!
Learn the best strategies for acing the Verbal section. From Sentence Correction tactics to 3 keys for solving Reading Comprehension questions and tips for Critical Reasoning questions. Video Premiere April 23rd at 8am PT
Join the Live Chat April 24th at 8 am PT. Learn the best strategies for acing the Verbal section. From Sentence Correction tactics to 3 keys for solving Reading Comprehension questions and tips for Critical Reasoning questions.
Join an exclusive workshop for GMAT Club members and learn how to cut your preparation time by 50% and still reach a 700+ on the GMAT. Limited for the first 99 registrants. Register today!
Target Test Prep is kicking off spring with a fresh giveaway contest! For a limited time, you have a chance to win 4 months of full, FREE access to our 5-star rated GMAT Quant course.
There are 15 points in a given plane, no three of which are
[#permalink]
Show Tags
Updated on: 18 Sep 2012, 01:32
2
11
00:00
A
B
C
D
E
Difficulty:
65% (hard)
Question Stats:
51% (01:22) correct 49% (01:40) wrong based on 327 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?
Re: There are 15 points in a given plane, no three of which are
[#permalink]
Show Tags
18 Sep 2012, 01:36
6
3
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 \(C^2_{14}=91\).
Re: There are 15 points in a given plane, no three of which are
[#permalink]
Show Tags
18 Sep 2012, 03:40
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
Re: There are 15 points in a given plane, no three of which are
[#permalink]
Show Tags
18 Sep 2012, 04:27
2
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.
Re: There are 15 points in a given plane, no three of which are
[#permalink]
Show Tags
05 Jan 2013, 01:43
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. _________________
Re: There are 15 points in a given plane, no three of which are
[#permalink]
Show Tags
29 Aug 2017, 09:02
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.
Re: There are 15 points in a given plane, no three of which are
[#permalink]
Show Tags
31 Aug 2017, 10:23
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