8 Round Tournament
(CAT 2022)
Pulak, Qasim, Ritesh, and Suresh participated in a tournament comprising of eight rounds. In each round, they formed two pairs, with each of them being in exactly one pair. The only restriction in the pairing was that the pairs would change in successive rounds. For example, if Pulak formed a pair with Qasim in the first round, then he would have to form a pair with Ritesh or Suresh in the second round. He would be free to pair with Qasim again in the third round. In each round, each pair decided whether to play the game in that round or not. If they decided not to play, then no money was exchanged between them. If they decided to play, they had to bet either ₹1 or ₹2 in that round. For example, if they chose to bet ₹2, then the player winning the game got ₹2 from the one losing the game.
At the beginning of the tournament, the players had ₹10 each. The following table shows partial information about the amounts that the players had at the end of each of the eight rounds. It shows every time a player had ₹10 at the end of a round, as well as every time, at the end of a round, a player had either the minimum or the maximum amount that he would have had across the eight rounds. For example, Suresh had ₹10 at the end of Rounds 1, 3, and 8 and not after any of the other rounds. The maximum amount that he had at the end of any round was ₹13 (at the end of Round 5), and the minimum amount he had at the end of any round was ₹8 (at the end of Round 2). At the end of all other rounds, he must have had either ₹9, ₹11, or ₹12.
It was also known that Pulak and Qasim had the same amount of money with them at the end of Round 4.
Pulak, Qasim, Ritesh, and Suresh participated in a tournament comprising of eight rounds. In each round, they formed two pairs, with each of them being in exactly one pair. The only restriction in the pairing was that the pairs would change in successive rounds. For example, if Pulak formed a pair with Qasim in the first round, then he would have to form a pair with Ritesh or Suresh in the second round. He would be free to pair with Qasim again in the third round. In each round, each pair decided whether to play the game in that round or not. If they decided not to play, then no money was exchanged between them. If they decided to play, they had to bet either ₹1 or ₹2 in that round. For example, if they chose to bet ₹2, then the player winning the game got ₹2 from the one losing the game.
At the beginning of the tournament, the players had ₹10 each. The following table shows partial information about the amounts that the players had at the end of each of the eight rounds. It shows every time a player had ₹10 at the end of a round, as well as every time, at the end of a round, a player had either the minimum or the maximum amount that he would have had across the eight rounds. For example, Suresh had ₹10 at the end of Rounds 1, 3, and 8 and not after any of the other rounds. The maximum amount that he had at the end of any round was ₹13 (at the end of Round 5), and the minimum amount he had at the end of any round was ₹8 (at the end of Round 2). At the end of all other rounds, he must have had either ₹9, ₹11, or ₹12.
It was also known that Pulak and Qasim had the same amount of money with them at the end of Round 4.
| Pulak | Qasim | Ritesh | Suresh | |
| Round 1 | ₹8 | ₹10 | ₹10 | |
| Round 2 | ₹13 | ₹10 | ₹8 | |
| Round 3 | ₹10 | |||
| Round 4 | ||||
| Round 5 | ₹10 | ₹10 | ₹13 | |
| Round 6 | ||||
| Round 7 | ₹12 | ₹4 | ||
| Round 8 | ₹13 | ₹10 |
1) What BEST can be said about the amount of money that Ritesh had with him at the end of Round 8?
4) How many games were played with a bet of ₹2?
5) Which of the following pairings was made in Round 5?
- Exactly ₹6
- ₹4 or ₹5
- Exactly ₹5
- ₹5 or ₹6
- Exactly ₹12
- ₹11 or ₹12
- Exactly ₹11
- ₹12 or ₹13
4) How many games were played with a bet of ₹2?
5) Which of the following pairings was made in Round 5?
- Pulak and Ritesh
- Pulak and Qasim
- Pulak and Suresh
- Qasim and Suresh
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