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There are 10 people in a room. If each person shakes hands with exactl

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10118
Location: Pune, India
Re: There are 10 people in a room. If each person shakes hands with exactl  [#permalink]

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24 Oct 2018, 04:41
prabsahi wrote:

I need your help in this!!

I understood the explanation that you gave but this reminded me of an OG problem

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64

This problem I understand we have to make selection of 2 players out of 10..

So I was little confused ..isn't it similar to the handsake problem??

If Team A player say 8th player plays with the 7th player --that means 7th has played with 8th..(much like handsake problem)

The only difference is in handsake is done by 3 people and here game is played by two teams..

If I use that approach..which I am very tempted to..I land up with a wrong answer..

Yes, the problems are similar, though not same. So you need to tweak the numbers a bit.

In the games problem, every team plays with "all" other teams (so each team plays with 7 other teams). In every game, exactly 2 teams are involved.
No of games = 8*7/2 = 28

In the handshake problem, every person shakes hands with 3 other people. In every handshake, exactly 2 people participate.
No of handshakes = 10*3/2 = 15
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Karishma
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Senior Manager
Joined: 09 Jun 2014
Posts: 344
Location: India
Concentration: General Management, Operations
Re: There are 10 people in a room. If each person shakes hands with exactl  [#permalink]

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24 Oct 2018, 04:58
prabsahi wrote:

I need your help in this!!

I understood the explanation that you gave but this reminded me of an OG problem

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64

This problem I understand we have to make selection of 2 players out of 10..

So I was little confused ..isn't it similar to the handsake problem??

If Team A player say 8th player plays with the 7th player --that means 7th has played with 8th..(much like handsake problem)

The only difference is in handsake is done by 3 people and here game is played by two teams..

If I use that approach..which I am very tempted to..I land up with a wrong answer..

Yes, the problems are similar, though not same. So you need to tweak the numbers a bit.

In the games problem, every team plays with "all" other teams (so each team plays with 7 other teams). In every game, exactly 2 teams are involved.
No of games = 8*7/2 = 28

In the handshake problem, every person shakes hands with 3 other people. In every handshake, exactly 2 people participate.
No of handshakes = 10*3/2 = 15

Wow..This is perfect.

Thank you so much!!
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Re: There are 10 people in a room. If each person shakes hands with exactl  [#permalink]

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01 Nov 2019, 12:23
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Re: There are 10 people in a room. If each person shakes hands with exactl   [#permalink] 01 Nov 2019, 12:23

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