Three football teams are taking part in a tournament. Each team plays each other team once. For a win the team scores 3 points, the other team 0 points. For a draw both teams get 1 point each. Which number of points is impossible, for any team to reach at the end of this tournament? (A) 1 (B) 2 (C) 4 (D) 5 (E) 6

Question

Bytelearn · Accepted Answer

Analyze Possible Outcomes: Let's analyze the possible outcomes for each match and the points that can be earned. - If a team wins both of its matches, it will earn 3 points per match, totaling 6 points. - If a team wins one match and draws the other, it will earn 3 points for the win and 1 point for the draw, totaling 4 points. - If a team draws both matches, it will earn 1 point per match, totaling 2 points. - If a team loses one match and draws the other, it will earn 0 points for the loss and 1 point for the draw, totaling 1 point. - If a team loses both matches, it will earn 0 points.Check Answer Options: Now let's check each answer option to see if it's possible for a team to reach that number of points: (A) 1 point is possible by losing one match and drawing one match. (B) 2 points are possible by drawing both matches. (C) 4 points are possible by winning one match and drawing one match. (D) 5 points are not listed in our possible outcomes, so we need to check if it's possible to achieve this score. (E) 6 points are possible by winning both matches.Check Possibility of 5 Points: To check if 5 points are possible, we need to consider the combinations of wins, draws, and losses that could lead to this total: - Winning both matches gives 6 points, not 5. - Winning one match (3 points) and drawing one match (1 point) gives 4 points, not 5. - Drawing both matches gives 2 points, not 5. - It is not possible to reach exactly 5 points with any combination of wins, draws, and losses in two matches.

Full solution

More problems from Compound events: find the number of sums

Related topics