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Joined: 10 Apr 2015
Posts: 6218
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In a room of 12 people, each person shook hands with exactly 3 other p
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23 Oct 2021, 05:54
23 Oct 2021, 05:54
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In a room of 12 people, each person shook hands with exactly 3 other people. How many handshakes took place?
A) 18
B) 36
C) 55
D) 110
E) 220
A) 18
B) 36
C) 55
D) 110
E) 220
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In a room of 12 people, each person shook hands with exactly 3 other p
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24 Oct 2021, 05:49
24 Oct 2021, 05:49
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GreenlightTestPrep wrote:
In a room of 12 people, each person shook hands with exactly 3 other people. How many handshakes took place?
A) 18
B) 36
C) 55
D) 110
E) 220
A) 18
B) 36
C) 55
D) 110
E) 220
Let's say the 12 people are A, B, C, D, ...., K and L
If each person shook hands with exactly 3 other people, then person A participated in 3 handshakes.
Similarly, person B participated in 3 handshakes.
Person C participated in 3 handshakes.
.
.
.
Person K participated in 3 handshakes.
Person L participated in 3 handshakes.
So, the total number of handshakes = (12)(3) = 36 (but the correct answer is not B)
Notice that every handshake has been counted TWICE.
For example, if B and G shook hands, then person B counted the handshake, AND person G counted the same handshake.
To account for this duplication, we'll divide 36 by 2 to get 18
Answer: A
Re: In a room of 12 people, each person shook hands with exactly 3 other p
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04 Jan 2024, 13:04
04 Jan 2024, 13:04
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Thanks to another GRE Prep 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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