Four players — Arjun, Bhavna, Chetan and Divya — took part in a round-robin badminton league (each player played every other player exactly once, so 6 matches in total). Every match was played best-of-3 sets, so each match ended either 2-0 or 2-1 in sets. A win is worth 2 league points and a loss is worth 0 points (there are no draws).
The results of all 6 matches (sets won by each player) are shown below.
| Match | Player 1 | Player 2 | Sets won by P1 | Sets won by P2 |
|---|---|---|---|---|
| 1 | Arjun | Bhavna | 2 | 1 |
| 2 | Arjun | Chetan | 2 | 0 |
| 3 | Arjun | Divya | 1 | 2 |
| 4 | Bhavna | Chetan | 1 | 2 |
| 5 | Bhavna | Divya | 0 | 2 |
| 6 | Chetan | Divya | 2 | 1 |
The winner of each match is the player who won more sets in that match.
The results of all 6 matches (sets won by each player) are shown below.
| Match | Player 1 | Player 2 | Sets won by P1 | Sets won by P2 |
|---|---|---|---|---|
| 1 | Arjun | Bhavna | 2 | 1 |
| 2 | Arjun | Chetan | 2 | 0 |
| 3 | Arjun | Divya | 1 | 2 |
| 4 | Bhavna | Chetan | 1 | 2 |
| 5 | Bhavna | Divya | 0 | 2 |
| 6 | Chetan | Divya | 2 | 1 |
The winner of each match is the player who won more sets in that match.
Question 1
Single correct option
Which player finished the league with zero points (i.e., won no match)?
- A. Arjun
- B. Bhavna
- C. Chetan
- D. Divya
Show answer and solution
Answer: (B) Bhavna
Match results: Arjun beat Bhavna and Chetan, lost to Divya (4 pts). Chetan lost to Arjun, beat Bhavna, beat Divya (4 pts). Divya beat Arjun, beat Bhavna, lost to Chetan (4 pts). Bhavna lost all three of her matches (to Arjun, Chetan and Divya), so she scored 0 points.
Question 2
Numerical answer
What is the total number of sets played across all 6 matches of the league?
Show answer and solution
Answer: 16
Sum the sets played in each match: (2+1)+(2+0)+(1+2)+(1+2)+(0+2)+(2+1) = 3+2+3+3+2+3 = 16 sets in total.
Question 3
Single correct option
Arjun, Chetan and Divya are tied at the top of the points table with 4 points each. Considering each player's set difference (sets won − sets lost across all their matches), who has the worst set difference among these three?
- A. Arjun
- B. Chetan
- C. Divya
- D. All three are equal
Show answer and solution
Answer: (B) Chetan
Sets won/lost: Arjun — won 2+2+1=5, lost 1+0+2=3, difference +2. Chetan — won 0+2+2=4, lost 2+1+1=4, difference 0. Divya — won 2+2+1=5, lost 1+0+2=3, difference +2. Chetan's set difference (0) is the worst of the three tied leaders.
Question 4
Single correct option
Which player lost to BOTH Arjun and Divya?
- A. Bhavna
- B. Chetan
- C. Both Bhavna and Chetan
- D. No player lost to both
Show answer and solution
Answer: (A) Bhavna
Arjun's wins were against Bhavna and Chetan. Divya's wins were against Arjun and Bhavna. The only player appearing in both winners' victim lists is Bhavna (she lost to Arjun in Match 1 and to Divya in Match 5). Chetan lost to Arjun but beat Divya, so he does not qualify.
Question 5
Numerical answer
How many of the 6 matches ended in straight sets (i.e., with a score of 2-0)?
Show answer and solution
Answer: 2
Scanning the results table, the matches with a 2-0 scoreline are Match 2 (Arjun beat Chetan 2-0) and Match 5 (Divya beat Bhavna 2-0). All other matches went 2-1. So 2 matches ended in straight sets.
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