CHALLENGE: 10 teams (A, B, C, D, E, F, G, H, I and J) partic

Brent@GMATPrepNow 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 for 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

Answer: E
Source: www.gmatprepnow.com
Difficulty level: 700+

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 games

For each game, 2 points are awarded.
So, the TOTAL number of POINTS awarded = (2)(45) = 90

Teams 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 points


Teams 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 points


How 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