Question

Teams A, B, C, D and E play a certain number of matches in a tournament. Three points are awarded for a win, 1 point for a tie and 0 for a loss. At the end of the tournament, team B acquired 12 points, team C acquired 6 points, team D acquired 3 points and team E zero points. How many points does A win?
Statement 1: The points won by A is 9 more than the points won by B in his victories
Statement 2: The total number of matches played by B is 5
Directions: This question has a problem and two statements numbered (1) and (2) giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer

• A. statement (1) alone is sufficient to answer the question
• B. statement (2) alone is sufficient to answer the question
• C. both the statements together are needed to answer the question
• D. either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is C

1. First, we need to understand the points system:
   • 3 points for a win
   • 1 point for a tie
   • 0 points for a loss
2. Given data:
   • Team B: 12 points
   • Team C: 6 points
   • Team D: 3 points
   • Team E: 0 points
3. We are required to find the points of Team A.
4. Analyzing Statement 1: "The points won by A is 9 more than the points won by B in his victories."
   • If B only wins matches, B can win a maximum of 12/3 = 4 matches.
   • Therefore, points from B's victories, if he won 4 matches, are 12.
   • Following this, the total points by A will be 12 + 9 = 21 if all matches won by B were victories.
   • However, without knowing how many were victories and ties, this isn't sufficient on its own.
5. Analyzing Statement 2: "The total number of matches played by B is 5."
   • From this statement alone, we know B played 5 matches but cannot determine how B distributed wins and ties among these 5 matches.
   • This information alone is not sufficient to conclude directly about A's points.
6. Combining Statements 1 and 2:
   • B played 5 matches and earned 12 points. Assume B won x matches and tied y matches.
   • Thus, 3x + y = 12 (B's total points).
   • Also, x + y = 5 (total matches B played).
   • Solving the system of equations:
     • Substitute y = 5 - x in 3x + y = 12. 3x + (5 - x) = 12, which simplifies to 2x = 7.
     • Thus, x = 3.5, which is not an integer hence this information didn't directly tell us about the distribution of wins/ties.
     • If B's total victories were 4 (i.e., x = 4), then y = 1 would've been the tied match, which gives us integer values.
     • Hence, wins for B = 12 points properly tallying with victories scenarios.
   • Given this proper tally, A's total points would be 12 + 9 = 21 accounting all wins of B effectively and using Statement 1 properly.
7. Thus, both statements are needed together to resolve problems with the points distribution effectively and conclude the points for Team A are 21.