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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 Rs.1 or Rs.2 in that round. For example, if they chose to bet Rs.2, then the player winning the game got Rs.2 from the one losing the game.

At the beginning of the tournament, the players had Rs.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 Rs.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 Rs.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 Rs.13 (at the end of Round 5), and the minimum amount he had at the end of any round was Rs.8 (at the end of Round 2). At the end of all other rounds, he must have had either Rs.9, Rs.11, or Rs.12.

It was also known that Pulak and Qasim had the same amount of money with them at the end of Round 4.

Figure for CAT 2022 DILR question 20 (Logical Reasoning)

Which of the following pairings was made in Round 5?

Solution

✅ Correct Option: 1
Slide 1/20

Understanding the set:

Pulak, Qasim, Ritesh, and Suresh participated in a tournament comprising eight rounds.

Rules of the tournament:

  1. Every round was played in a pair, which changes in every successive round.

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.

  1. If players play in a round, they had to bet either ₹1 or ₹2 in that round.
  1. At the beginning of the tournament, the players had ₹10 each.

This is a table for games and tournament set:

In this, you will follow the rules/instructions of the game (as given in the set), to fill the following table.

PulakQasimRiteshSureshTotal
Round 1₹8₹10₹10₹40
Round 2₹13₹10₹8₹40
Round 3₹10₹40
Round 4₹40
Round 5₹10₹10₹13₹40
Round 6₹40
Round 7₹12₹4₹40
Round 8₹13₹10₹40

This is a table given in the set, which gives information about two things:

  1. every time a player has ₹10 at the end of a round is already listed in the table.
  1. It tells us about the minimum and maximum amounts that they would have had across the eight rounds.

=> We have the min. and max. amounts that a player will have in these 8 rounds.

PulakQasimRiteshSureshTotal
Round 1₹8₹10₹10₹40
Round 2₹13₹10₹8₹40
Round 3₹10₹40
Round 4₹40
Round 5₹10₹10₹13₹40
Round 6₹40
Round 7₹12₹4₹40
Round 8₹13₹10₹40

Firstly, let's find the money QASIM has at the end of every round.

We know the minimum money Qasim had at the end of any round = Rs 8

and maximum = Rs 12

Also, he will have Rs 10 at the end of round 2 & 5.

Now, the amount he can have at the end of other rounds = Rs 9 or Rs 11

PulakQasimRiteshSureshTotal
Round 1₹8₹10₹10₹40
Round 2₹13₹10₹8₹40
Round 3₹10₹40
Round 4₹40
Round 5₹10₹10₹13₹40
Round 6₹40
Round 7₹12₹4₹40
Round 8₹13₹10₹40

Doing the same for Pulak,

The minimum money he has = Rs 10

And maximum = Rs 13

=> He will have Rs 11 or Rs 12 at the end of other rounds.

PulakQasimRiteshSureshTotal
Round 1₹8₹10₹10₹40
Round 2₹13₹10₹8₹40
Round 3₹10₹40
Round 4₹40
Round 5₹10₹10₹13₹40
Round 6₹40
Round 7₹12₹4₹40
Round 8₹13₹10₹40

For Ritesh,

The minimum money he has = Rs 4

And maximum = Rs 12

=> He will have Rs 5 / Rs 6 / Rs 7 / Rs 8 / Rs 9 / Rs 11 at the end of other rounds.

PulakQasimRiteshSureshTotal
Round 1₹8₹10₹10₹40
Round 2₹13₹10₹8₹40
Round 3₹10₹40
Round 4₹40
Round 5₹10₹10₹13₹40
Round 6₹40
Round 7₹12₹4₹40
Round 8₹13₹10₹40

Doing the same for Suresh,

The minimum money he has = Rs 8

And maximum = Rs 13

=> He will have Rs 9 / Rs 11 / Rs 12 at the end of other rounds.

PulakQasimRiteshSureshTotal
Round 1₹12₹8₹10₹10₹40
Round 2₹13₹10₹9₹8₹40
Round 3₹10₹40
Round 4₹40
Round 5₹10₹10₹7₹13₹40
Round 6₹40
Round 7₹12₹4₹40
Round 8₹13₹10₹40

Now, we know everyone started with Rs 10

=> Total amount = ₹10 + 10 + 10 + 10 = 40 rs

This will remain constant in every round, as they are betting among themselves.

=> Pulak's money at the end of 1st round = 40 - 8 - 10 - 10 = Rs 12

Also, Ritesh's money at the end of 2nd round = 40 - 13 - 10 - 8 = Rs 9

Similarly, Ritesh's money at the end of round 5 = 40 - 10 - 10 - 13 = Rs 7

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40
Round 2₹13₹10₹9₹8₹40
Round 3₹10₹40
Round 4₹40
Round 5₹10₹10₹7₹13₹40
Round 6₹40
Round 7₹12₹4₹40
Round 8₹13₹11₹6₹10₹40

For round 8:

We know the amount bet is either Rs1 or Rs2

Also, Qasim can only have Rs 9 or Rs 11 at the end of any round

=> Qasim's money at the end of Round 8 can't be Rs 9

(as it will imply that he had lost Rs 3, which is not possible since the maximum amount that can be bet is Rs 2)

=> Qasim had Rs 11 at the end of round 8.

Therefore, Ritesh's money at the end of Round 8 = 40 - 13 - 11 - 10 = 6

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40
Round 2₹13₹10₹9₹8₹40
Round 3₹10₹40
Round 4₹40
Round 5₹10₹10₹7₹13₹40
Round 6₹40
Round 7₹12₹12₹4₹12₹40
Round 8₹13₹11₹6₹10₹40

Doing the same for round 7:

We know the amount bet is either Rs1 or Rs2

Also, Pulak can only have Rs 11 or Rs 12 at the end of any round

Let Pulak's money at the end of round 7 be Rs 11

=> Suresh's money will be 40 - 11 - 12 - 4 = Rs 13

But Suresh had Rs 10 at the end of round 8

=> Suresh lost Rs 3 (Rs 13 - Rs 10) in round 8, which is not possible.

(As the maximum amount to bet is Rs 2)

=> Pulak had Rs 12 at the end of round 7.

Therefore, Suresh's money at the end of Round 7 = 40 - 12 - 12 - 4 = Rs 12

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40
Round 2₹13₹10₹9₹8₹40
Round 3₹10₹40
Round 4₹40
Round 5₹10₹10₹7₹13₹40
Round 6₹11₹40
Round 7₹12₹12₹4₹12₹40
Round 8₹13₹11₹6₹10₹40

For round 6:

We know Qasim can have Rs 9 or Rs 11 at the end of any round.

If Qasim has Rs 9 at the end of round 6,

it will imply that he gained Rs 3 (Rs 12 - Rs 9) in round 7

which is not possible.

Therefore, Qasim will have Rs 11 at the end of round 6

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40
Round 2₹13₹10₹9₹8₹40
Round 3₹10₹40
Round 4₹11₹11₹6₹12₹40
Round 5₹10₹10₹7₹13₹40
Round 6₹11₹40
Round 7₹12₹12₹4₹12₹40
Round 8₹13₹11₹6₹10₹40

For round 4,

We are given that Pulak and Qasim had the same amount of money with them at the end of Round 4.

Since Pulak can only have Rs 11 or Rs 12

and Qasim can only have Rs 9 or Rs 11

=> both Pulak and Qasim had Rs 11 at the end of Round 4.

=> Pulak and Qasim were in different teams (as both of them have lost Rs 1), and they would have played with Ritesh or Suresh.

=> Ritesh and Suresh will have a gain of Rs 1 each in round 4.

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40P-Q & R-S
Round 2₹13₹10₹9₹8₹40
Round 3₹10₹40
Round 4₹11₹11₹6₹12₹40
Round 5₹10₹10₹7₹13₹40
Round 6₹11₹40
Round 7₹12₹12₹4₹12₹40
Round 8₹13₹11₹6₹10₹40

We know there will be 2 pairs in every round.

In the first round, as we can see, Pulak has gained Rs 2 and Qasim has lost Rs 2

Also, Ritesh and Suresh have neither gained nor lost any money

=> Pairs were:

  1. Pulak and Qasim

  2. Ritesh and Suresh - did not play.

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40P - Q & R - S
Round 2₹13₹10₹9₹8₹40P - R & Q - S
Round 3₹10₹40
Round 4₹11₹11₹6₹12₹40
Round 5₹10₹10₹7₹13₹40
Round 6₹11₹40
Round 7₹12₹12₹4₹12₹40
Round 8₹13₹11₹6₹10₹40

At the end of Round 2 -

we can see Pulak has gained Rs 1 and Ritesh has lost Rs 1

Also, Qasim has gained Rs 2 and Suresh has lost Rs 2

Therefore, the pairs are:

  1. Pulak (gained Rs 1) and Ritesh (lost Rs 1)

  2. Qasim (Gained Rs 2) & Suresh (lost Rs 2)

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40P - Q & R - S
Round 2₹13₹10₹9₹8₹40P - R & Q - S
Round 3₹11₹10₹40
Round 4₹11₹11₹6₹12₹40
Round 5₹10₹10₹7₹13₹40
Round 6₹11₹40
Round 7₹12₹12₹4₹12₹40
Round 8₹13₹11₹6₹10₹40

In round 3:

We know Q and S were grouped in Round 2

=> they can't be in the same group in round 3.

=> In round 3 Qasim will be grouped with either Pulak or Ritesh.

Also, Qasim will have either Rs 9 or Rs 11 at the end of every round.

CASE 1: If Qasim had Rs 9 in round 3

=> either Pulak or Ritesh will gain Rs 1

But if Pulak gains Rs 1, his amount will become Rs 14 (not possible)

Also, if Ritesh has gained Rs 1, his amount will become Rs 10

=> he will lose Rs 4 in round 4 (which is also not possible)

Therefore, Qasim had Rs 11 in round 3.

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40P - Q & R - S
Round 2₹13₹10₹9₹8₹40P - R & Q - S
Round 3₹11₹11₹8₹10₹40P - S & Q - R
Round 4₹11₹11₹6₹12₹40P - Q & R - S
Round 5₹10₹10₹7₹13₹40
Round 6₹11₹40
Round 7₹12₹12₹4₹12₹40
Round 8₹13₹11₹6₹10₹40

For round 4,

As we can see, Qasim has the same amount in round 4,

=> there will be one more person who has neither gained nor lost.

Now, we already know Suresh had Rs 10.

Also, if Ritesh has neither gained nor lost => Ritesh will have Rs 6 in round 3

=> he lost Rs 3 (Rs 9 - Rs 6) in round 3, which is not possible.

=> In round 4, Pulak and Qasim were in the same group and both of them did not play.

Therefore, Ritesh (lost Rs 2) and Suresh (gained Rs 2) were in the same group.

=> In round 3 groups were,

  1. Pulak (lost Rs 2) and Suresh (gained Rs 2)

  2. Qasim (gained Rs 1) and Ritesh (lost Rs 1)

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40P - Q & R - S
Round 2₹13₹10₹9₹8₹40P - R & Q - S
Round 3₹11₹11₹8₹10₹40P - S & Q - R
Round 4₹11₹11₹6₹12₹40P - Q & R - S
Round 5₹10₹10₹7₹13₹40
Round 6₹11₹40
Round 7₹12₹12₹4₹12₹40
Round 8₹13₹11₹6₹10₹40P - Q & R - S

For round 8,

Pairs will be:

  1. Pulak (gained Rs 1) and Qasim (lost Rs 1)

  2. Ritesh (gained Rs 2) and Suresh (lost Rs 2)

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40P - Q & R - S
Round 2₹13₹10₹9₹8₹40P - R & Q - S
Round 3₹11₹11₹8₹10₹40P - S & Q - R
Round 4₹11₹11₹6₹12₹40P - Q & R - S
Round 5₹10₹10₹7₹13₹40
Round 6₹11₹12₹40P - R & Q - S
Round 7₹12₹12₹4₹12₹40
Round 8₹13₹11₹6₹10₹40P - Q & R - S

For ROUND 6:

Qasim has gained Rs 1 at the end of round 6.

=> There will be someone losing Rs 1.

It can be either Ritesh or Suresh.

Case 1: Ritesh has lost Rs 1

=> Ritesh will have Rs 6 in round 6.

=> Ritesh will lose Rs 2 in round 7 (Rs 6 - Rs 4)

Therefore, there would be someone in round 7 earning Rs 2

But it can't be either Pulak or Suresh, as both of them have Rs 12

and if they lose Rs 2, it will make their amount 12 - 2 = Rs 10, but we already have the data for everyone having Rs 10,

therefore, this case is rejected.

Therefore, Suresh will lose Rs 1 in round 6 and will be grouped with Qasim.

Consequently, Pulak and Ritesh will be in the same group.

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40P - Q & R - S
Round 2₹13₹10₹9₹8₹40P - R & Q - S
Round 3₹11₹11₹8₹10₹40P - S & Q - R
Round 4₹11₹11₹6₹12₹40P - Q & R - S
Round 5₹10₹10₹7₹13₹40
Round 6₹12₹11₹5₹12₹40P - R & Q - S
Round 7₹12₹12₹4₹12₹40P - S & Q - R
Round 8₹13₹11₹6₹10₹40P - Q & R - S

Round 7,

We can see Suresh has not played in this round.

=> there will be one more person who has not played in round 7

No, that person can't be Ritesh, as his amount would become Rs 4

=> he lost Rs 3 in round 6, which is not possible.

Therefore, Pulak and Suresh will be in the same group and have not played.

Consequently, Qasim and Ritesh will be in the same group, with Qasim losing Rs 1.

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40P - Q & R - S
Round 2₹13₹10₹9₹8₹40P - R & Q - S
Round 3₹11₹11₹8₹10₹40P - S & Q - R
Round 4₹11₹11₹6₹12₹40P - Q & R - S
Round 5₹10₹10₹7₹13₹40P - S & Q - R
Round 6₹12₹11₹5₹12₹40P - R & Q - S
Round 7₹12₹12₹4₹12₹40P - S & Q - R
Round 8₹13₹11₹6₹10₹40P - Q & R - S

For round 5:

Pulak has lost Rs 1

=> he will be grouped with either Ritesh or Suresh (both gained Rs 1)

But Pulak and Ritesh will be in the same group in round 6

=> In round 5, Pulak and Suresh will be in the same group,

and Qasim and Ritesh will be in the same group.

PulakQasimRiteshSureshTotal (₹40)Group
Beginning₹10₹10₹10₹10₹40
Round 1₹12₹8₹10₹10₹40P - Q & R - S
Round 2₹13₹10₹9₹8₹40P - R & Q - S
Round 3₹11₹11₹8₹10₹40P - S & Q - R
Round 4₹11₹11₹6₹12₹40P - Q & R - S
Round 5₹10₹10₹7₹13₹40P - S & Q - R
Round 6₹12₹11₹5₹12₹40P - R & Q - S
Round 7₹12₹12₹4₹12₹40P - S & Q - R
Round 8₹13₹11₹6₹10₹40P - Q & R - S

Pulak and Suresh made a pair in round 5.

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