CAT 2021 Slot 2 — DILR Question 11
Answer the next 4 questions based on the information given
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:
- Chitra did not win the championship.
- Aruna did not play against Arif. Brij did not play against Brinda.
- 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?
Answer & solution
- A
Brij
- B
Chitra
Dipen
- D
Aruna
According to the information given we can draw the following table.
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The winner of any group will have to play at least 2 games (at least one game in the group stage and 1 semi-final)
Let us first consider group B:
The winner of group B cannot be Brinda or Brij hence it has to be Biju.
Biju must have played one game each with Brinda and Brij in any order. Biju must have won both his group matches and qualified for the semi-finals.
Now, in the semi-final Biju must have played against the winner of group A. Biju would have lost this match since Biju only plays 3 matches.
∴ The winner of semi-final between group A and B is the winner of group B.
Let us now consider group D:
This case is same as that of group B.
Here, Dipen must have played one game each with Donna and Deb in any order. Dipen must have won both his group matches and qualified for the semi-finals.
Now, in the semi-final Dipen must have played against the winner of group C. Dipen would have lost this match since Dipen only plays 3 matches.
∴ The winner of semi-final between group C and D is the winner of group C.
∴ Final will be played between winners of group A and C.
Now winners of group A and group C must have played at least 3 matches (at least one match in group stage, 1 semi-final and 1 final)
∴ Winner of group A can only be Aruna and winner of group C can only be Chitra.
Since Chitra cannot be the champion hence Aruna will win the final and become the Champion.
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As per the rules of the game, one of 2nd or 3rd ranked player of any group will play 2 matches in the group stage and the 1st ranked player will play only 1 match in group stage.
In group D, Dipen is definitely playing 2 matches during group stage, hence Dipen is definitely not the 1st ranked player in group D.
Hence, option (c).