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Maritadelcarmen
- Newbie | Next Rank: 10 Posts
- Posts: 2
- Joined: Wed Apr 17, 2013 7:33 pm
is there another approach to answer question #133? the explanation on the OG is too complicated and time consuming.
Here's a quick solution that doesn't require any "fancy" counting techniques.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
Each team plays each of the other teams exactly once.
So, for example, Team A will play 7 games (i.e., it plays Teams B, C, D, E, F, G and H)
Team B will play 7 games (it plays Teams A, C, D, E, F, G and H)
Team C plays 7 games (it plays Teams A, B, D, E, F, G and H)
.
.
.
Team H plays 7 games.
So, we have 8 teams, and each team plays 7 games.
The total # of games = (7)(8) = 56
BUT, the answer here is NOT 56.
Notice that we've inadvertently counted every game twice.
For example, we counted A vs B as one game, and we counted B vs A as another game.
Since we've counted every game twice, we must take 56 and divide it by 2 to get 28
Answer: C
Cheers,
Brent
