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

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Math Expert
Joined: 02 Sep 2009
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If a polygon has n sides which of the following represents the number  [#permalink]

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06 Sep 2018, 23:56
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Difficulty:

35% (medium)

Question Stats:

57% (01:37) correct 43% (02:02) wrong based on 27 sessions

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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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Posts: 7334
Re: If a polygon has n sides which of the following represents the number  [#permalink]

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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

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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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

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08 Sep 2018, 22:20
1
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.
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Re: If a polygon has n sides which of the following represents the number  [#permalink]

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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

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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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

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

Posted from my mobile device

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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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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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.
Pentagon - 3 triangles
Hexagon - 4 triangles
Hope it is clear.
Attachments

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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