The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 9 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament? (A) 6 (B) 7 (C) 8 (D) 9 (E) 10
Total number of games = 20
Number of games already played = 5
Number of games left = 15
Number of points after 5 games = 9
Number of points after 20 games = 40
So, they got to score 31 points in 15 games with the least number of wins
Here are a list of possibilities:
15 games, 10 wins and a draw = 10*3 + 1 = 31 Points
15 games, 9 wins and 4 draws = 9*3 + 4 = 31 points
15 games , 8 wins and 7 draws = 8*3 + 7 = 31 points
15 games, 7 wins and 10 draws = 7*3 + 10 = 31 points, but the total number of games is > 15 (17)
So the least number of wins to reach the 40 point mark = 8
Answer C
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