Read the following and answer the Questions that follow

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.

The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.

Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.

i) The minimum among the numbers of coins in the three sacks in the box is 1.
ii) The median of the numbers of coins in the three sacks is 1.
iii) The maximum among the numbers of coins in the three sacks in the box is 9.

1) What is the total number of coins in all the boxes in the 3rd row?

(1) 45
(2) 36
(3) 30
(4) 15

2) How many boxes have at least one sack containing 9 coins?

(1) 3
(2) 4
(3) 8
(4) 5

3) For how many boxes are the average and median of the numbers of coins contained in the three sacks in that box the same?

Answer:

4) How many sacks have exactly one coin?

Answer:

5) In how many boxes do all three sacks contain different numbers of coins?

Answer:

Read the following and answer the Questions that follow

Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively.

Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.

Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.

1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.

After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.

6) Which two candidates can belong to the same department?

(1) Prof. Ramaswamy and Prof. Samuel
(2) Prof. Qureshi and Prof. Ramaswamy
(3) Prof. Pakrasi and Prof. Samuel
(4) Prof. Pakrasi and Prof. Qureshi

7) Which of the following can be the number of votes that Prof. Qureshi received from a single department?

(1) 6
(2) 9
(3) 8
(4) 7

8) If Prof. Samuel belongs to B&H, which of the following statements is/are true?

Statement A: Prof. Pakrasi belongs to M&S.
Statement B: Prof. Ramaswamy belongs to O&Q.

(1) Both statements A and B
(2) Only statement B
(3) Only statement A
(4) Neither statement A nor statement B

9) What best can be concluded about the candidate from O&Q?

(1) It was Prof. Ramaswamy.
(2) It was either Prof. Pakrasi or Prof. Qureshi.
(3) It was Prof. Samuel.
(4) It was either Prof. Ramaswamy or Prof. Samuel.

10) Which of the following statements is/are true?

Statement A: Non-candidates from M&S voted for Prof. Qureshi.
Statement B: Non-candidates from F&A voted for Prof. Qureshi.

(1) Both statements A and B
(2) Neither statement A nor statement B
(3) Only statement B
(4) Only statement A

Read the following and answer the Questions that follow

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.

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

(1) Station D
(2) Station F
(3) Station E
(4) Station C

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

Answer:

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

(1) Team 1
(2) Team 2
(3) Team 3
(4) Team 4

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

Answer:

15) How many teams pass through Station C in a day?

(1) 3
(2) 4
(3) 1
(4) 2

Read the following and answer the Questions that follow

Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.

Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.

The table below provides partial information about the five firms.

16) For which firm(s) can the amounts raised by them be concluded with certainty in each year?

(1) Only Czechy
(2) Only Czechy and Drjbna
(3) Only Bzygoo and Czechy and Drjbna
(4) Only Drjbna

17) What best can be concluded about the total amount of money raised in 2015?

(1) It is exactly Rs. 8 crores.
(2) It is either Rs. 7 crores or Rs. 8 crores or Rs. 9 crores.
(3) It is either Rs. 7 crores or Rs. 8 crores.
(4) It is either Rs. 8 crores or Rs. 9 crores.

18) What is the largest possible total amount of money (in Rs. crores) that could have been raised in 2013?

Answer:

19) If Elavalaki raised Rs. 3 crores in 2013, then what is the smallest possible total amount of money (in Rs. crores) that could have been raised by all the companies in 2012?

(1) 11
(2) 9
(3) 12
(4) 10

20) If the total amount of money raised in 2014 is Rs. 12 crores, then which of the following is not possible?

(1) Bzygoo raised more money than Elavalaki in 2014.
(2) Bzygoo raised the same amount of money as Elavalaki in 2013.
(3) Alfloo raised the same amount of money as Drjbna in 2013.
(4) Alfloo raised the same amount of money as Bzygoo in 2014.

CAT 2025 Lesson : DILR: Sep '25 to Oct '25 - Tough Cases - 11 Sep 2025

Dilr Sep 25 To Oct 25