GreenlightTestPrep wrote:
10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tournament in which each team plays every other team once.
For each game played, points are awarded to the teams as follows:
0 points for losing the game
1 point each or tying the game
2 points for winning the game
After all the games are played, we learn that:
- teams A, B, C, D and E each won 5 games and tied 3 games.
- teams F, G, H and I each tied 2 games and lost 5 games.
How many games did team J lose?
A) 0
B) 2
C) 4
D) 6
E) 8
First determine the TOTAL number of games played.We can select 2 teams from 10 teams in 10C2 ways (= 45 ways)
So, there will be 45 games in TOTAL
IMPORTANT: Each team plays 9 gamesFor each game, 2 points are awarded.
So, the TOTAL number of POINTS awarded = (2)(45) =
90Teams A, B, C, D and E each won 5 games and tied 3 games. NOTE: This info tells about 8 of the games. Since each team plays 9 games, we can conclude that each of the above teams LOST 1 game each.
For ONE team, 5 wins = 10 points, and 3 ties = 3 points, for a total of 13 points.
So, the total points awarded to all 5 teams = (5)(13) =
65 pointsTeams F, G, H and I each tied 2 games and lost 5 games. NOTE: Since each team plays 9 games, we can conclude that each of the above teams WON 2 games each.
For ONE team, 2 wins = 4 points, and 2 ties = 2 points, for a total of 6 points.
So, the total points awarded to all 4 teams = (4)(6) =
24 pointsHow many games did team J lose? So, far we've accounted for
89 points [
65 + 24 = 89 points]
We know that a TOTAL of
90 points are awarded
So, Team J must have received
1 point
If Team J received only
1 point, then we know that Team J TIED 1 game
This also means that Team J WON 0 games (otherwise, Team J's point total would be greater than 1)
So, we can conclude that Team J LOST 8 games
Answer: E
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep