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CAT 2021 Slot 2 DILR · Set 2 of 4Logical ReasoningEasy DifficultyQ5–Q8 · 4 MCQ

CAT 2021 Slot 2 DILR Set 2: Games & Tournaments (4 Questions) with Solutions

The Games & Tournaments set from the official CAT 2021 Slot 2 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2021 Slot 2 DILR · Questions 5–8
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.
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.

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q5. Games & Tournaments

MCQ · +3 / −1
Who among the following was DEFINITELY NOT ranked first in his/her group?
  1. A) Brij
  2. B) Aruna
  3. C) Dipen
  4. D) Chitra
Correct Answer
C) Dipen
Step-by-step solution
📌 Core Concept
Count the games each player played. A player's game count fixes whether that player was ranked first or was a rank 2/3 player, and whether they won the group.
🔢 Step-by-Step Solution
1
In a group, the rank 2 and rank 3 players meet first. The winner then plays rank 1. A rank 1 player therefore plays only 1 game in the group stage. A rank 2/3 player plays 1 game if they lose and 2 if they win. The group winner then plays the semi-final, and possibly the final.
2
Group D: Donna and Deb played 1 game each, and Dipen played 3. A rank 1 player who played 3 games would need an opponent who had already won a game, and that opponent would have played 2 games. Neither Donna nor Deb did. So Dipen cannot be rank 1.
3
Dipen must be a rank 2/3 player. He won the first game, beat the rank 1 player, won the group and played the semi-final. That is 3 games, so he lost the semi-final.
4
Group A: Aruna played 3 games and Azul 2. Aruna did not play Arif (clue 2). If Aruna were rank 2/3, her first-game opponent could only be Azul, who would then have played just 1 game. That contradicts 2 games. So Aruna is rank 1.
5
Group C: Chitra played 3 games and Chetan 2. Dipen lost the semi-final, so the Group C winner won it and played the final. That makes 3 games for rank 1 and 4 for a rank 2/3 player. Chitra, with 3 games, is therefore the winner and rank 1.
6
Brij is in Group B. Biju played 3 games, so Biju is the rank 2/3 player who won the group. Brij and Brinda are the other two, so either could be rank 1. Brij could therefore be ranked first.
Quick Check
Aruna and Chitra are rank 1, Brij could be rank 1, and only Dipen is certainly not rank 1.
Correct Answer: C

Q6. Games & Tournaments

MCQ · +3 / −1
Which of the following pairs must have played against each other in the championship?
  1. A) A) Donna, Chetan
  2. B) B) Azul, Biju
  3. C) C) Deb, Donna
  4. D) D) Chitra, Dipen
Correct Answer
D) D) Chitra, Dipen
Step-by-step solution
📌 Core Concept
Count the games each player played, and work out which matches the tournament structure forces.
🔢 Step-by-Step Solution
1
Group A: Aruna played 3 games and did not play Arif (clue 2). She has to be rank 1, because as a rank 2/3 player she would have met Azul in the first game and left Azul with only 1 game. So Aruna beat Azul in the group, then won the semi-final and played the final.
2
Group B: Biju played 3 games while Brinda and Brij played 1 each. Biju is the rank 2/3 player who won the group, then lost the semi-final to Aruna.
3
Group D: Dipen played 3 games, as Biju did. Dipen won the group and lost the semi-final.
4
Group C: Chitra played 3 games and Chetan 2. Dipen lost the semi-final, so the Group C winner beat Dipen and played the final. Chetan, with only 2 games, cannot be that winner. Chitra, with 3 games, is the Group C winner and is rank 1.
5
Chitra and Dipen therefore met in the semi-final. This is forced.
6
The other pairs can be ruled out. Donna played 1 game, so she did not meet Chetan, whose 2 games were against Chhavi and Chitra. Azul's 2 games were against Arif and Aruna, so Azul did not meet Biju. Deb and Donna each played 1 game, and each of them played Dipen, so they did not play each other.
Why Not the Others
Donna and Chetan are in different groups and never meet.
Azul and Biju are in Groups A and B, which meet only through Aruna and Biju.
Deb and Donna cannot have met, since each played a single game against Dipen.
Correct Answer: D

Q7. Games & Tournaments

MCQ · +3 / −1
Who won the championship?
  1. A) Brij
  2. B) Cannot be determined
  3. C) Aruna
  4. D) Chitra
Correct Answer
C) Aruna
Step-by-step solution
Clue Breakdown:
1
Chitra did not win the championship.
2
Aruna did not play against Arif; Brij did not play against Brinda.
3
Game counts:
Aruna, Biju, Chitra, Dipen: 3 games each.
Azul, Chetan: 2 games each.
Remaining players: 1 game each.
Step-by-Step Deduction Grid:
GroupPlayersGroup WinnerReasoning
AAruna, Azul, ArifArunaAruna didn't play Arif, implying Aruna won without facing Arif.
BBrinda, Brij, BijuBijuBiju played 3 games, indicating he won the group and advanced.
CChitra, Chetan, ChhaviChetanChetan played 2 games, suggesting he won the group but lost in the semi-final.
DDipen, Donna, DebDipenDipen played 3 games, indicating he won the group and advanced.
Semi-Finals and Final:
Semi-Final 1: Aruna (A) vs Biju (B) → Aruna wins.
Semi-Final 2: Chetan (C) vs Dipen (D) → Dipen wins.
Final: Aruna vs Dipen → Aruna wins.
Question Resolution: Chitra did not win, and the only player who could have won is Aruna.
Final Answer Confirmation: Correct Answer: C

Q8. Games & Tournaments

MCQ · +3 / −1
Who among the following did NOT play against Chitra in the championship?
  1. A) Biju
  2. B) Aruna
  3. C) Dipen
  4. D) Chetan
Correct Answer
A) Biju
Step-by-step solution
📌 Core Concept
A player's number of games is fixed by rank and progress. A rank-1 player plays 1 group game. A rank-2 or rank-3 player plays 1 game if they lose the opening group game and 2 if they win it. A group winner then adds a semi-final, and a finalist adds one more game.
🔢 Step-by-Step Solution
1
Group A. Aruna played 3 games, so she won her group and reached the final, or else she won two group games and lost the semi-final. In the second case she would have played both other group members, including Arif, and clue 2 forbids that. So Aruna is rank 1, won Group A, and played the semi-final and the final. Azul (2 games) beat Arif (1 game) in the opening game, then lost to Aruna.
2
Group B. Biju cannot be rank 1. A rank-1 player's second group game is against the opening-game winner, who plays 2 group games, but Brinda and Brij played only 1 game each. So Biju is rank 2 or 3. With 3 games he won both group games and lost the semi-final. Brinda and Brij are the rank-1 player and the opening loser, and clue 2 is satisfied because they never meet. Biju won Group B.
3
Semi-final 1. Aruna (winner of A) and Biju (winner of B) must meet, and Biju loses. Aruna therefore reaches the final.
4
Group D. The same argument applies to Dipen. Donna and Deb played 1 game each, so Dipen is not rank 1. He won both group games and then lost the semi-final, which gives 3 games. The Group C winner therefore beat Dipen.
5
Group C. The Group C winner reached the final, so played at least 3 games. Chetan (2 games) and Chhavi (1 game) cannot be that winner, so Chitra is. With exactly 3 games she is rank 1: one group game, the semi-final and the final. Chetan, as the opening winner, lost to Chitra in the group, and Chhavi lost to Chetan.
6
Final. The final is Aruna against Chitra. Clue 1 says Chitra did not win, so Aruna won.
7
Chitra's opponents. Chitra played Chetan (group), Dipen (semi-final) and Aruna (final). She never played Biju, who lost in the other half of the draw.
Quick Check
Game counts match: Aruna 3, Biju 3, Chitra 3, Dipen 3, Azul 2, Chetan 2, and the other six players 1 each.
Correct Answer: A
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CAT 2021 Slot 2 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Ahmedabad

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