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There are 8 teams in a certain league and each team plays each of the

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There are 8 teams in a certain league and each team plays each of the [#permalink] New post   23 Mar 2011, 22:56
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There are 8 teams in a certain league and each team plays each of the other teams exactly twice. 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
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D
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gmihir
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Re: There are 8 teams in a certain league and each team plays each of the [#permalink] New post   Updated on: 11 May 2012, 01:13
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IMO 54 matches

Let's say first team plays with 7 other teams - resulting in 7 matches, taking this further in the similar way, the number of matches between 8 teams would be 7+6+5+4+3+2+1 = 28.. as in this case each team is playing with other twice, the no of matches would be 28*2 = 56

Originally posted by gmihir on 10 May 2012, 22:16.
Last edited by gmihir on 11 May 2012, 01:13, edited 1 time in total.
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Re: There are 8 teams in a certain league and each team plays each of the [#permalink] New post   10 May 2012, 22:37
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Smita04 wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly twice. 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


# of different pairs possible from 8 teams is \(C^2_{8}=28\), since each pair plays twice between each other than total # of games is 2*28=56.

Answer: D.
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Re: There are 8 teams in a certain league and each team plays each of the [#permalink] New post   14 Sep 2013, 10:44
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Thanks Bunuel! I caught my mistake. I was looking for other ways of solving question 133 OG 13th edi (121 in 12th edi), and that is how I landed here. Similar version of this question in the 13th and 12th edi OGs has the word 'once' instead of 'twice', as in the above question. My bad :( !!
Is my approach at solving the question correct?
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Re: There are 8 teams in a certain league and each team plays each of the [#permalink] New post   14 Sep 2013, 10:55
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vjns wrote:
Thanks Bunuel! I caught my mistake. I was looking for other ways of solving question 133 OG 13th edi (121 in 12th edi), and that is how I landed here. Similar version of this question in the 13th and 12th edi OGs has the word 'once' instead of 'twice', as in the above question. My bad :( !!
Is my approach at solving the question correct?


Yes, for that question you solved correctly. Discussed here: there-are-8-teams-in-a-certain-league-and-each-team-plays-134582.html

Similar questions to practice:
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All OG13 questions with solutions: the-official-guide-quantitative-question-directory-143450.html

Hope it helps.
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Re: There are 8 teams in a certain league and each team plays each of the [#permalink] New post   19 Sep 2015, 17:01
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Hi All,

This prompt is remarkably similar to the following prompt:

there-are-8-teams-in-a-certain-league-and-each-team-plays-134582.html

However, since each team plays each other team TWICE (and not just once), the total number of games played is doubled.

Final Answer:
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D


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Re: There are 8 teams in a certain league and each team plays each of the [#permalink] New post   23 Jul 2018, 18:32
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Smita04 wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly twice. 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


When each team plays each of the other teams exactly once, the total number of games played would be 8C2 = (8 x 7)/2! = 28 games, so when each team plays the other teams twice, 28 x 2 = 56 games are played.

Answer: D
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Re: There are 8 teams in a certain league and each team plays each of the [#permalink] New post   29 Jun 2020, 00:46
It is a permutation solution,

8P2, (8x7x6!)/6!= 56
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Re: There are 8 teams in a certain league and each team plays each of the [#permalink] New post   14 Oct 2022, 03:07
Total number of games played = 8C2×2 = 56
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Re: There are 8 teams in a certain league and each team plays each of the [#permalink] New post   20 Jan 2024, 16:12
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Re: There are 8 teams in a certain league and each team plays each of the [#permalink]
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