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There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played

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by M7MBA » Wed May 20, 2020 7:50 am
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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

[spoiler]OA=C[/spoiler]

Source: Official Guide
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Re: There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is play

by Brent@GMATPrepNow » Wed May 20, 2020 5:50 pm
M7MBA wrote: ↑
Wed May 20, 2020 7:50 am
 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

[spoiler]OA=C[/spoiler]

Source: Official Guide
There are 8 teams. If we ask each team, "How many teams did you play?" we'll find that each team played 7 teams, which gives us a total of 56 games (since 8 x 7 = 56).

From here we need to recognize that each game has been COUNTED TWICE.
For example, if Team A and Team B play a game, then Team A counts it as a game, and Team B ALSO counts it as a game.

So, to account for the DUPLICATION, we'll divide 56 by 2 to get 28

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is play

by Scott@TargetTestPrep » Sun May 24, 2020 7:23 am
M7MBA wrote: ↑
Wed May 20, 2020 7:50 am
 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

[spoiler]OA=C[/spoiler]

Source: Official Guide
Solution:

When each team plays each of the other teams exactly once, the total number of games played is 8C2 = (8 x 7)/2! = 28 games.

Answer: C

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