# CAT 2022 LRDI Slot 1 | Previous Year CAT Paper

**Directions for next 5 questions**

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.)

**1. CAT 2022 LRDI Slot 1 | DI - Routes & Networks**

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?

- A.
9:06 am

- B.
9:01 am

- C.
9:13 am

- D.
9:11 am

Answer: Option D

**Explanation** :

A train leaves M every 10 minutes starting at 6 am.

If Hari reaches M at 8:05, he can catch the train that leaves at 8:10 am.

Time taken by Hari to reach N:

There are total 20 stations from M till N, hence total travelling time = 20 × 2 = 40 minutes.

There are 2 junctions, hence stoppage time = 2 × 2 = 4 mins

There are 17 other stations, hence stoppage time = 17 × 1 = 17 mins

∴ Total time taken = 40 + 4 + 17 = 61 mins.

∴ Hari reaches N at 8:10 am + 61 minutes = 9:11 am.

Hence, option (d).

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**2. CAT 2022 LRDI Slot 1 | DI - Routes & Networks**

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?

- A.
11:12 am

- B.
11:07 am

- C.
11:28 am

- D.
11:22 am

Answer: Option A

**Explanation** :

Priya can go from T to S via R or V.

**Case 1:** T – R – S

The first train to depart T will be at (6 am + 9 + 2 + 2 =) 6:13 am.

∴ Now a train will depart T every 15 minutes, hence the train which Priya can catch for T → R is at 10:28.

Time taken to reach R = 12 + 3 = 15 mins.

∴ Priya reaches R at 10:43 am.

The first train to depart R will be at (6 am + 8 + 3 + 2 =) 6:13 am.

∴ Now a train will depart R every 10 minutes, hence the train which Priya can catch for R → S is at 10:43 itself.

Time taken to reach S = 20 + 9 = 29 mins.

∴ Priya reaches S at 11:12 am.

**Case 2:** T – S – R

The first train to depart T will be at (6 am + 8 + 3 + 2 =) 6:13 am.

∴ Now a train will depart T every 10 minutes, hence the train which Priya can catch for T → V is at 10:33 itself.

Now time taken from T → V is 29 mins and time taken from V → S is 15 mins.

Even if Priya does not have to wait at V she can S latest by 10:33 am + 29 + 15 = 11:17 am.

∴ Priya can reach S latest by 11:12 am.

Hence, option (a).

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**3. CAT 2022 LRDI Slot 1 | DI - Routes & Networks**

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?

- A.
11:35 pm

- B.
11:49 am

- C.
11:39 pm

- D.
11:43 pm

Answer: Option C

**Explanation** :

Route taken by Haripriya: S → R → B

**Time taken from S → R**:

Travel time = 10 × 2 = 20 mins

Stoppage time = 9 × 1 = 9 mins

Total time = 20 + 9 = 29 mins

Similarly, **Time taken from R → B**: 7 × 3 + 7 = 28 mins

In the north-south direction, the first train from A arrives at R at time = 6 am + (3 × 3) + (2 × 1) mins = 6:11 am.

Since R is a junction so this train will halt for 2 minutes at R and leave at 6:13.

Every 15 minutes, a train starts from A in the north-south direction.

The last train that leaves A will be at 12:00 am and it will leave R at 12:13 am, so Haripriya must reach R till 12:13 am.

If she catches this train from R at 12:13, she will reach B by 12:13 + 28 = 12:41 am.

Travelling time between S and R = (10 × 2) + (9 × 1) = 29

So Haripriya must board the train at S by (12:13 - 29 =) 11:44 pm

In the east-west direction, the first train from N arrives at S at time = 6 am + (6 × 2) + (5 × 1) = 6:17 am.

Since S is a junction so this train will halt for 2 minutes at S and leave at 6:19.

Every 10 minutes, a train starts from N in the east-west direction.

Therefore, Haripriya should board the train which leaves S at 11:39.

Hence, option (c).

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**4. CAT 2022 LRDI Slot 1 | DI - Routes & Networks**

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

Answer: 8

**Explanation** :

A train leaves A for B and B to A every 15 minutes starting from 6 am.

Total time taken by a north-south train:

There are total 10 stations from M till N, hence total travelling time = 10 * 3 = 30 minutes.

There are 2 junctions, hence stoppage time = 2 * 2 = 4 mins

There are 7 other stations, hence stoppage time = 7 * 1 = 7 mins

∴ Total time taken = 30 + 4 + 7 = 41 mins.

The train which starts from A to B at 6 am reaches B at 6:41 am. It needs to rest for 15 minutes before it can start the journey back to A i.e., it can start it’s journey at 6:56 or after that.

As per schedule north-south trains leave every 15 minutes starting from 6 am. Hence, the train that starts from A to B at 6 am, can start its backward journey at 7 am.

∴ There have to be trains starting at 6 am, 6:15 am, 6:30 am and 6:45 am before trains coming from A can start their journey back.

Hence, we need at least 4 trains from B to A and similarly from A to B.

∴ We need at least 8 trains on the route AB.

Hence, 8.

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**5. CAT 2022 LRDI Slot 1 | DI - Routes & Networks**

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

Answer: 48

**Explanation** :

Consider the solution to previous question.

We need at least 8 trains on AB route as well as 8 trains on CD route.

∴ 16 trains on north-south routes.

Total time taken by a east-west train = 61 mins (calculated in first question of this set)

A train going from M to N at 6 am will reach N at 7:01 and will be ready for journey back at 7:16 am. A train starts from N every 10 mins. Hence, this train can start its journey at 7:20 am.

∴ There have to be trains starting at 6 am, 6:10 am, 6:20 am, 6:30 am, 6:40 am, 6:50 am, 7 am and 7:10 am before trains coming from M can start their journey back.

Hence, we need at least 8 trains from N to M and similarly from M to N.

∴ We need at least 16 trains on the route MN and 16 trains on PQ route

∴ 32 trains on east-west routes.

⇒ we need at least 16 + 32 = 48 trains.

Hence, 48.

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**Directions for next 5 queestions.**

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 get-together. 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.

**6. CAT 2022 LRDI Slot 1 | LR - Venn Diagram**

How many boys are there in the class?

Answer: 50

**Explanation** :

There are boys and girls in the class. Each of the boy or girl is either a dance or singer or none of these but not both.

There are 6 singers in the class, 4 of them are boys.

⇒ There are 4 male singers and 2 female singers

There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer

⇒ There are 6 male dances and 4 female dancers

From (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.

Since all 4 male singers are interested in a 3-day event, they all must also be interested in a 2-day and a 1-day event.

Since 2 male dancers are interested in a 3-day event, male dancers interested in a 2-day event must be greater than or equal to 2.

From (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.

From (3): 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. Hence, 30% of those who are interested in a 2-day event are dancers or singers.

Now, (2 + b) = 30% of 60% of (10 + x)

⇒ 2 + b + 4 = $\frac{3}{10}$ × $\frac{3}{5}$ × (10 + x)

⇒ 6 + b = $\frac{9}{50}$ × (10 + x)

Here b has to be an integer, hence (10 + x) should be completely divisible by 50.

∴ x should be 40 or 90 or 140 and so on.

But since b cannot be greater than 4, x should be 40 and b = 3.

From (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.

This is only possible when 2 female singers while no female dance is interested in a 2-day event.

From (3): 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.

⇒ 0 + 2 = $\frac{2}{5}$ × (0 + 2 + females interested in a 2-day event who are neither singer nor dancer)

females interested in a 2-day event who are neither singer nor dancer = 3

∴ There are 50 boys in the class.

Hence, 50.

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**7. CAT 2022 LRDI Slot 1 | LR - Venn Diagram**

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.

- A.
Only II

- B.
Neither I nor II

- C.
Only I

- D.
Both I and II

Answer: Option A

**Explanation** :

Consider the solution to first question of this set.

I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers – we don’t this data yet.

II. The number of female dancers who are interested in attending a 1-day event - 5

Hence, option (a).

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**8. CAT 2022 LRDI Slot 1 | LR - Venn Diagram**

What fraction of the class are interested in attending a 2-day event?

- A.
2/3

- B.
7/10

- C.
7/13

- D.
9/13

Answer: Option C

**Explanation** :

Consider the solution to first question of this set.

Total students in the class = 15 + 50 = 65

Total students interested in a 2-day event = 5 + 30 = 35

∴ Required fraction = 35/65 = 7/13

Hence, option (c).

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**9. CAT 2022 LRDI Slot 1 | LR - Venn Diagram**

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

- A.
5 or 6

- B.
5

- C.
6

- D.
4 or 6

Answer: Option A

**Explanation** :

Consider the solution to first question of this set.

Number of male dancers who are interested in attending a 1-day event has to be more than or equal to number of male dancers who are interested in attending a 2-day event i.e., 5 or 6.

Hence, option (a).

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**10. CAT 2022 LRDI Slot 1 | LR - Venn Diagram**

How many female dancers are interested in attending a 2-day event?

- A.
0

- B.
1

- C.
2

- D.
Cannot be determined

Answer: Option A

**Explanation** :

Consider the solution to first question of this set.

Female dancers are interested in attending a 2-day event = 0.

Hence, option (a).

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**Answer the next 5 questions based on the information given below:**

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.

**11. CAT 2022 LRDI Slot 1 | LR - Mathematical Reasoning**

How many tokens did Qahira receive?

Answer: 2

**Explanation** :

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 product of tokes = 390, 210, 165, 77, 66

⇒ Break of tokens received

390 = 2 × 3 × 5 × 13

210 = 2 × 3 × 5 × 7

165 = 3 × 5 × 11

77 = 7 × 11

66 = 2 × 3 × 11

From (1): Fathima awarded tokens to everyone except Qahira,

∴ Fatima must have awarded token number 3 to everyone and Qahira received tokens whose product is 77.

From (1): Adhara awarded tokens to no one except Pragnyaa

∴ Adhara must have awared token 13 and Pragnyaa received tokens whose product is 390.

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

∴ Rashida must have received 4 tokes whose product can only be 210. Also, since Esther did not give her the token, hence Esther must have distributed token number 11.

From (3): Dhanavi awarded a token to Qahira but not to Smera.

∴ Dhanavi must have awared token number 7.

From (3): Bithi awarded a token to Smera but not to Qahira

∴ Bithi/Chhaya could have awared token 2/5 in any order.

If Bithi gives token number 2 to S/T, then Chhaya will given token number 5 to T/S and vice-a-versa.

∴ Qahira received two tokens i.e., 7 and 11.

Hence, 2.

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**12. CAT 2022 LRDI Slot 1 | LR - Mathematical Reasoning**

Who among the following definitely received a token from Bithi but not from Dhanavi?

- A.
Qahira

- B.
Tantra

- C.
Rasheeda

- D.
Pragnyaa

Answer: Option D

**Explanation** :

Consider the solution to first question of this set.

In any of the cases, Pragnyaa definitely received a token from Bithi but not from Dhanavi

Hence, option (d).

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**13. CAT 2022 LRDI Slot 1 | LR - Mathematical Reasoning**

How many tokens did Chhaya award?

Answer: 3

**Explanation** :

Consider the solution to first question of this set.

In any of the cases, Chhaya will definitely distribute 3 tokens.

i.e., to (Pragnyaa, Rasheeda and Smera) or to (Pragnyaa, Rasheeda and Tantra)

Hence, 3.

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**14. CAT 2022 LRDI Slot 1 | LR - Mathematical Reasoning**

How many tokens did Smera receive?

Answer: 3

**Explanation** :

Consider the solution to first question of this set.

In any of the cases, Smera will definitely receive 3 tokens.

i.e., (2, 3 and 11) or (3, 5 and 11)

Hence, 3.

Workspace:

**15. CAT 2022 LRDI Slot 1 | LR - Mathematical Reasoning**

Which of the following could be the amount of funding that Tantra received?

(a) Rs. 66,000

(b) Rs. 165,000

- A.
Neither (a) nor (b)

- B.
Both (a) and (b)

- C.
Only (b)

- D.
Only (a)

Answer: Option B

**Explanation** :

Consider the solution to first question of this set.

Tanta could receive either (2, 3 and 11) tokes or (3, 5 and 11) tokes

i.e., Tanta’s funds can either be Rs. 66,000 or Rs. 165,000

Hence, option (b).

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**Answer the next 5 questions based on the information given below:**

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.

**16. CAT 2022 LRDI Slot 1 | DI - Games & Tournaments**

How many goals were scored in Match 7?

- A.
3

- B.
2

- C.
Cannot be determined

- D.
1

Answer: Option D

**Explanation** :

Total 12 goals were scored by 4 players such that each player scored at least one goal and distinct number of total goals.

There are two possibilities for this:

12 = 1 + 2 + 3 + 6

12 = 1 + 2 + 4 + 5

From (1): Only one goal was scored in every even numbered match.

From (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.

Let the number of goals scored in Match 3 and 7 be x each.

From (6): The match in which the highest number of goals was scored was unique and it was not Match 5.

⇒ Highest goals were scored in Match 1.

From (4): Bimla scored a goal in Match 1 and one each in three other consecutive matches.

From (2): Harita scored more goals than Bimla.

⇒ Bimla scored at least 4 goals while Harita scored at least 5 goals.

∴ 12 = 1 + 2 + 4 + 5

⇒ Bimla scored 4 goals while Harita scored at 5 goals.

From (3): The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.

∴ Harita can score maximum 1 goal each in Match 4 and 5, hence she scores 3 goals in one more Match.

The only match Harita can score 3 goals is Match 1 since highest numbers of goals are scored in Match 1.

From (4): Bimla scored a goal in Match 1 and one each in three other consecutive matches.

∴ Three consecutive matches Bimla can score in are Match 5, 6 and 7.

Now, a + 1 + x + 1 + b + 1 + x + 1 = 12

⇒ a + b + 2x = 8

[Match 7: x has to be greater than or equal to 1.]

**Case 1:** x = 1

⇒ a + b = 6

⇒ a = 4 and b = 2 [a has to be uniquely highest and a, b ≠ x]

**Case 2:** x = 2

⇒ a + b = 4

Rejected as minimum value of a is 4 and that of b is 1.

∴ x = 1, a = 4 and b = 2

Amla or Sarita could have scored 1 or 2 goal in any order.

Number of goals scored in Match 7 = 1.

Hence, option (d).

Workspace:

**17. CAT 2022 LRDI Slot 1 | DI - Games & Tournaments**

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

- A.
4, 1, 2, 1

- B.
5, 1, 0, 1

- C.
3, 1, 2, 1

- D.
3, 2, 1, 2

Answer: Option A

**Explanation** :

Consider the solution to first question of this set.

Goal scored in Match 1, 3, 5 and 7 are 4, 1, 2 and 1 respectively.

Hence, option (a).

Workspace:

**18. CAT 2022 LRDI Slot 1 | LR - Logical Connectives**

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.

- A.
None of the statements

- B.
Statement-2 only

- C.
Statement-1 only

- D.
Both the statements

Answer: Option D

**Explanation** :

Consider the solution to first question of this set.

Statement-1: Amla and Sarita never scored goals in the same match - true

Statement-2: Harita and Sarita never scored goals in the same match - true

∴ Both statements are true.

Hence, option (d).

Workspace:

**19. CAT 2022 LRDI Slot 1 | DI - Games & Tournaments**

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.

- A.
None of the statements

- B.
Both the statements

- C.
Statement-2 only

- D.
Statement-1 only

Answer: Option A

**Explanation** :

Consider the solution to first question of this set.

Statement-1: In every match at least one player scored a goal - true

Statement-2: No two players scored goals in the same number of matches - true

∴ None of the statements is false.

Hence, option (a).

Workspace:

**20. CAT 2022 LRDI Slot 1 | DI - Games & Tournaments**

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.

- A.
Statement-1 only

- B.
None of the statements

- C.
Both the statements

- D.
Statement-2 only

Answer: Option B

**Explanation** :

Consider the solution to first question of this set.

If Harita scored goals in one more match as compared to Sarita, then Sarita scored 2 goals while Amla scored 1 goal.

Statement-1: Amla scored goals in consecutive matches – false

Statement-2: Sarita scored goals in consecutive matches. – not necessarily true

∴ None of the statements is necessarily true.

Hence, option (bs).

Workspace:

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