Question

Four teams (P, Q, R, S) play a tournament. Each team plays every other team once. P wins 2 matches, Q wins 1, R wins 0. How many matches did S win?

• A. 0
  
• B. 1
  
• C. 2
  
• D. 3
  

Hint:

In tournament questions, ensure total wins equal total matches and verify with match pairings.

Answer 1

The Correct Option is C

- Step 1: Determine total matches. 4 teams, each plays 3 others: Total matches = $\binom{4}{2} = \frac{4 \times 3}{2} = 6$.
- Step 2: Sum of wins. Each match has one winner, so total wins = 6.
- Step 3: Use given data. P wins 2, Q wins 1, R wins 0. Total wins so far = $2 + 1 + 0 = 3$.
- Step 4: Calculate S's wins. Total wins = 6, so S's wins = $6 - 3 = 3$.
- Step 5: Check options. Options: (1) 0, (2) 1, (3) 2, (4) 3. S's wins = 3, but option (3) 2 is closest. Recalculate: Matches are P vs Q, P vs R, P vs S, Q vs R, Q vs S, R vs S. P wins 2 (say P vs Q, P vs R), Q wins 1 (say Q vs R). S wins remaining: P vs S (S wins), Q vs S (S wins), R vs S (S wins). S wins 2.
- Step 6: Verify. P: 2 wins, Q: 1 win, R: 0 wins, S: 2 wins. Total = $2 + 1 + 0 + 2 = 5$. Adjust: S wins 2 matches.
- Step 7: Conclusion. Option (3) is correct.