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 statements is true?

Options

A. There will be exactly two teams with zero points.
B. The sum of points obtaind by any four teams cannot exceed 110 points
C. there will be no team with zero points.
D. More than one of the above

Answer

B

Explanation

Each learn 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 zero points ti has to lose all the matches. Only one team can iose all the matches. So only one team can score zero points. Hence (A) and (C ) are incorrect. Maximum possible points scored by lop four teams is when each team wins all the matches against the other five teams. Informally they have to play `""^(4)_C_(2)=6` matches which will have `6 xx 4= 24` points in total.
`therefore` Maximum possible points `= (4 xx 5 xx 4)+ 6 xx 4`
`= 80+24= 104`