There are exactly 6 teams in league X. What was the total number of games played by the 6 teams last season?
I. Each team in league X played each of the other teams atleast once.
II. No team in league Xplayed more than 7 games.

Statement 1:

Each team in league x played each of the other teams at least once So,  if each team played each of the other teams ONLY once then there was total games played

6C2 = 15.  but if each team played each of the other teams TWICE then there was total of 2*6C2 = 30 games played.

Not sufficient

Statement 2:

No team in league x played more than 7 games. 

So,  insufficient.

Both together:

 If each team played each of the other teams only once then there was total of 6C2 = 15 games played (each of the 6 teams played 5 games), but if after each

team played each of the other teams only once, some two teams played between each other once more then the total number of games played was 16 (4 teams

played 5 games and 2 teams played 6 games). 

Not sufficient.