2015 AMC 12A Question 13 - thichhoctoan.com

Question 13

A league with $12$ teams holds a round-robin tournament, with each team playing every other team exactly once. Games either end with one team victorious or else end in a draw. A team scores $2$ points for every game it wins and $1$ point for every game it draws. Which of the following is not a true statement about the list of $12$ scores?

There must be an even number of odd scores.
There must be an even number of even scores.
There cannot be two scores of $0.$
The sum of the scores must be at least $100.$
The highest score must be at least $12.$