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The greatest number of diagonals that can be drawn from one

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The greatest number of diagonals that can be drawn from one [#permalink] New post 18 Mar 2018, 09:10
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Question Stats:

54% (00:20) correct 45% (00:44) wrong based on 11 sessions
The greatest number of diagonals that can be drawn from one vertex of a regular 6-sided polygon is

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
[Reveal] Spoiler: OA

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Re: The greatest number of diagonals that can be drawn from one [#permalink] New post 04 Apr 2018, 04:19
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Just draw a hexagon and try it. It's painful to do it here, but easy to do on paper. When you've picked one vertex, you'll notice you only have 3 vertices you can draw a diagonal to. The one you picked doesn't work, and neither do the two on either side of it, since they won't be diagonals but will just be retracing the sides of the hexagon.

The answer is therefore B.
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Re: The greatest number of diagonals that can be drawn from one [#permalink] New post 04 Apr 2018, 06:37
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Not just a regular hexagon, any polygon with n sides will have maximum (n-3) diagonals that can be drawn from any vertex. First chose any vertex from which we want to draw diagonals, then select any other vertex of the polygon. Selecting the same vertex again as that would result in a point only. If we select the adjacent vertices, that would result in a side of the polygon. Hence, n-3

The question would have been more interesting, had the total number of diagonals in a hexagon that can be drawn been asked.
Re: The greatest number of diagonals that can be drawn from one   [#permalink] 04 Apr 2018, 06:37
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The greatest number of diagonals that can be drawn from one

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