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

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Manager
Joined: 26 Nov 2018
Posts: 72
Concentration: Technology, Entrepreneurship
GPA: 3.3
WE: Manufacturing and Production (Manufacturing)
On the occasion of a certain meeting, each member exchanged shake hand  [#permalink]

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04 Mar 2019, 07:22
2
1
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:13) correct 33% (01:35) wrong based on 9 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
Intern
Joined: 21 Feb 2019
Posts: 36
Re: On the occasion of a certain meeting, each member exchanged shake hand  [#permalink]

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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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