Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2014, 20:08

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If convex polygon C has 7 sides, then the number of distinct

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1270
Location: Madrid
Followers: 23

Kudos [?]: 114 [0], given: 0

If convex polygon C has 7 sides, then the number of distinct [#permalink] New post 01 Sep 2006, 13:27
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
If convex polygon C has 7 sides, then the number of distinct quadrilaterals than can be formed by drawing one or two straight lines between non-adjacent vertices of C is...
Manager
Manager
avatar
Joined: 25 Jul 2006
Posts: 100
Followers: 1

Kudos [?]: 2 [0], given: 0

 [#permalink] New post 03 Sep 2006, 08:14
Giving it a try...

n = 7

Now we can form a polygon in 4 ways
1) 3 sides of the polygon are common to the quadrilateral.
we can choose x consecutive sides from an n sided polygon in n ways.
so we can choose 3 consecutive sides from an 7 sided polygon in 7 ways.

Now given any three sides of a polygon there is only 1 way to form a quadrilateral ( by joining th two points not connected)
so total # of quad = 7*1

2) 2 consecutive sides of a polygon are taken as sides of a quadrilateral.

We can select 2 consecutive side of a polygon in 7 ways.

Given two consecutive sides we can have two possible quadrilaterals
As total # of vertex = 7;
3 are linked by the 2 consecutive sides=> remaining = 7-3; 4 other vertex;
2 of these 4 are already connected by the sides of the polygon; => 4-2 = 2 vertex can be connected by diagonals
so total # of quad = = 7*2 = 14

3) 1 side of the polygon is shared by the quad; # of ways in which a side can be selected = 7
Total vertex = 7
vetex on the common side = 2; so remaining = 7-2 =5
2 other vertex are directly linked by the previous 2 to form the polygon; so remaining = 5-2 = 3
we can choose 2 points from these 3 in 3C2 ways = 6
so total # of quad = 7*6 = 42/2 = 21

4)the polygon and quad do not have any side common;
we can choose vertex 1 in 7 ways;
not of the remaing 6 two are connected by sides of polygon;
so remaing vertex = 4
now among these 4 we CANNOT choose 3 non consecutive vertex; so this cmbination does not seem possbile

so total # of quad = 21+14+7 = 42

anyone else? ans?
Director
Director
User avatar
Joined: 28 Dec 2005
Posts: 761
Followers: 1

Kudos [?]: 8 [0], given: 0

GMAT Tests User
 [#permalink] New post 06 Sep 2006, 13:36
Interestingly used the same method:-

Quad has 4 sides. Can share 1, 2, or 3 sides with the polygon.

Sharing one side:
7 (sides) x 3C2 = 7 x 3 = 21

Sharing 2 sides:
7 (set of 2 adjacent sides) x 2C1 = 7 x 2 = 14

Sharing 3 sides:
7 (set of 3 adjacent sides) x 1 = 7

Answer = 21+14+7 = 42?

Kev?
Senior Manager
Senior Manager
avatar
Joined: 15 Jul 2006
Posts: 382
Followers: 1

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

GMAT Tests User
 [#permalink] New post 13 Sep 2006, 05:59
so kavincan, you are saying it's 42?

it does not make sense to me because if quadrilateral is to share only one side with the polygon than we'd need to draw 3 lines. But we can only draw 1 or 2 lines?

I must be missing something.....
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1270
Location: Madrid
Followers: 23

Kudos [?]: 114 [0], given: 0

 [#permalink] New post 13 Sep 2006, 08:01
EconGirl wrote:
so kavincan, you are saying it's 42?

it does not make sense to me because if quadrilateral is to share only one side with the polygon than we'd need to draw 3 lines. But we can only draw 1 or 2 lines?

I must be missing something.....


I'm not saying it's 42, but the work so far is on the right track. When they say one side, they mean two non-adjacent sides. But there is a small mistake in their reasoning. Can you find it? Alternatively, an elegant solution can be found using the first reply as a base.
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1270
Location: Madrid
Followers: 23

Kudos [?]: 114 [0], given: 0

 [#permalink] New post 13 Sep 2006, 08:12
EconGirl wrote:
so kavincan, you are saying it's 42?

it does not make sense to me because if quadrilateral is to share only one side with the polygon than we'd need to draw 3 lines. But we can only draw 1 or 2 lines?

I must be missing something.....


The work so far is on the right track, but the answer is not 42. When they say one side, they should be thinking about two non-adjacent sides. But there is a mistake in their reasoning. Can you find and fix it? Also, can you use the first reply to come up with an elegant solution?
Senior Manager
Senior Manager
avatar
Joined: 15 Jul 2006
Posts: 382
Followers: 1

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

GMAT Tests User
 [#permalink] New post 14 Sep 2006, 04:53
Ah, at last I see what you mean though I may not be able to solve it. but let me try:

Sharing 2 sides:
7 (set of 2 adjacent sides) x 2C1 = 7 x 2 = 14

Sharing 3 sides:
7 (set of 3 adjacent sides) x 1 = 7

Sharing 2 Non-Adacent sides: 7

Total: 14+7+7 = 28?
  [#permalink] 14 Sep 2006, 04:53
    Similar topics Author Replies Last post
Similar
Topics:
R is a convex polygon. Does R have at least 8 sides? (1) kevincan 3 26 Nov 2006, 06:43
A polygon has 44 diagonals, and then numbers of sides are conocieur 1 11 Nov 2006, 00:39
R is a convex polygon. Does R have at least 8 sides? (1) kevincan 1 23 Sep 2006, 08:56
1 Experts publish their posts in the topic R is a convex polygon. Does R have at least 8 sides? kevincan 11 13 Aug 2006, 14:44
A convex polygon has 629 distinct diagonals. How many sides kevincan 5 14 Jul 2006, 03:09
Display posts from previous: Sort by

If convex polygon C has 7 sides, then the number of distinct

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

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®.