Following questions are based on the information given below.
In a cricket tournament nine team participated. Each team played exactly one match with every other team. The winning team was awarded 4 points, the loosing team was awarded 0 points. If a match ends in a draw both the team were awarded two points each.
Which of the following is true?

Options

A. There is exactly one team with 30 points
B. There may be more than two teams with 30 points each.
C. There may be two teams with 30 points each
D. There cannot be two teams with 30 points each.

Answer

C

Explanation

Each team plays eight matches. Total number of matches = `c_(2)= 36`
Maximum possible points a team can get `8 xx 4= 32`
Minimum possible points a learn can get `=8 xx 0 = 0`
If a team has to score 30 points it has to win 7 matches and draw one match so there can be a maximum of two learns which have won all matches with other learns and the match between these two learns can end in a draw. So two teams can have a score of 30