It is currently 20 Feb 2018, 01:52

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many diagonals does a polygon with 21 sides have, if one

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
avatar
Joined: 02 Dec 2007
Posts: 448
How many diagonals does a polygon with 21 sides have, if one [#permalink]

Show Tags

New post 27 Aug 2008, 07:33
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many diagonals does a polygon with 21 sides have, if one of its vertices does not connect to any diagonal?

a) 21
b) 170
c) 340
d) 357
e) 420
Manager
Manager
avatar
Joined: 15 Jul 2008
Posts: 205
Re: Diagonals [#permalink]

Show Tags

New post 27 Aug 2008, 08:18
Nihit wrote:
How many diagonals does a polygon with 21 sides have, if one of its vertices does not connect to any diagonal?

a) 21
b) 170
c) 340
d) 357
e) 420



I think 170...

take any point. You have 20 other points. Of these 20, 2 will be adjacent and so no diagonal with them. 18 possibilities. But one point has no diagonal with any other point. So for the chosen point, there are 17 diagonals possible.
This applies to 20 points (excluding the one that does not have diagonal with any point)

So you have 17*20. This includes double counting. So divide by 2

170.


I am interested in knowing how combination can be used to tackle this problem.
SVP
SVP
User avatar
Joined: 07 Nov 2007
Posts: 1789
Location: New York
Re: Diagonals [#permalink]

Show Tags

New post 27 Aug 2008, 08:33
bhushangiri wrote:
Nihit wrote:
How many diagonals does a polygon with 21 sides have, if one of its vertices does not connect to any diagonal?

a) 21
b) 170
c) 340
d) 357
e) 420



I think 170...

take any point. You have 20 other points. Of these 20, 2 will be adjacent and so no diagonal with them. 18 possibilities. But one point has no diagonal with any other point. So for the chosen point, there are 17 diagonals possible.
This applies to 20 points (excluding the one that does not have diagonal with any point)

So you have 17*20. This includes double counting. So divide by 2

170.


I am interested in knowing how combination can be used to tackle this problem.


Let say polygon has n points.
chose any 2 points to make line.
= nC2 combinations (include all sides and all diagnols)
= n(n-1)/2
no of diagnols = n(n-1)/2 - n = n(n-3)/2

Here one vertex is not participating..
visualize that it is 20 sides polygon..
= 20*17/2 - 1 (side is actually not present ) +1 ( actually that side is diagnol)
=170
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Current Student
User avatar
Joined: 11 May 2008
Posts: 553
Re: Diagonals [#permalink]

Show Tags

New post 27 Aug 2008, 17:22
im getting 171. how come??
total poss diagonals = 21*18/2=189
but one vertex is not connected with any diagonal,
so we reduce the total no. by 21-3= 18 diagonals.
so 189-18=171.
?????
Re: Diagonals   [#permalink] 27 Aug 2008, 17:22
Display posts from previous: Sort by

How many diagonals does a polygon with 21 sides have, if one

  post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderator: chetan2u



GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.