LogicalAndReasoning AMC10/12

Problem - 364
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?

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