## Games and Tournaments

Six teams A, B, C, D, E and F play a game. In the first round of the game every team plays with every other team exactly once. If a team wins, it scores 40 points, if it loses, it loses 10 points and a draw results in 20 points for each team. After the first round, the top two teams advance to the finals. The following are the results of the first round.

(i) Team C neither won nor lost a match.
(ii) Teams B and E lost exactly one match.
(iii) Team F lost exactly three matches.
(iv) Team D won as well as lost exactly two matches.
(v) Team A lost exactly two matches.
(vi) The match played between team E and team F was drawn.

1. Which of the following teams advanced to the finals?
(A) A, B (B) A, E (C) B, E (D) B, C

2. Which of the following teams scored the same number of points at the end of the first round?
(A) B, D (B) A, D (C) D, E (D) None

3. The total number of winners in the first round is ____.
(A) 10 (B) 9 (C) 8 (D) Cannot be determined

1. I took 12mins to solve this question.
Listed, all the possible games and started filling the results-based on the extreme conditions.
Could anyone suggest me a better trick?

• Nice instruction, thanks

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