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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] New post 12 Sep 2018, 22:57
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Question Stats:

100% (00:33) correct 0% (00:00) wrong based on 2 sessions
How many diagonals are there in an octagon?

A)56

B)28

C)20

D)16

E)8
[Reveal] Spoiler: OA
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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Re: How many diagonals are there in an octagon? [#permalink] New post 13 Sep 2018, 06:27
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main-qimg-573a958b0d99881264dee10d716934b7.png [ 140.01 KiB | Viewed 149 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] New post 13 Sep 2018, 07:56
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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
Image

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

Answer: C

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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How many diagonals are there in an octagon?

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