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

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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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26 Mar 2019, 08:31
Experts please comment on my way of solution. I think combinatorics formulas are often restrictive and confusing. I solved this problem by the following way:

So, there are 8 teams and each team plays with each team, meaning that each team plays 7 games (except with itself, of course). So, there are 8*7= 56 games (counting as if only one team plays a game) will be played in total. If a game is played by 2 teams, so there should be 56/2=28 games as a result.

Is this a viable mehtod?
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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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26 Mar 2019, 12:11
Hi Mehemmed,

YES - your way is a valid way to approach this question. As you continue to study, you'll find that most questions in the Quant and Verbal sections can be approached in more than one way. Thus, maximizing your performance on Test Day involves more than just answering questions correctly - you have to ALSO be efficient with your approach. By extension, honing multiple skills (so that you can choose which approach is easiest on any given question) is an idea that you might want to implement in your broader study plan.

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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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27 Mar 2019, 18:06
Yes and no. If you think because a game is played by 2 teams, thus it means dividing by 2, then no. Since 2 here really means 2!. The actual reason for dividing 56 by 2 is that when we find 8*7 = 56, each game is counted twice. For example, if a game is played by 3 teams, then it should be divided by 3!, not the number 3.
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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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15 Apr 2020, 12:54
sarb wrote:
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

Bunuel
Discussed: https://gmatclub.com/forum/there-are-8- ... fl=similar
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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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15 Apr 2020, 13:00
EMPOWERgmatRichC wrote:
Hi All,

Using the Combination Formula IS one way to approach these types of questions, but it's not the only way. Sometimes the easiest way to get to a solution on Test Day is to just draw a little picture and keep track of the possibilities....

Let's call the 8 teams: ABCD EFGH

We're told that each team plays each other team JUST ONCE.

A plays BCD EFGH = 7 games total

Team B has ALREADY played team A, so those teams CANNOT play again...
B plays CD EFGH = 6 more games

Team C has ALREADY played teams A and B, so the following games are left...
C plays D EFGH = 5 more games

At this point, you should notice a pattern: the additional number of games played is reduced by 1 each time. So what we really have is:

7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 = 28 games played

GMAT assassins aren't born, they're made,
Rich

EMPOWERgmatRichC
Thanks for the nice explanation.
In your explanation, zero (in the highlighted part) indicates that team H payed with team H. We should not count H vs H here, actually. Isn't it?
Thanks__
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Joined: 02 Sep 2009
Posts: 64243
Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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15 Apr 2020, 13:07
1
sarb wrote:
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

Bunuel
Discussed: https://gmatclub.com/forum/there-are-8- ... fl=similar

That question is not the same:

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?
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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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15 Apr 2020, 15:38
1
EMPOWERgmatRichC wrote:
Hi All,

Using the Combination Formula IS one way to approach these types of questions, but it's not the only way. Sometimes the easiest way to get to a solution on Test Day is to just draw a little picture and keep track of the possibilities....

Let's call the 8 teams: ABCD EFGH

We're told that each team plays each other team JUST ONCE.

A plays BCD EFGH = 7 games total

Team B has ALREADY played team A, so those teams CANNOT play again...
B plays CD EFGH = 6 more games

Team C has ALREADY played teams A and B, so the following games are left...
C plays D EFGH = 5 more games

At this point, you should notice a pattern: the additional number of games played is reduced by 1 each time. So what we really have is:

7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 = 28 games played

GMAT assassins aren't born, they're made,
Rich

EMPOWERgmatRichC
Thanks for the nice explanation.
In your explanation, zero (in the highlighted part) indicates that team H payed with team H. We should not count H vs H here, actually. Isn't it?
Thanks__

The "0" at the end represents the additional number of games that Team H would have to play. Since Team H already played all of the other teams (and those games have been 'counted' already), there's nothing else to add to the total.

GMAT assassins aren't born, they're made,
Rich
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Re: There are 8 teams in a certain league and each team plays each of the   [#permalink] 15 Apr 2020, 15:38

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