GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Feb 2019, 16:07

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# How many triangles can be formed by joining 12 points, 7 of which are

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53020
How many triangles can be formed by joining 12 points, 7 of which are  [#permalink]

### Show Tags

28 Jan 2019, 23:44
00:00

Difficulty:

45% (medium)

Question Stats:

64% (02:37) correct 36% (02:30) wrong based on 16 sessions

### HideShow timer Statistics

How many triangles can be formed by joining 12 points, 7 of which are collinear?

A. 255
B. 220
C. 185
D. 35
E. 10

_________________
Director
Joined: 18 Jul 2018
Posts: 675
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
How many triangles can be formed by joining 12 points, 7 of which are  [#permalink]

### Show Tags

29 Jan 2019, 00:45
The number of triangles that can be formed from 12 points is $$5C_3$$ = 10 as 7 points are collinear.

_________________

Press +1 Kudo If my post helps!

SVP
Joined: 18 Aug 2017
Posts: 1887
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
How many triangles can be formed by joining 12 points, 7 of which are  [#permalink]

### Show Tags

Updated on: 29 Jan 2019, 02:57
Bunuel wrote:
How many triangles can be formed by joining 12 points, 7 of which are collinear?

A. 255
B. 220
C. 185
D. 35
E. 10

given 7 points are collinear ,which means 7 out of 12 points are on same line and 5 are random points

so total triangles which can be formed ; 7c2*5c1+7c1*5c2+5c3 = 21*5+7*10+10 = 185
IMO C
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 29 Jan 2019, 01:49.
Last edited by Archit3110 on 29 Jan 2019, 02:57, edited 1 time in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2581
Re: How many triangles can be formed by joining 12 points, 7 of which are  [#permalink]

### Show Tags

29 Jan 2019, 02:50

Solution

Given:
• Total number of points = 12
o Number of collinear points = 7

To find:
• The number of triangles that can be formed

Approach and Working:
• The number of triangles that can be formed, N = number of ways of selecting 2 points from 7 and the other from the remaining 5 + the number of ways of selecting 1 from 7 and 2 from the remaining 5 + the number of ways of selecting 3 points from the remaining 5
• Therefore, $$N = ^7C_2 * ^5C_1 + ^7C_1 * ^5C_2 + ^5C_3 = 21 * 5 + 7 * 10 + 10 = 185$$

Hence, the correct answer is Option C

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: How many triangles can be formed by joining 12 points, 7 of which are   [#permalink] 29 Jan 2019, 02:50
Display posts from previous: Sort by