# CAT 2022 Question Paper Slot 3

Instructions

There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto.During the onset of a pandemic, the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of newcases recorded in any of the neighbourhoods was either 0, 1, 2 or 3.

The following facts are also known:

1.There was at least one new case in every neighbourhood on Day 1.
2.On each of the five days, there were more new cases in Kitmisto than in Pesmisto.
3.The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.
4.The maximum number of new cases in a day in Pesmisto was 2, and this happened only once during the five-day period.
5.Kitmisto is the only place to have 3 new cases on Day 2.
6.The total numbers of new cases in Levmisto, Tyhrmisto, Pesmisto and Kitmisto over the five-day period were 12, 12, 5 and 14 respectively.

Question 31

Question 32

Question 33

Question 34

## On how many days did Levmisto and Tyhrmisto have the same number of new cases?

Instructions

All the first-year students in the computer science (CS) department in a university take both the courses (i) AI and (ii) ML. Students from other departments (non-CS students) can also take one of these two courses, but not both. Students who fail in a course get an F grade;others pass and are awarded A or B or C grades depending on their performance. The following are some additional facts about the number of students who took these two courses this year and the grades they obtained.

1.The numbers of non-CS students who took AI and ML were in the ratio 2 : 5.
2.The number of non-CS students who took either AI or ML was equal to the number of CS students.
3.The numbers of non-CS students who failed in the two courses were the same and their total is equal to the number of CS students who got a C grade in ML.
4. In both the courses, 50% of the students who passed got a B grade. But, while the numbers of students who got A and C grades were the same for AI, they were in the ratio 3 :2 for ML.
5. No CS student failed in AI, while no non-CS student got an A grade in AI.
6.The numbers of CS students who got A, B and C grades respectively in AI were in the ratio 3 : 5 : 2, while in ML the ratio was 4 : 5 : 2.
7.The ratio of the total number of non-CS students failing in one of the two courses to theÂ Â number of CS students failing in one of the two courses was 3 : 1.
8. 30 students failed in ML.

Question 35

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Question 38

Question 39

## How many non-CS students got B grade in ML?

Instructions

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 â‚¹1 or â‚¹2 in that round. For example, if they chose to bet â‚¹2, then the player winning the game got â‚¹2 from the one losing the game.

At the beginning of the tournament, the players had â‚¹10 each. The following table shows partial information about the amounts that the players had at the end of each of the eightrounds. It shows every time a player had â‚¹10 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 â‚¹10 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 â‚¹13 (at the end of Round 5), and the minimum amount he had at the end of any round was â‚¹8 (at the end of Round 2). At the end of all other rounds, he must have had either â‚¹9, â‚¹11, or â‚¹12.

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

Question 40