GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 21 Jan 2020, 01:33

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

Thirteen distinct points lie in a plane with exactly n of the points

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60526
Thirteen distinct points lie in a plane with exactly n of the points  [#permalink]

Show Tags

02 Dec 2019, 00:39
00:00

Difficulty:

95% (hard)

Question Stats:

33% (02:35) correct 67% (02:36) wrong based on 43 sessions

HideShow timer Statistics

Thirteen distinct points lie in a plane with exactly n of the points lying on the same line and the other 13-n points non-collinear. If 276 unique triangles can be drawn using these points as vertices, what is the value of n?

A. 2
B. 3
C. 4
D. 5
E. 7

Are You Up For the Challenge: 700 Level Questions

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5700
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Thirteen distinct points lie in a plane with exactly n of the points  [#permalink]

Show Tags

02 Dec 2019, 02:43
1
total ∆ ; 13c3 ; 286
and since 276 unique ∆ are to be formed ; 286-nc3 ; 276
n has to be 5
IMO D

Bunuel wrote:
Thirteen distinct points lie in a plane with exactly n of the points lying on the same line and the other 13-n points non-collinear. If 276 unique triangles can be drawn using these points as vertices, what is the value of n?

A. 2
B. 3
C. 4
D. 5
E. 7

Are You Up For the Challenge: 700 Level Questions
Director
Joined: 27 May 2012
Posts: 945
Thirteen distinct points lie in a plane with exactly n of the points  [#permalink]

Show Tags

18 Dec 2019, 09:55
Bunuel wrote:
Thirteen distinct points lie in a plane with exactly n of the points lying on the same line and the other 13-n points non-collinear. If 276 unique triangles can be drawn using these points as vertices, what is the value of n?

A. 2
B. 3
C. 4
D. 5
E. 7

Are You Up For the Challenge: 700 Level Questions

$$n_{c_1} *{(13-n)}_{c_2} +n_{c_2} *{(13-n)}_{c_1}+{(13-n)}_{c_3}$$=276

Where $$n_{c_1}$$ = Choose 1 point from the n collinear points
$${(13-n)}_{c_2}$$= Choose 2 points from the (13-n ) NON-collinear points
$${(13-n)}_{c_3}$$= Choose 3 points from the (13-n) NON-collinear points

It is better to substitute answer choices after this , we see that for n = 5 , the above equation gives 276

Ans-D

Hope it's clear.
_________________
- Stne
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9066
Location: United States (CA)
Re: Thirteen distinct points lie in a plane with exactly n of the points  [#permalink]

Show Tags

23 Dec 2019, 18:34
1
Bunuel wrote:
Thirteen distinct points lie in a plane with exactly n of the points lying on the same line and the other 13-n points non-collinear. If 276 unique triangles can be drawn using these points as vertices, what is the value of n?

A. 2
B. 3
C. 4
D. 5
E. 7

Are You Up For the Challenge: 700 Level Questions

If all 13 points are non-collinear, then 13C3 = (13 x 12 x 11) / (3 x 2) = 13 x 2 x 11 = 286 unique triangles can be drawn. However, since only 276 triangles can be drawn, 10 triangles must have been created by the n collinear points. Therefore, we can create the equation:

nC3 = 10

n! / [3! x (n - 3)!]

n(n - 1)(n - 2) / (3 x 2) = 10

n(n - 1)(n - 2) = 60

From the above equation, we see n must be 5 since 5(4)(3) = 60.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star 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.

Re: Thirteen distinct points lie in a plane with exactly n of the points   [#permalink] 23 Dec 2019, 18:34
Display posts from previous: Sort by