Last visit was: 23 May 2024, 14:06 It is currently 23 May 2024, 14:06
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

how many internal diagonals does a decagon (ten sided polygon) have?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
P
Turkish
Manager
Manager
Joined: 13 Jun 2012
Posts: 166
Own Kudos [?]: 498 [12]
Given Kudos: 467
Location: United States
WE:Supply Chain Management (Computer Hardware)
Send PM
GMAT ToolKit User
how many internal diagonals does a decagon (ten sided polygon) have? [#permalink] how many internal diagonals does a decagon (ten sided polygon) have?   27 Feb 2015, 03:18
1
Kudos
11
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

72% (00:56) correct 28% (01:31) wrong based on 219 sessions
Hide Show timer Statistics
how many internal diagonals does a decagon (ten sided polygon) have?

A. 90
B. 85
C. 70
D. 35
E. 25
ShowHide Answer
Official Answer
D
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11286
Own Kudos [?]: 32731 [4]
Given Kudos: 307
Send PM
Reviews Badge
Re: how many internal diagonals does a decagon (ten sided polygon) have? [#permalink] how many internal diagonals does a decagon (ten sided polygon) have?   27 Feb 2015, 03:30
3
Kudos
1
Bookmarks
Expert Reply
Turkish wrote:
how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25


hi,
the questions means we have to choose two vertices out of 10=10c2..
but these will also contain vertices adjoining to each other as these form sides and not diagonals..
ans=10c2-10=45-10=35
ans D..35
avatar
B
OptimusPrepJanielle
SVP
SVP
Joined: 06 Nov 2014
Posts: 1798
Own Kudos [?]: 1373 [2]
Given Kudos: 23
Send PM
Re: how many internal diagonals does a decagon (ten sided polygon) have? [#permalink] how many internal diagonals does a decagon (ten sided polygon) have?   28 Feb 2015, 03:20
1
Kudos
1
Bookmarks
Expert Reply
Turkish wrote:
how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25


Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 10
No. of diagonals = 10(10 - 3)/2
= 35
Hence option 4.

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course
User avatar
G
eabhgoy
Manager
Manager
Joined: 12 Apr 2011
Posts: 115
Own Kudos [?]: 200 [1]
Given Kudos: 86
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21 Yale '21 INSEAD Jan'21 Intake IMD '21 (A)
GMAT 1: 670 Q50 V31
GMAT 2: 720 Q50 V37
GPA: 3.2
WE:Marketing (Telecommunications)
Send PM
Re: how many internal diagonals does a decagon (ten sided polygon) have? [#permalink] how many internal diagonals does a decagon (ten sided polygon) have?   03 Jan 2019, 09:06
1
Kudos
Turkish wrote:
how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25


Well I took a different approach:

Square with 4 sides = 2 diagonals
Pentagon 5 sides = 5 diagonals (increase of 3)
Hexagon 6 sides = 9 diagonals (increase of 4)
Septagon 7 side = 14 diagons (increase of 5 from previous)

Hence the diagonals are increasing in a certain orders and their difference increase is a normal AP: 3, 4, 5....so on
Hence for 8 sides = 20
9 sides = 27
10 sides = 35 diagonals

Hence the answer is D
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5350
Own Kudos [?]: 4016 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: how many internal diagonals does a decagon (ten sided polygon) have? [#permalink] how many internal diagonals does a decagon (ten sided polygon) have?   05 May 2020, 22:16
Turkish wrote:
how many internal diagonals does a decagon (ten sided polygon) have?

1.90
2.85
3.70
4.35
5.25


Asked: how many internal diagonals does a decagon (ten sided polygon) have?

The number of diagonals = ^nC_2 - n = n(n-1)/2 - n = n(n-3)/2 = 10*7/2 = 35

IMO D
User avatar
L
Russ19
VP
VP
Joined: 29 Oct 2019
Posts: 1367
Own Kudos [?]: 1466 [0]
Given Kudos: 582
Send PM
Re: how many internal diagonals does a decagon (ten sided polygon) have? [#permalink] how many internal diagonals does a decagon (ten sided polygon) have?   15 Oct 2021, 21:45
Quote:
hi,
the questions means we have to choose two vertices out of 10=10c2..
but these will also contain vertices adjoining to each other as these form sides and not diagonals..
ans=10c2-10=45-10=35
ans D..35


Dear chetan2u, Could you please help me understand how you have found 10, which you have subtracted from 10c2? You don't know how much you've helped me with my preparation. Thanks a million!
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11286
Own Kudos [?]: 32731 [1]
Given Kudos: 307
Send PM
Reviews Badge
Re: how many internal diagonals does a decagon (ten sided polygon) have? [#permalink] how many internal diagonals does a decagon (ten sided polygon) have?   16 Oct 2021, 03:40
1
Kudos
Expert Reply
sjuniv32 wrote:
Quote:
hi,
the questions means we have to choose two vertices out of 10=10c2..
but these will also contain vertices adjoining to each other as these form sides and not diagonals..
ans=10c2-10=45-10=35
ans D..35


Dear chetan2u, Could you please help me understand how you have found 10, which you have subtracted from 10c2? You don't know how much you've helped me with my preparation. Thanks a million!


Glad to hear that.

What you get from 10C2 is choosing 2 vertices from 10 vertices. Thus you will get 10C2 lines.

However, these 10C2 consist of 10 sides of decagon. For example, if ABCDEFGHJK is decagon, then AB, BC, CD, DE, EF, FG, GH, HJ, JK and KA are 10 sides that have to be subtracted.
The remaining are diagonals, that is AC, AD, AE and so on
GMAT Club Bot
gmatclubot
Re: how many internal diagonals does a decagon (ten sided polygon) have? [#permalink]
16 Oct 2021, 03:40
Moderator:
Bunuel
Math Expert
93437 posts