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# How many diagonals are there in an octagon?

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How many diagonals are there in an octagon? [#permalink]  12 Sep 2018, 22:57
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Question Stats:

99% (00:35) correct 0% (00:00) wrong based on 7 sessions
How many diagonals are there in an octagon?

A)56

B)28

C)20

D)16

E)8
[Reveal] Spoiler: OA
Retired Moderator
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 2973 [1] , given: 394

Re: How many diagonals are there in an octagon? [#permalink]  13 Sep 2018, 06:27
1
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Expert's post
Attachment:

main-qimg-573a958b0d99881264dee10d716934b7.png [ 140.01 KiB | Viewed 2433 times ]

For each of the 8 vertices you can draw 5 diagonals and hence you have constructed $$5 \times 8 = 40$$ diagonals.
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Re: How many diagonals are there in an octagon? [#permalink]  13 Sep 2018, 07:56
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Expert's post
AchyuthReddy wrote:
How many diagonals are there in an octagon?

A)56

B)28

C)20

D)16

E)8

Let's examine ONE vertex in an octagon (an 8-sided polygon)

We can draw 5 diagonal lines from that one vertex

So, each of the 8 vertices can have 5 diagonal lines
So, the total number of diagonal lines = (8)(5) = 40

But wait!!

We have inadvertently counted every diagonal TWICE.
For example, we counted the diagonal from vertex A to vertex B AND we counted the diagonal from vertex B to vertex A

So, to account for this DUPLICATION, we must divide 40 by 2 to get 20

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: How many diagonals are there in an octagon?   [#permalink] 13 Sep 2018, 07:56
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