NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 07:31 It is currently 25 Apr 2024, 07:31
Decision Tracker
My Rewards
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 triangles can be inscribed in the heptagon pictured

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
fozzzy
Director
Director
Joined: 29 Nov 2012
Posts: 580
Own Kudos [?]: 6042 [20]
Given Kudos: 543
Send PM
How many triangles can be inscribed in the heptagon pictured [#permalink] New post   Updated on: 12 Jun 2013, 23:28
4
Kudos
16
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

69% (01:11) correct 31% (01:38) wrong based on 394 sessions
Hide Show timer Statistics
Attachment:
heptagon.png
heptagon.png [ 15.64 KiB | Viewed 30750 times ]
How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

A. 9
B. 21
C. 35
D. 140
E. 210
ShowHide Answer
Official Answer
C

Originally posted by fozzzy on 12 Jun 2013, 22:38.
Last edited by Bunuel on 12 Jun 2013, 23:28, edited 1 time in total.
Edited the question.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618951 [16]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   12 Jun 2013, 23:58
8
Kudos
8
Bookmarks
Expert Reply
fozzzy wrote:
Attachment:
heptagon.png
How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

A. 9
B. 21
C. 35
D. 140
E. 210


Generally in a plane if there are \(n\) points of which no three are collinear, then:
1. The number of triangles that can be formed by joining them is \(C^3_n\).

2. The number of quadrilaterals that can be formed by joining them is \(C^4_n\).

3. The number of polygons with \(k\) sides that can be formed by joining them is \(C^k_n\).


Since no 3 vertices in given heptagon are collinear, then the number of triangles possible is \(C^3_7=35\).

Answer: C.

Similar questions to practice:
if-4-points-are-indicated-on-a-line-and-5-points-are-132677.html
abcde-is-a-regular-pentagon-with-f-at-its-center-how-many-d-86284.html
abcde-is-a-regular-pentagon-with-f-at-its-center-how-many-133328.html
the-sides-bc-ca-ab-of-triangle-abc-have-3-4-5-interior-109690.html
gmat-diagnostic-test-question-79373.html
m03-71107.html
how-many-triangles-with-positive-area-can-be-drawn-on-the-98236.html
right-triangle-abc-is-to-be-drawn-in-the-xy-plane-so-that-88958.html
how-many-circles-can-be-drawn-on-the-line-segment-128149.html

Hope it helps.
User avatar
Zarrolou
Director
Director
Joined: 02 Sep 2012
Status:Far, far away!
Posts: 859
Own Kudos [?]: 4891 [10]
Given Kudos: 219
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Send PM
GMAT ToolKit User
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   12 Jun 2013, 22:45
7
Kudos
3
Bookmarks
fozzzy wrote:
How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

a) 9
b) 21
c) 35
d) 140
e) 210


You have 7 vertices, you have to pick three vertices to form a triangle.

You can pick the first one in 7 ways, the second in 6 and the third in 5.
\(7*6*5\), then you divide by \(3!\) because the order does not matter (triangle ABC=CAB for example)

Tot ways \(\frac{7*6*5}{3!}=35\), or if you want you can solve it with the formula \(7C3=35\)
General Discussion
User avatar
arpanpatnaik
Manager
Manager
Joined: 25 Feb 2013
Status:*Lost and found*
Posts: 102
Own Kudos [?]: 196 [0]
Given Kudos: 14
Location: India
Concentration: General Management, Technology
Schools: CBS '17 INSEAD Jan '15 Haas '16 Ross '16 Yale '16 Darden '16 Anderson '16
GMAT 1: 640 Q42 V37
GPA: 3.5
WE:Web Development (Computer Software)
Send PM
GMAT ToolKit User
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   13 Jun 2013, 00:09
fozzzy wrote:
Attachment:
heptagon.png
How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

A. 9
B. 21
C. 35
D. 140
E. 210


I guess another way to look at it is that if we are to consider any line under the heptagon, we can see there are 5 other vertices left with which the line can form a traingle. For example for a line composed of AB, there are vertices C,D,E,F,G with which traingles can be constructed.

In total there are 7 possible lines fo the heptagon. Hence total traingles = 7*5 = 35. Hence [C].

Regards,
A
avatar
fozzzy
Director
Director
Joined: 29 Nov 2012
Posts: 580
Own Kudos [?]: 6042 [0]
Given Kudos: 543
Send PM
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   13 Jun 2013, 00:09
so in the same question if we were asked how many quadrilaterals to be formed it would be 7C4?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618951 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   13 Jun 2013, 00:11
Expert Reply
fozzzy wrote:
so in the same question if we were asked how many quadrilaterals to be formed it would be 7C4?


Yes, that's correct.
avatar
B
ajay2121988
Manager
Manager
Joined: 08 Feb 2016
Posts: 53
Own Kudos [?]: 60 [0]
Given Kudos: 25
Location: India
Concentration: Technology
Schools: AGSM '20 (A)
GMAT 1: 650 Q49 V30
GPA: 4
Send PM
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   12 Feb 2017, 00:31
Bunuel,

I don't seem to remember formulas during exam. Can you please point out the flaw in my approach ?

We are required to make triangles inside the heptagon such that three vertices of the triangle are also vertices of the heptagon.
This means we are simply drawing lines to connect the vertices of the heptagon, connecting 2 vertices of the heptagon at a time (that's how we form the triangles as directed in the problem)

That means we have to choose 2 points at a time from 7 points. That is \(C^2_7=21\).

Bunuel wrote:
fozzzy wrote:
Attachment:
heptagon.png
How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

A. 9
B. 21
C. 35
D. 140
E. 210


Generally in a plane if there are \(n\) points of which no three are collinear, then:
1. The number of triangles that can be formed by joining them is \(C^3_n\).

2. The number of quadrilaterals that can be formed by joining them is \(C^4_n\).

3. The number of polygons with \(k\) sides that can be formed by joining them is \(C^k_n\).


Since no 3 vertices in given heptagon are collinear, then the number of triangles possible is \(C^3_7=35\).

Answer: C.

Similar questions to practice:
https://gmatclub.com/forum/if-4-points-a ... 32677.html
https://gmatclub.com/forum/abcde-is-a-re ... 86284.html
https://gmatclub.com/forum/abcde-is-a-re ... 33328.html
https://gmatclub.com/forum/the-sides-bc- ... 09690.html
https://gmatclub.com/forum/gmat-diagnost ... 79373.html
https://gmatclub.com/forum/m03-71107.html
https://gmatclub.com/forum/how-many-tria ... 98236.html
https://gmatclub.com/forum/right-triangl ... 88958.html
https://gmatclub.com/forum/how-many-circ ... 28149.html

Hope it helps.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92914
Own Kudos [?]: 618951 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   12 Feb 2017, 01:14
Expert Reply
ajay2121988 wrote:
Bunuel,

I don't seem to remember formulas during exam. Can you please point out the flaw in my approach ?

We are required to make triangles inside the heptagon such that three vertices of the triangle are also vertices of the heptagon.
This means we are simply drawing lines to connect the vertices of the heptagon, connecting 2 vertices of the heptagon at a time (that's how we form the triangles as directed in the problem)

That means we have to choose 2 points at a time from 7 points. That is \(C^2_7=21\).

Bunuel wrote:
fozzzy wrote:
Attachment:
heptagon.png
How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

A. 9
B. 21
C. 35
D. 140
E. 210


Generally in a plane if there are \(n\) points of which no three are collinear, then:
1. The number of triangles that can be formed by joining them is \(C^3_n\).

2. The number of quadrilaterals that can be formed by joining them is \(C^4_n\).

3. The number of polygons with \(k\) sides that can be formed by joining them is \(C^k_n\).


Since no 3 vertices in given heptagon are collinear, then the number of triangles possible is \(C^3_7=35\).

Answer: C.

Similar questions to practice:
https://gmatclub.com/forum/if-4-points-a ... 32677.html
https://gmatclub.com/forum/abcde-is-a-re ... 86284.html
https://gmatclub.com/forum/abcde-is-a-re ... 33328.html
https://gmatclub.com/forum/the-sides-bc- ... 09690.html
https://gmatclub.com/forum/gmat-diagnost ... 79373.html
https://gmatclub.com/forum/m03-71107.html
https://gmatclub.com/forum/how-many-tria ... 98236.html
https://gmatclub.com/forum/right-triangl ... 88958.html
https://gmatclub.com/forum/how-many-circ ... 28149.html

Hope it helps.


Sorry don't follow you. We need three vertices for a triangle not two.
avatar
B
ajay2121988
Manager
Manager
Joined: 08 Feb 2016
Posts: 53
Own Kudos [?]: 60 [0]
Given Kudos: 25
Location: India
Concentration: Technology
Schools: AGSM '20 (A)
GMAT 1: 650 Q49 V30
GPA: 4
Send PM
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   13 Feb 2017, 04:25
It's alright, I was confusing this with another question. All clear now. Thanks.

Bunuel wrote:
ajay2121988 wrote:
Bunuel,

I don't seem to remember formulas during exam. Can you please point out the flaw in my approach ?

We are required to make triangles inside the heptagon such that three vertices of the triangle are also vertices of the heptagon.
This means we are simply drawing lines to connect the vertices of the heptagon, connecting 2 vertices of the heptagon at a time (that's how we form the triangles as directed in the problem)

That means we have to choose 2 points at a time from 7 points. That is \(C^2_7=21\).



Sorry don't follow you. We need three vertices for a triangle not two.
User avatar
S
Shrey9
Current Student
Joined: 23 Apr 2018
Posts: 130
Own Kudos [?]: 63 [0]
Given Kudos: 176
Send PM
Reviews Badge
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   15 Nov 2018, 08:35
Bunuel wrote:
fozzzy wrote:
so in the same question if we were asked how many quadrilaterals to be formed it would be 7C4?


Yes, that's correct.



and that will also give the same answer as number of triangles.. as 35 ?
7C4
avatar
B
khalid9338
Intern
Intern
Joined: 28 Jun 2016
Posts: 1
Own Kudos [?]: 5 [0]
Given Kudos: 1
Location: India
Concentration: Operations, Strategy
Schools: Fisher '17
GMAT 1: 710 Q49 V38
GPA: 3.4
WE:Operations (Transportation)
Send PM
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   15 Jan 2019, 10:06
things become interesting when specific number of sides of heptagon is asked 2 include
User avatar
G
KanishkM
Director
Director
Joined: 09 Mar 2018
Posts: 783
Own Kudos [?]: 453 [0]
Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
Send PM
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   15 Jan 2019, 10:15
fozzzy wrote:
Attachment:
heptagon.png
How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

A. 9
B. 21
C. 35
D. 140
E. 210


Since you need 3 non collinear points to make a triangle

7C3 = 35

Answer C
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18758
Own Kudos [?]: 22051 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   17 Jan 2019, 18:56
Expert Reply
fozzzy wrote:
Attachment:
heptagon.png
How many triangles can be inscribed in the heptagon pictured, where the three vertices of the triangle are also vertices of the heptagon?

A. 9
B. 21
C. 35
D. 140
E. 210


Since there are 7 vertices on the heptagon and any of its 3 vertices will form a triangle, then the number of possible triangles is 7C3 = 7!/(3! x 4!) = (7 x 6 x 5)/3! = (7 x 6 x 5)/(3 x 2) = 35.

Answer: C
User avatar
B
vivek920368
Intern
Intern
Joined: 09 Apr 2017
Posts: 41
Own Kudos [?]: 17 [0]
Given Kudos: 42
Location: India
Schools: HEC ESMT Mannheim WHU MBA
Send PM
Re: How many triangles can be inscribed in the heptagon pictured [#permalink] New post   27 May 2023, 00:09
what about the repeating Triangles? Should we not take that into consideration?
Side GA can make 5 triangles, and seven sides can produce 7*5= 35, but GAB and ABG are the same triangles.

please advise on this.
GMAT Club Bot
gmatclubot
Re: How many triangles can be inscribed in the heptagon pictured [#permalink]
27 May 2023, 00:09
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions