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OG: If each of the 12 teams participating in a certain tournament plays exactly one game

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by AbeNeedsAnswers » Thu May 21, 2020 6:38 pm

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If each of the 12 teams participating in a certain tournament plays exactly one game with each of the other teams, how many games will be played?

A. 144
B. 132
C. 66
D. 33
E. 23

C
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Re: OG: If each of the 12 teams participating in a certain tournament plays exactly one game

by Scott@TargetTestPrep » Mon May 25, 2020 5:06 am
AbeNeedsAnswers wrote: ↑
Thu May 21, 2020 6:38 pm
 If each of the 12 teams participating in a certain tournament plays exactly one game with each of the other teams, how many games will be played?

A. 144
B. 132
C. 66
D. 33
E. 23

C
Solution:

The number of games played is 12C2 = 12! / (2! x 10!) = (12 x 11) / 2 = 66.

Answer: C

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Re: OG: If each of the 12 teams participating in a certain tournament plays exactly one game

by Brent@GMATPrepNow » Mon May 25, 2020 7:18 am
AbeNeedsAnswers wrote: ↑
Thu May 21, 2020 6:38 pm
 If each of the 12 teams participating in a certain tournament plays exactly one game with each of the other teams, how many games will be played?

A. 144
B. 132
C. 66
D. 33
E. 23

C
A different approach:

There are 12 teams.
If we ask each team, "How many teams did you play?" we'll find that each team played 11 teams, which gives us a total of 132games (since 12 x 11 = 132).

From here we must 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 counts it as a game.

So, to account for the DUPLICATION, we'll divide 132 by 2 to get 66

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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