{"status": "success", "data": {"description_md": "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?\n\n$\\textbf{(A)}\\ \\text{There must be an even number of odd scores.}$\n
$\\textbf{(B)}\\ \\text{There must be an even number of even scores.}$
$\\textbf{(C)}\\ \\text{There cannot be two scores of }0\\text{.}$
$\\textbf{(D)}\\ \\text{The sum of the scores must be at least }100\\text{.}$
$\\textbf{(E)}\\ \\text{The highest score must be at least }12\\text{.}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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?

\\textbf{(A)}\\ \\text{There must be an even number of odd scores.}

\\textbf{(B)}\\ \\text{There must be an even number of even scores.}
\\textbf{(C)}\\ \\text{There cannot be two scores of }0\\text{.}
\\textbf{(D)}\\ \\text{The sum of the scores must be at least }100\\text{.}
\\textbf{(E)}\\ \\text{The highest score must be at least }12\\text{.}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2015 AMC 12A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12A_p14", "prev": "/problem/15_amc12A_p12"}}