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On the occasion of a certain meeting, each member exchanged shake hand

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Joined: 26 Nov 2018
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On the occasion of a certain meeting, each member exchanged shake hand  [#permalink]

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New post 04 Mar 2019, 07:22
2
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A
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C
D
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Difficulty:

  35% (medium)

Question Stats:

63% (01:11) correct 38% (01:44) wrong based on 16 sessions

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On the occasion of a certain meeting, each member exchanged shake hand with one another. If the total shake hands were 21, then how many members are there in the meeting?

A. 6
B. 5
C. 7
D. 4
E. 3
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Joined: 21 Feb 2019
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Location: Italy
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Re: On the occasion of a certain meeting, each member exchanged shake hand  [#permalink]

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New post 04 Mar 2019, 09:50
2
If there are \(n\) people,the first one will have \((n-1)\) handshakes (all except himself).
The second one will have \(n -2\) handshakes (the first person has already been counted for). And so on...

We obtain:

\(\frac{n(n-1)}{2} = 21\)

\(n^2 - n -42 = 0\)

\((n - 7) (n + 6) = 0\)

\(n = 7\)
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Re: On the occasion of a certain meeting, each member exchanged shake hand   [#permalink] 04 Mar 2019, 09:50
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On the occasion of a certain meeting, each member exchanged shake hand

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