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If a polygon has n sides which of the following represents the number

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If a polygon has n sides which of the following represents the number  [#permalink]

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New post 06 Sep 2018, 23:56
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If a polygon has n sides which of the following represents the number of distinct triangles that can be formed by joining a corner of the polygon to all other corners of the polygon?


A. n/3

B. (3n - 2)/5

C. n - 2

D. 5n - 2

E. 180(n - 2)

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Re: If a polygon has n sides which of the following represents the number  [#permalink]

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New post 07 Sep 2018, 05:23
Bunuel wrote:
If a polygon has n sides which of the following represents the number of distinct triangles that can be formed by joining a corner of the polygon to all other corners of the polygon?


A. n/3

B. (3n - 2)/5

C. n - 2

D. 5n - 2

E. 180(n - 2)


Easiest way is to choose a triangle and a square..

1) say it is a triangle so n =3 and triangle that can be formed is just 1
A is 3/3=1 and C is n-2=3-2=1
So two possible answer

2) now take n =4 that is a quadrilateral.
Number of triangles are 2
Check A and C
A. n/3=4/3...NO
C. n-2=4-2=2...yes

C
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Re: If a polygon has n sides which of the following represents the number  [#permalink]

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New post 08 Sep 2018, 22:20
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Bunuel wrote:
If a polygon has n sides which of the following represents the number of distinct triangles that can be formed by joining a corner of the polygon to all other corners of the polygon?


A. n/3

B. (3n - 2)/5

C. n - 2

D. 5n - 2

E. 180(n - 2)


Observe that joining a given corner of quadrilateral with the other corners, 2 triangles can be formed.
Eliminate A, D, E.
In a pentagon, similarly 3 triangles can be formed. Again checking answer choices B and C. Only C remains.
Answer C.
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Re: If a polygon has n sides which of the following represents the number  [#permalink]

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New post 08 Sep 2018, 22:41
chetan2u wrote:
Bunuel wrote:
If a polygon has n sides which of the following represents the number of distinct triangles that can be formed by joining a corner of the polygon to all other corners of the polygon?


A. n/3

B. (3n - 2)/5

C. n - 2

D. 5n - 2

E. 180(n - 2)


Easiest way is to choose a triangle and a square..

1) say it is a triangle so n =3 and triangle that can be formed is just 1
A is 3/3=1 and C is n-2=3-2=1
So two possible answer

2) now take n =4 that is a quadrilateral.
Number of triangles are 2
Check A and C
A. n/3=4/3...NO
C. n-2=4-2=2...yes

C


I'm not sure I understood this method. Why is it not possible to use combination formula? Nc3

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Re: If a polygon has n sides which of the following represents the number  [#permalink]

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New post 08 Sep 2018, 22:47
rahulkashyap wrote:
chetan2u wrote:
Bunuel wrote:
If a polygon has n sides which of the following represents the number of distinct triangles that can be formed by joining a corner of the polygon to all other corners of the polygon?


A. n/3

B. (3n - 2)/5

C. n - 2

D. 5n - 2

E. 180(n - 2)


Easiest way is to choose a triangle and a square..

1) say it is a triangle so n =3 and triangle that can be formed is just 1
A is 3/3=1 and C is n-2=3-2=1
So two possible answer

2) now take n =4 that is a quadrilateral.
Number of triangles are 2
Check A and C
A. n/3=4/3...NO
C. n-2=4-2=2...yes

C


I'm not sure I understood this method. Why is it not possible to use combination formula? Nc3

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Hi
The combinations formula considers all the triangles that can be formed through joining all corners of the polygon, whereas question asks about the triangles formed though joining any one corner with the others.
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Re: If a polygon has n sides which of the following represents the number  [#permalink]

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New post 08 Sep 2018, 22:53
Can you please elaborate your solution? Shouldn't it then be pick any one (out of 4) and then 2 out of 3?

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Re: If a polygon has n sides which of the following represents the number  [#permalink]

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New post 08 Sep 2018, 23:29
rahulkashyap wrote:
Can you please elaborate your solution? Shouldn't it then be pick any one (out of 4) and then 2 out of 3?

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Refer the attachment. Triangle made by joining any one corner with the others.
Quadrilateral - 2 triangles
Pentagon - 3 triangles
Hexagon - 4 triangles
Hope it is clear.
Attachments

Untitled.png
Untitled.png [ 4.81 KiB | Viewed 367 times ]


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Re: If a polygon has n sides which of the following represents the number   [#permalink] 08 Sep 2018, 23:29
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