It is currently 24 Jun 2017, 00:41

### 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

# m06 Q 37

Author Message
Intern
Joined: 13 Jan 2010
Posts: 23

### Show Tags

31 Jul 2010, 15:58
There are 6 points on the plain. Any 3 points of these 6 don't lie on the same line. How many unique triangles can be drawn using these 6 points as vertices?

5
10
20
30
60

Why isn't the answer 60. We can choose 1 vertice and there are 5C2 = 10 ways to 2 choose the remain 2 vertices. 10*6 choices = 60 (10 choices each for each vertex)?
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2784
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35

### Show Tags

31 Jul 2010, 16:23
suhasrao wrote:
There are 6 points on the plain. Any 3 points of these 6 don't lie on the same line. How many unique triangles can be drawn using these 6 points as vertices?

5
10
20
30
60

Why isn't the answer 60. We can choose 1 vertice and there are 5C2 = 10 ways to 2 choose the remain 2 vertices. 10*6 choices = 60 (10 choices each for each vertex)?

$$6C_3 =$$ Number of triangles that can be formed using 6 points = Number of ways in which you can select 3 points out of 6.
Since it is clearly stated that " Any 3 points of these 6 don't lie on the same line" , the above statement holds true.

thus answer is $$6C_3 = 20$$

Your logic is wrong as you are counting the items repeatedly.

Suppose a b c d e f are 6 points
you can select 1 out of 6 in 6 ways, and remaining 2 in 10 ways.
Let the first selection is a , and the later two are b and c.
Now when you will select b as first selection and remaining 2 in 10 ways, a and c are counted again.
The selection becomes b , a , c.
But the triangle formed by a b c should be counted once but you have counted it 3 times.

which is a part of gmat-math-book-87417.html
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Affiliations: The Earth organization, India
Joined: 25 Dec 2010
Posts: 191
WE 1: SAP consultant-IT 2 years
WE 2: Entrepreneur-family business 2 years

### Show Tags

30 May 2011, 11:36
why not pick 2 points out of 6 ?
=6C2

now since every 2 point will form a triangle with the 4 remaining points.

hence answer = 6C2*4 = 60

help me
_________________

Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

Re: m06 Q 37   [#permalink] 30 May 2011, 11:36
Similar topics Replies Last post
Similar
Topics:
m06 Q 37 2 03 Aug 2010, 07:59
2 m06 Q 37 5 30 May 2011, 23:00
5 m06 q30 12 29 Jul 2014, 05:39
48 M06 Q9 20 21 May 2014, 04:07
12 m06 Q5 19 20 Apr 2014, 07:40
Display posts from previous: Sort by

# m06 Q 37

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.