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At a gathering of 30 people, there are 20 people who all know each oth

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Math Expert
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Joined: 02 Sep 2009
Posts: 59266
At a gathering of 30 people, there are 20 people who all know each oth  [#permalink]

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New post 23 Oct 2019, 01:16
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

47% (01:54) correct 53% (01:24) wrong based on 43 sessions

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GMAT Club Legend
GMAT Club Legend
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Joined: 18 Aug 2017
Posts: 5325
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
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Re: At a gathering of 30 people, there are 20 people who all know each oth  [#permalink]

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New post 23 Oct 2019, 02:11
1
Bunuel wrote:
At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the group?

(A) 240

(B) 245

(C) 290

(D) 480

(E) 490


total of hugs and hand shakes ; 30c2 ; 435
total hugs ; 20c2; 190
total handshakes ; 435-190 ; 245
IMO B
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Re: At a gathering of 30 people, there are 20 people who all know each oth  [#permalink]

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New post 23 Oct 2019, 02:48
Since 10 People doesn't know any one, so they will shake hands, which can be calculated by using the formula n(n-1)/2 = 10*9/2 => 45

Also, we have to consider that other 20 people will also shake hands withe these 10 people, which will be = 20*10=> 200

So total hand shakes = 200+45=245
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Joined: 26 Jan 2018
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Re: At a gathering of 30 people, there are 20 people who all know each oth  [#permalink]

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New post 30 Oct 2019, 20:33
10 will handshake with remaining 29 out of 30.

1-29
2-28
3-27
4
5
.
.
10-20

50*4+25+20 = 245

Total 245
GMAT Club Bot
Re: At a gathering of 30 people, there are 20 people who all know each oth   [#permalink] 30 Oct 2019, 20:33
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At a gathering of 30 people, there are 20 people who all know each oth

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