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In a kickball competition of 9 teams, how many possible...

by BTGmoderatorLU » Sat Dec 23, 2017 2:01 pm
In a kickball competition of 9 teams, how many possible matches can each team play which each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54

The OA is D.

I'm really confused with this PS question because if there are 9 teams, each team can play a single game with each other, I don't understand it. Experts, any suggestion? Thanks in advance.
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by [email protected] » Sat Dec 23, 2017 2:10 pm
Hi LUANDATO,

We're told that a kickball competition has 9 teams in it. We're asked for the number of possible matches that can be played between 2 teams. This question can be solved in a variety of ways, including simply listing out the possibilities for each team.

Let's call the teams ABCDE FGHI
Team A plays all 8 teams, so that's 8 games
Team B already played Team A, so Team B could play 7 additional games
Team C already played Teams A and B, so Team C could play 6 additional games.

Notice how the number of 'new' games decreases by 1 with each team. That means the total number of possible games would be:

8+7+6+5+4+3+2+1+0 = 36 possible games

Final Answer: D

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by Scott@TargetTestPrep » Sun Sep 08, 2019 5:42 am
BTGmoderatorLU wrote:In a kickball competition of 9 teams, how many possible matches can each team play which each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54

The OA is D.

I'm really confused with this PS question because if there are 9 teams, each team can play a single game with each other, I don't understand it. Experts, any suggestion? Thanks in advance.
The total possible number of matches is 9C2 = (9 x 8)/2 = 36.

Answer: D

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by Brent@GMATPrepNow » Sun Sep 08, 2019 7:53 am
BTGmoderatorLU wrote:In a kickball competition of 9 teams, how many possible matches can each team play which each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54

The OA is D.

A DIFFERENT approach

I'm really confused with this PS question because if there are 9 teams, each team can play a single game with each other, I don't understand it. Experts, any suggestion? Thanks in advance.
If each of the 9 teams plays every team, then each team plays 8 games (since a team can't play itself)
So, the total number of game = (9)(8) = 72

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 72 by 2 to get 36

Answer: D

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Cheers,
Brent
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