# CAT 2023 LRDI Slot 3 | Previous Year CAT Paper

**Answer the following questions based on the information given below:**

In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months – January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.

1. In every month, both online and offline registration numbers were multiples of 10.

2. In January, the number of offline registrations was twice that of online registrations.

3. In April, the number of online registrations was twice that of offline registrations.

4. The number of online registrations in March was the same as the number of offline registrations in February.

5. The number of online registrations was the largest in May.

**1. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

What was the total number of registrations in April?

Answer: 120

**Explanation** :

We get the following table based on the conditions given.

Total registrations in April is 120.

Hence, 120.

Workspace:

**2. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

What was the number of online registrations in January?

Answer: 40

**Explanation** :

We get the following table based on the conditions given.

Number of online registrations in January is 40.

Hence, 40.

Workspace:

**3. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

Which of the following statements can be true?

I. The number of offline registrations was the smallest in May.

II. The total number of registrations was the smallest in February.

- A.
Only II

- B.
Only I

- C.
Both I and II

- D.
Neither I nor II

Answer: Option B

**Explanation** :

We get the following table based on the conditions given.

Offline registrations is smallest in May. Hence, I is correct.

Total registrations was highest in Feb. Hence, II is incorrect.

Hence, option (b).

Workspace:

**4. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

What best can be concluded about the number of offline registrations in February?

- A.
50

- B.
30 or 50 or 80

- C.
50 or 80

- D.
80

Answer: Option A

**Explanation** :

We get the following table based on the conditions given.

Number of offline registrations in February is 50.

Hence, option (a).

Workspace:

**5. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

Which pair of months definitely had the same total number of registrations?

I. January and April

II. February and May

- A.
Neither I nor II

- B.
Only II

- C.
Only I

- D.
Both I and II

Answer: Option D

**Explanation** :

We get the following table based on the conditions given.

Jan and April both have 120 total registrations.

Feb and May both have 130 total registrations.

Hence, optiono (d).

Workspace:

**Answer the following questions based on the information given below:**

There are only three female students – Amala, Koli and Rini – and only three male students – Biman, Mathew and Shyamal – in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1.

The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project.

The following additional facts are known about the scores in the project and the test.

1. The minimum, maximum and the average of both project and test scores were identical – 40, 80 and 60, respectively.

2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores.

3. Amala’s score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score.

4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate.

5. Biman scored the second lowest in the test and the lowest in the aggregate.

6. Mathew scored more than Rini in the project, but less than her in the test.

**6. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

What was Rini’s score in the project?

Answer: 60

**Explanation** :

We get the following table from conditions given in the question.

Rani's score in project is 60.

Hence, 60.

Workspace:

**7. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

What was the weight of the test component?

- A.
0.75

- B.
0.60

- C.
0.40

- D.
0.50

Answer: Option B

**Explanation** :

We get the following table from conditions given in the question.

Weight of test componenet is 0.6.

Hence, option (b).

Workspace:

**8. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

What was the maximum aggregate score obtained by the students?

- A.
66

- B.
80

- C.
62

- D.
68

Answer: Option D

**Explanation** :

We get the following table from conditions given in the question.

Aggregate score was maximum for Amal.

Amala's maximum score = 80 × 0.4 + 60 × 0.6 = 32 + 36 = 68.

Hence, option (d).

Workspace:

**9. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

What was Mathew’s score in the test?

Answer: 40

**Explanation** :

We get the following table from conditions given in the question.

Mathew's score in test is 40.

Hence, 40.

Workspace:

**10. CAT 2023 LRDI Slot 3 | LR - Mathematical Reasoning**

Which of the following pairs of students were part of the same project team?

i) Amala and Biman

ii) Koli and Mathew

- A.
Neither i) nor ii)

- B.
Only ii)

- C.
Only i)

- D.
Both i) and ii)

Answer: Option A

**Explanation** :

We get the following table from conditions given in the question.

A and B are not in same team.

K and M are not in same team.

Neither i) nor ii) is correct.

Hence, option (a).

Workspace:

**Answer the following questions based on the information given below:**

An air conditioner (AC) company has four dealers – D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of ACs – Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.

The following information is also known:

1. Every dealer sold at least two window ACs.

2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.

3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.

4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.

5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.

6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.

7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

**11. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution**

How many Split Inverter ACs did D2 sell?

Answer: 14

**Explanation** :

We can make the following table based on the conditions given in the question.

Number of Split Inverter ACs sold by D2 = 14.

Hence, 14.

Workspace:

**12. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution**

What percentage of ACs sold were of Non-inverter type?

- A.
33.33%

- B.
75.00%

- C.
20.00%

- D.
25.00%

Answer: Option D

**Explanation** :

We can make the following table based on the conditions given in the question.

Total non-Inverter ACs = 6 + 9 = 15.

∴ Required % = 15/60 × 100 = 25%

Hence, option (d).

Workspace:

**13. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution**

What was the total number of ACs sold by D2 and D4?

Answer: 33

**Explanation** :

We can make the following table based on the conditions given in the question.

D1 and D3 sold a total of 27 ACs.

Hence, D2 and D4 sold a total of 60 - 27 = 33 ACs

Hence, 33.

Workspace:

**14. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution**

Which of the following statements is necessarily false?

- A.
D1 and D3 sold an equal number of Split ACs.

- B.
D1 and D3 together sold more ACs as compared to D2 and D4 together.

- C.
D2 sold the highest number of ACs.

- D.
D4 sold more Split ACs as compared to D3.

Answer: Option B

**Explanation** :

We can make the following table based on the conditions given in the question.

D1 and D3 together sold 27 ACs whereas D2 and D4 together sold 33 ACs.

Therefore, option (b) is false.

Hence, option (b).

Workspace:

**15. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution**

If D3 and D4 sold an equal number of ACs, then what was the number of Non-inverter ACs sold by D2?

- A.
7

- B.
5

- C.
6

- D.
4

Answer: Option B

**Explanation** :

We can make the following table based on the conditions given in the question.

D3 and D4 sold equal number of ACs i.e., each of them sold 12 ACs.

For D3: 12 = 2 + 0 + 7 + (4 - c)

⇒ c = 1

∴ Number of non-Inverter ACs sold by D2 = 4 + 1 = 5

Hence, option (b).

Workspace:

**Answer the following questions based on the information given below:**

A, B, C, D, E and F are the six police stations in an area, which are connected by streets as shown below. Four teams – Team 1, Team 2, Team 3 and Team 4 – patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.

The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.

The following facts are known.

1. None of the streets has more than one team traveling along it in any direction at any point in time.

2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.

3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.

4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.

5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.

6. Team 4 never passes through Stations B, D or F.

**16. CAT 2023 LRDI Slot 3 | DI - Routes & Networks**

Which one among the following stations is visited the largest number of times?

- A.
Station C

- B.
Station D

- C.
Station E

- D.
Station F

Answer: Option C

**Explanation** :

We get the following schedule based on the conditions given in the question.

Number of times each station is visited (excluding the starting station)

C - 3

D - 2

E - 4/5

F - 3

Of the stations mentioned in options, E is visited the maximum number of times.

Hence, option (c).

Workspace:

**17. CAT 2023 LRDI Slot 3 | DI - Routes & Networks**

How many times do the teams pass through Station B in a day?

Answer: 2

**Explanation** :

We get the following schedule based on the conditions given in the question.

Station B is passed through twice by T1 at 9:30 am and at 11:30 am.

Hence, 2.

Workspace:

**18. CAT 2023 LRDI Slot 3 | DI - Routes & Networks**

Which team patrols the street connecting Stations D and E at 10:15 hrs?

- A.
Team 3

- B.
Team 1

- C.
Team 2

- D.
Team 4

Answer: Option A

**Explanation** :

We get the following schedule based on the conditions given in the question.

Team 3 is patrolling D-E route from 10 to 10:30.

Hence, option (a).

Workspace:

**19. CAT 2023 LRDI Slot 3 | DI - Routes & Networks**

How many times does Team 4 pass through Station E in a day?

Answer: 2

**Explanation** :

We get the following schedule based on the conditions given in the question.

Team 4 passes through station E at 9:30 am and at 11:30 am, i.e., 2 times.

Hence, 2.

Workspace:

**20. CAT 2023 LRDI Slot 3 | DI - Routes & Networks**

How many teams pass through Station C in a day?

- A.
3

- B.
4

- C.
1

- D.
2

Answer: Option D

**Explanation** :

We get the following schedule based on the conditions given in the question.

Team 3 and 4, i.e., 2 teams pass through C at least once.

Hence, option (d).

Workspace:

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