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# 6 people meet for a business lunch. Each person shakes hands once with

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Math Expert
Joined: 02 Sep 2009
Posts: 59623
6 people meet for a business lunch. Each person shakes hands once with  [#permalink]

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12 May 2016, 01:56
1
3
00:00

Difficulty:

15% (low)

Question Stats:

74% (00:42) correct 26% (00:50) wrong based on 161 sessions

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6 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?

A. 30
B. 21
C. 18
D. 15
E. 10

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Joined: 07 May 2016
Posts: 25
6 people meet for a business lunch. Each person shakes hands once with  [#permalink]

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12 May 2016, 08:07
1
Bunuel wrote:
6 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?

A. 30
B. 21
C. 18
D. 15
E. 10

Hi
the formula to count handshakes is $$\frac{n(n-1)}{2}$$
Where n is the number of people

=> 6(6-1)/2 = 6*5/2 = 30/2 = 15

Here why:
if there are 2 people at the business lunch
=> the number of handshakes will be 1 (obviously)

people | handshakes
2 | 1
3 | 3
4 | 6
=> we can see

2 people = 1 handshakes
3 people = 2 + 1 handshakes
4 people = 3 + 2 +1 handshakes
5 people = 4 + 3 + 2 + 1 handshakes
6 people = 5 + 4 + 3 + 2 +1 handshakes

=> the formula will be $$\frac{n(n-1)}{2}$$
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Joined: 18 Oct 2014
Posts: 796
Location: United States
GMAT 1: 660 Q49 V31
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Re: 6 people meet for a business lunch. Each person shakes hands once with  [#permalink]

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12 May 2016, 11:10
3
Let's look at the logic.

Every person shakes hand with other '5'. So, 6 people shake hands with 6X5= 30 people

But in this 30 we have counted two times the total handshakes (A shakes hand with B and B shakes hand with A)

So just divide 30/2= 15 total handshakes
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Intern
Joined: 12 Aug 2013
Posts: 45
Re: 6 people meet for a business lunch. Each person shakes hands once with  [#permalink]

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12 May 2016, 21:16
1
Its a combination problem :-

Out of 6 we just need 2 ..order doesn't matter

6c2 = 15

Thanks
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Joined: 09 Sep 2013
Posts: 13730
Re: 6 people meet for a business lunch. Each person shakes hands once with  [#permalink]

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23 Nov 2018, 08:17
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: 6 people meet for a business lunch. Each person shakes hands once with   [#permalink] 23 Nov 2018, 08:17
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