# CAT 2022 DILR - Slot 1

Get the complete CAT 2022 paper with answers and explanations

## CAT 2022 Question Paper With Answers & Explanation

### Section-1

Question Numbers (1 to 5): The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals.

The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.

1. Only one goal was scored in every even numbered match.
2. Harita scored more goals than Bimla.
3. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
4. Bimla scored a goal in Match 1 and one each in three other consecutive matches.
5. An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.
6. The match in which the highest number of goals was scored was unique and it was not Match 5.

#### Q. 1 How many goals were scored in Match 7?

1

###### Explanation

In Match 7, one goal was scored.

#### Q. 2 Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?

4

###### Explanation

The correct sequence of goals scored in matches 1, 3, 5 and 7 is 4, 1, 2, 1.

#### Q. 3 Which of the following statement(s) is/are true?Statement-1: Amla and Sarita never scored goals in the same match.Statement-2: Harita and Sarita never scored goals in the same match.

2

###### Explanation

Both the statements are true.

#### Q. 4 Which of the following statement(s) is/are false?Statement-1: In every match at least one player scored a goal.Statement-2: No two players scored goals in the same number of matches.

2

###### Explanation

None of the statements is false.

#### Q. 5 If Harita scored goals in one more match as compared to Sarita, which of the following statement(s) is/are necessarily true?Statement-1: Amla scored goals in consecutive matches.Statement-2: Sarita scored goals in consecutive matches.

3

###### Explanation

None of the statements is true.

Question Numbers (6 to 10): There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer.

Some students are not interested in attending the gettogether. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event.

The following facts are also known:
1. All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.
2. Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.
3. 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
4. No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.
5. The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.

#### Q. 6 How many boys are there in the class?

50

###### Explanation

50 boys are there in the class.

#### Q. 7 Which of the following can be determined from the given information? I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers. II. The number of female dancers who are interested in attending a 1-day event.

1

###### Explanation

Statement I cannot be determined.

#### Q. 8 What fraction of the class are interested in attending a 2-day event?

2

###### Explanation

The fraction of the class interested in attending a 2-day event is 7/13.

#### Q. 9 What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?

4

###### Explanation

The numbers of male dancers who are interested in attending a 1-day event can be either 5 or 6.

#### Q. 10 How many female dancers are interested in attending a 2-day event?

3

###### Explanation

Number of female dancers interested in attending a 2-day event is equal to ‘0’.

Question Numbers (11 to 15): Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only.

Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000.

Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000. The following additional facts are known:

1. Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.

2. Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.

3. Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.

2

#### Q. 12 Who among the following definitely received a token from Bithi but not from Dhanavi?

4

###### Explanation

Pragnyaa definitely received a token from Bithi but not from Dhanavi.

#### Q. 13 How many tokens did Chhaya award?

3

###### Explanation

Chhaya awarded 3 tokens – Pragnyaa, Rashida and either Smera or Tantra.

#### Q. 14 How many tokens did Smera receive?

3

###### Explanation

Total funds received by Smera was either 66000 or 165000, so tokens received were either (3, 2, 11) or (3, 5, 11). In either case the total number of tokens was 3.

#### Q. 15 Which of the following could be the amount of funding that Tantra received? (a) Rs. 66,000 (b) Rs. 165,000

2

###### Explanation

The funds received by Tantra could be either Rs.66,000 or Rs.1,65,000. Hence, option (2) is correct.

Question Numbers (16 to 20):

Given above is the schematic map of the metro lines in a city with rectangles denoting terminal stations (e.g. A), diamonds denoting junction stations (e.g. R) and small filled-up circles denoting other stations. Each train runs either in east-west or north-south direction, but not both. All trains stop for 2 minutes at each of the junction stations on the way and for 1 minute at each of the other stations. It takes 2 minutes to reach the next station for trains going in east-west direction and 3 minutes to reach the next station for trains going in north-south direction. From each terminal station, the first train starts at 6 am; the last trains leave the terminal stations at midnight. Otherwise, during the service hours, there are metro service every 15 minutes in the north-south lines and every 10 minutes in the east-west lines. A train must rest for at least 15 minutes after completing a trip at the terminal station, before it can undertake the next trip in the reverse direction. (All questions are related to this metro service only. Assume that if someone reaches a station exactly at the time a train is supposed to leave, (s)he can catch that train.)

#### Q. 16 If Hari is ready to board a train at 8:05 am from station M, then when is the earliest that he can reach station N?

3

###### Explanation

Given that Hari is ready to board a train at 8:05 am from station M.
Trains leave after every 10 minutes. So Hari can catch the 8:10 train from M.
There are 17 stations, 2 junctions and 20 intervals, so time taken to travel = 20 × 2 + 17 × 1 + 2 × 2 = 61 minutes
Hence, time at which Hari reaches station N = 8:10 + 1:01 = 9:11 am.

#### Q. 17 If Priya is ready to board a train at 10:25 am from station T, then when is the earliest that she can reach station S?

2

###### Explanation

There can be two routes that Priya can take.
Case 1: First travel by East-West line and then North-South line.
Trains leave after every 10 minutes on the East- West line.
The 10:20 am train from P reaches and then leaves T at = 10:20 + 00:11 + 00:02 = 10:33 am In the first case Priya will have to wait for 8 minutes at the station before boarding the train.
So let us see if the waiting time is reduced in case 2.
Case 2: First travel by North-South line and then East-West line.
Trains leave after every 15 minutes on the North- South line. The 10:15 am train from B will reach T at = 10:15 + 00:11 = 10:26 am and leave T at 10:28 am. In this case Priya’s train leaves within 3 minutes of her reaching the station. This train reaches R at = 10:28 + 00:15 = 10:43 am.
From R Priya has to catch the East-West train for station S.
The 10:30 am train from M reaches R at = 10:30 + 00:11 = 10:41 am and leaves at 10:43 am.
Priya can catch this train and reach station S at = 10:43 + 00:29 = 11:12 am.

#### Q. 18 Haripriya is expected to reach station S late. What is the latest time by which she must be ready to board at station S if she must reach station B before 1 am via station R?

4

###### Explanation

The last (midnight) train from A reaches R at 12:11 am and leaves at 12:13 am. It will reach B at = 12:13 + 00:17 + 00:11 = 12:41 am.
From S to R the travel time is 29 minutes. To catch the 12:13 am train Haripriya will have to start from S at = 12:13 – 00:29 = 11:44 pm or before that.
Trains start from N after every 10 minutes and the time taken to reach S is 17 minutes.
There is a stoppage of 2 minutes at S.
The 11:30 pm train from N reaches S at 11:47 pm, which does not serve the purpose.
The 11:20 pm train from N reaches S at 11:37 pm and leaves at 11:39 pm.
This train will reach R by 11:39 + 00:29 = 12:08 am.
Then she can catch the last train from A going to B at 12:13 am.
Haripriya can catch the train at S if she reaches the station latest by 11:39 pm.

#### Q. 19 What is the minimum number of trains that are required to provide the service on the AB line (considering both north and south directions)?

8

###### Explanation

Total time for a train to travel from A to B and to start back = 11 + 2 + 15 + 2 + 11 + 15 = 56 minutes.
Trains leave after every 15 minutes.
The minimum number of trains that are required to provide the service on the AB line (in the North-South direction) = [56/15] = [3.733] = 4 trains
Hence, for both directions = 4 + 4 = 8 trains.

#### Q. 20 What is the minimum number of trains that are required to provide the service in this city?

48

###### Explanation

The minimum number of trains that are required to provide the service in this city
= Trains in AB and CD lines + Trains in MN and PQ lines.
Time taken for a train to travel from M to N and start back
= 11 + 2 + 29 + 2 + 17 + 15 = 76 minutes.
Trains leave after every 10 minutes on this line.
The minimum number of trains required on the MN line in the East-West direction
= [76/10] = [7.6] = 8 trains
Minimum number of trains required in both directions on the MN line = 16 trains Hence, total number of trains required
= (AB + CD) + (MN + PQ) = (8 + 8) + ( 16 + 16) = 48.