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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]

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23 Mar 2011, 22:56
1
2
00:00

Difficulty:

15% (low)

Question Stats:

77% (00:48) correct 23% (00:53) wrong based on 79 sessions

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

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Joined: 14 Feb 2011
Posts: 143
Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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24 Mar 2011, 03:20
1
GMATD11 wrote:
There are 8 teams in a certain league and each team plays each of the other team 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

Unable to understand how to break the statements to draw solution.

Each team has to play every other team, so each team plays 7 matches. So, 8 teams playing 7 matches each gives us 56 matches. However, each match is counted twice in this calculation, so we divide by 2 to get total number of unique matches. 56/2=28. Answer C
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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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24 Mar 2011, 18:40
1
GMATD11 wrote:
There are 8 teams in a certain league and each team plays each of the other team 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

Unable to understand how to break the statements to draw solution.

Another approach to understand this question:

Make everyone stand in a line:
A B C D E F G H
A plays a game with each of the 7 others so 7 games. Now all A's games are done.
B plays a game with each of the 6 others ( C D E F G H) so 6 games. (The game of B with A has already been counted when we were counting A's games. So you just have to move forward, not back). All B's games are done.
Now C plays a game with each of the 5 others (D E F G H) so 5 games and so on till G plays 1 game with H.
Adding 7+6+5+...+1 = 7*8/2 = 28
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Re: There are 8 teams in a certain league and each team plays...  [#permalink]

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Updated on: 11 May 2012, 01:13
1
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...  [#permalink]

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10 May 2012, 22:19
1
Every team plays with 7 teams...so total no of matches = 8 x 7 = 56.
Now, each match is played twice => 56 x 2
But 2 teams play a match => 56 x 2 /2 = 56.
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Posts: 59147
Re: There are 8 teams in a certain league and each team plays  [#permalink]

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10 May 2012, 22:37
2
1
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.

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Re: There are 8 teams in a certain league and each team plays  [#permalink]

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14 Sep 2013, 10:44
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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Posts: 59147
Re: There are 8 teams in a certain league and each team plays  [#permalink]

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14 Sep 2013, 10:55
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  [#permalink]

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19 Sep 2015, 17:01
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.

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Re: There are 8 teams in a certain league and each team plays  [#permalink]

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23 Jul 2018, 18:32
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.

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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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08 Sep 2019, 09:58
GMATD11 wrote:
There are 8 teams in a certain league and each team plays each of the other team 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

total games played games would be 8c2 ; 28
IMO C
Re: There are 8 teams in a certain league and each team plays each of the   [#permalink] 08 Sep 2019, 09:58
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