How many diagonals does a polygon with 21 sides have, if one : PS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 11:57

### 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

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

Author Message
Manager
Joined: 20 Mar 2005
Posts: 170
Followers: 2

Kudos [?]: 71 [0], given: 0

How many diagonals does a polygon with 21 sides have, if one [#permalink]

### Show Tags

06 Aug 2007, 17:32
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

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
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5062
Location: Singapore
Followers: 30

Kudos [?]: 358 [0], given: 0

### Show Tags

06 Aug 2007, 17:49
I'm tempted to go with B.

# of diagonals a polygon with 21 side have = 21(21-3)/2 = 189
So if one vertex does not connect anywhere else, then the # of diagonals must be less than 189. This leaves only A and B. Choice A seems to be a little on the low side, so I'll take B.
Intern
Joined: 06 Aug 2007
Posts: 15
Followers: 0

Kudos [?]: 0 [0], given: 0

### Show Tags

06 Aug 2007, 19:28
Here are my thoughts:

21 (# vertices) * 18 (# diagonals leaving from each vertex) / 2 (to avoid double counting) = 189 unique diagonals

If one vertex has no diagonals, the equation becomes
20 (# vertices) * 17 (# diagonals leaving from each vertex) / 2 (to avoid double counting) = 170 unique diagonals
Senior Manager
Joined: 13 May 2007
Posts: 250
Followers: 2

Kudos [?]: 14 [0], given: 0

### Show Tags

06 Aug 2007, 23:37
another way to look at this :

2 vertices out of 20 can be chosen in : 20 C 2 : 190

since this also include the sides of the polygon so for 20 of those you need to subtract 20 out of the 190.

Hence : 190 - 20 = 170
06 Aug 2007, 23:37
Display posts from previous: Sort by

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

 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®.