The game of Chango is a game where two people play against each other; one of them wins and the other loses, i.e., there are no drawn Chango games. 12 players participated in a Chango championship. They were divided into four groups: Group A consisted of Aruna, Azul, and Arif; Group B consisted of Brinda, Brij, and Biju; Group C consisted of Chitra, Chetan, and Chhavi; and Group D consisted of Dipen, Donna, and Deb. CAT 2021
Players within each group had a distinct rank going into the championship. The players have NOT been listed necessarily according to their ranks. In the group stage of the game, the second and third ranked players play against each other, and the winner of that game plays against the first ranked player of the group. The winner of this second game is considered as the winner of the group and enters a semi-final.
The winners from Groups A and B play against each other in one semi-final, while the winners from Groups C and D play against each other in the other semi-final. The winners of the two semi-finals play against each other in the final to decide the winner of the championship.
It is known that:
1. Chitra did not win the championship.
2. Aruna did not play against Arif. Brij did not play against Brinda.
3. Aruna, Biju, Chitra, and Dipen played three games each, Azul and Chetan played two games each, and the remaining players played one game each.
Who among the following was DEFINITELY NOT ranked first in his/her group?
1) Dipen 2) Aruna 3) Chitra 4) Brij
Which of the following pairs must have played against each other in the championship?
1) Deb, Donna 2) Azul, Biju 3) Donna, Chetan 4) Chitra, Dipen
Who won the championship?
1) Chitra 2) Brij 3) Aruna 4) Cannot be determined
Who among the following did NOT play against Chitra in the championship?
1) Dipen 2) Biju 3) Chetan 4) Aruna.
Solutions
Let’s walk through each of the four questions using the image and clues provided. Here’s the breakdown:
Key Rules Recap (from question prompt):
- Each group has 3 players.
- Players are internally ranked 1st, 2nd, 3rd (though not in the order shown).
- 2nd and 3rd ranked in each group play first, winner plays the 1st ranked.
- Winner of that second game is Group Winner → enters semi-final.
- Semi-finals:
- Group A winner vs Group B winner
- Group C winner vs Group D winner
- Final: Winners of semi-finals
- Champion: Final winner
✅ Let’s decode the known facts (from image and question):
From the tournament flow chart:
| Group | Winner | Semi-final Opponent | Final? |
|---|---|---|---|
| A | Aruna | vs Biju | ✅ |
| B | Biju | vs Aruna | ❌ |
| C | Chitra | vs Dipen | ✅ |
| D | Dipen | vs Chitra | ❌ |
| Final: Aruna vs Chitra | ✅ | ||
| Champion: Aruna | ✅ |
Also known:
- Aruna did not play against Arif → So Arif ≠ 2nd or 3rd ranked (else Aruna would face him).
- Brij did not play against Brinda → So Brij ≠ 2nd or 3rd ranked (same reason).
- Games played per player (critical clue):
- Played 3 games: Aruna, Biju, Chitra, Dipen
- Played 2 games: Azul, Chetan
- Played 1 game: everyone else
🔎 Question 1: Who among the following was DEFINITELY NOT ranked first in his/her group?
Options:
- Dipen 2) Aruna 3) Chitra 4) Brij
Let’s verify who could NOT be 1st in their group.
→ Option 1: Dipen
- Dipen won Group D (reached semi-final) and played 3 games.
- If he were ranked 1st:
- Would play only 1 match (against winner of Donna vs Deb).
- That’s impossible – he played 3 games!
- ✅ So Dipen is NOT ranked 1st
→ Option 2: Aruna
- Aruna won Group A, then played Semi-final and Final → 3 games ✅.
- If she were 1st ranked:
- She would play 1 game in group, 1 semi, 1 final → total 3 games.
- Consistent ✅ → Possible
→ Option 3: Chitra
- Same logic as Aruna. Group win + Semi + Final = 3 games → ✅ Possible
→ Option 4: Brij
- Brij played only 1 game
- If he were 1st ranked: he would play only 1 game → ✅ possible
- Cannot be sure → Not definite
✅ Correct Answer: 1) Dipen
🔎 Question 2: Which of the following pairs must have played against each other in the championship?
Options:
- Deb, Donna
- Azul, Biju
- Donna, Chetan
- Chitra, Dipen
Let’s check each:
→ Option 1: Deb vs Donna
- Both are in Group D.
- Only 2nd vs 3rd ranked play.
- Deb and Donna both played only 1 game each.
- One must have lost that first match → plausible but not definite they played against each other.
→ Option 2: Azul vs Biju
- Azul → Group A; Biju → Group B → different groups.
- Azul played 2 games, Biju played 3.
- No phase where they must meet → ❌ Not must-have
→ Option 3: Donna vs Chetan
- Donna in Group D, Chetan in C → only meet if both win groups → they didn’t.
- Chitra & Dipen went to semis → ❌ Not possible.
→ Option 4: Chitra vs Dipen
- Confirmed by semi-final: Chitra (Group C winner) vs Dipen (Group D winner).
✅ They definitely played.
✅ Correct Answer: 4) Chitra, Dipen
🔎 Question 3: Who won the championship?
Options:
- Chitra
- Brij
- Aruna
- Cannot be determined
- From the tournament tree (image), Aruna won her semi-final vs Biju and beat Chitra in the final.
✅ Correct Answer: 3) Aruna
🔎 Question 4: Who among the following did NOT play against Chitra?
Options:
- Dipen
- Biju
- Chetan
- Aruna
Let’s track Chitra’s 3 games (from data):
- Chitra vs Chetan or Chhavi (group match)
- Chetan played 2 games → means he beat Chhavi (1), then lost to Chitra (2) → ✅ Chitra vs Chetan
- Chitra vs Dipen (semi-final) → ✅
- Chitra vs Aruna (final) → ✅
Biju lost semi-final to Aruna and is from different half of bracket → ❌ No match with Chitra
✅ Correct Answer: 2) Biju
✅ Final Answers Recap:
| Q. No | Question | Answer |
|---|---|---|
| 1 | Who was definitely not ranked 1st? | 1) Dipen |
| 2 | Which pair must have played each other? | 4) Chitra, Dipen |
| 3 | Who won the championship? | 3) Aruna |
| 4 | Who did not play against Chitra? | 2) Biju |
Let me know if you want a diagram of matches or semi-filled table too!
Who among the following was DEFINITELY NOT ranked first in his/her group? 1) Dipen
Which of the following pairs must have played against each other in the championship? 4) Chitra, Dipen
Who won the championship? 3) Aruna
Who among the following did NOT play against Chitra in the championship? 2) Biju
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