# Tough Logical Reasoning Questions for CAT

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## Tough Logical Reasoning Questions for CAT:

Download important CAT Tough Logical Reasoning Questions PDF based on previous asked questions in CAT and other MBA exams. Top 25 Tough Logical Reasoning questions for CAT quantitative aptitude.

Instructions: Answer the questions on the basis of the information given below.

In a football tournament, all six teams in a pool play each other exactly once. If a team wins, it gets 3 points, if it’s a draw, both the teams get 1 point each. If a team loses, it gets 0 points. The top two teams in each pool qualify for the semi-finals. In case of a tie, the team with the highest goal difference (Goal For -Goals Against) qualifies.

It is known that, in the opening match, Australia lost to India. After the second round (after each team played two matches), the pool table looked as shown in the pic.

In the third round, Australia played South Africa, Sri Lanka played India, and New Zealand played Zimbabwe. All the third round matches were drawn. The following are some results from the fourth and fifth round matches.

(a) Australia won both the fourth and fifth round matches.

(b) Both Sri Lanka and India won their fifth round matches by 3 goals to 0.

(c) South Africa won both the fourth and fifth round matches by 1 goal to 0.

Pool table after the first two rounds:

<img “=”” alt=”” class=”img-responsive” src=”https://cracku.in/media/questionGroup/Screenshot_2014-09-30_18.38.30_1.png “/>

Question 1: Select the statement which is true about the matches played in the first two rounds.

a) India beat New Zealand by 1 goal to 0.

b) Australia beat New Zealand by 4 goals to 0.

c) Australia beat Zimbabwe by 2 goals to 0.

d) India beat Zimbabwe by 2 goals to 1

Question 2: Select the statement which is true about the matches played in the first two rounds.

a) South Africa beat Zimbabwe by 2 goals to 1.

b) Sri Lanka beat South Africa by 1 goal to 0.

c) India beat South Africa by 2 goals to 1

d) India beat Australia by 2 goals to 1.

Question 3: Which team finished at the top of the pool after five rounds of matches?

a) Sri Lanka

b) India

c) Australia

d) Cannot be determined

Question 4: If Australia qualified as one of the two teams from the pool, which was the other team that qualified?

a) Sri Lanka

b) India

c) Australia

d) Cannot be determined

Question 5: What is the number of matches played in the 5th round?

a) 2

b) 3

c) 4

d) Cannot be determined

Instructions: Study the information given below and answer the following questions:

Six school friends, Aarati, Divya, Gayatri, Ila, Janaki and Seema decide to meet-up at a coffee shop near their school. All six of them have pursued 6 different professions (Dentist, Doctor, Engineer, IAS, Interior Designer, Lawyer) and settled in different cities (Bangalore, Chennai, Hyderabad, Kolkatta, Mumbai, Pune). We know the following about the get-together

1) Aarti who lives in Pune came in just after Janaki

2) Seema who is a lawyer and does not stay in Mumbai reached the coffee shop just before the Dentist

3) The Doctor arrived last

4) The woman who lives in Mumbai arrived first at the coffee shop

5) Divya lives in Chennai

6) Ila came in just after the IAS and just before the Doctor

Question 6: What is the profession of the person who arrived third to the coffee-shop?

a) Dentist

b) IAS

c) Interior Designer

d) Lawyer

Question 7: Based on the information given above, we know the professions of how many women?

a) 2

b) 3

c) 4

d) 6

Question 8: Based on the information given above, how many person-city pairs do we know?

a) 1

b) 3

c) 4

d) 6

Question 9: If Ila is an Interior Designer, what is Gayatri’s profession?

a) IAS

b) Doctor

c) Dentist

d) Engineer

Question 10: If Ila is not from Hyderabad, how many different combinations of person-profession-place are possible?

a) 4

b) 6

c) 8

d) None of the above

Instructions: Study the information given below and answer the following questions:

In a neighbourhood, there are 8 boys who play sports among Tennis, Cricket, Rugby, Table-Tennis and Kabaddi. Three of them play 2 games each whereas the other 5 play a single sport each. No two of the boys who play 2 sports each, play the same set of sports.

The following information is known:

1. Sachin played Tennis and Cricket and was the shortest boy.
2. Saurav played Rugby and was taller than Dhoni, Dravid and Kumble. It is also known that Saurav was the third tallest person.
3. Srinath played Cricket and was shorter than only Ishant, who played two sports.
4. Dravid was taller than Kumble but shorter than Dhoni.
5. Kumble played Tennis and was taller than Sehwag, who played Cricket and Kabaddi.
6. 2 boys played Table-Tennis.
7. All the 8 boys were of different heights.
8. Nobody who played 2 sports played Rugby or Table-Tennis.

Question 11: Who played Table-Tennis?

a) Dhoni

b) Dravid

c) Both a) or b)

d) Either a) and b)

Question 12: Which sport(s) does Ishant play?

a) only Cricket

b) Cricket, Tennis

Question 13: Which of the following is a correct combination of Person – Sport – Height (#1 being the tallest and #8 being the shortest)?

a) Sehwag – Cricket – #2

b) Dhoni – Table-Tennis – #4

c) Saurav – Rugby – #5

d) Ishant – Tennis, Kabaddi – #8

Question 14: Which of the following are definitely true?

1. Sehwag is the second shortest person and Srinath is the second tallest person.
2. Sehwag and Sachin play a common sport, while Kumble and Dhoni do not play any sport in common.
3. Kumble is the third tallest person.

a) 1 and 2 only

b) 1 and 3 only

c) 2 and 3 only

d) 1, 2 and 3

Question 15: If the last condition is not given, how many combinations of player-sports can be exactly determined?

a) 3

b) 6

c) 4

d) 5

Instructions: Study the information given carefully and answer the following questions:

Amit needs to get his project approved by the Environment Ministry. He knows that Mr Jain, Mr Kulkarni, Mr Mehra, Mr Mukherjee, Mr Sharma and Mr Verma are the head clerks of the different departments within the ministry. The six departments are Accounts, Administration, Archives, Clearance, Maina and Technical. The ministry building is a two floor building with 3 offices on each floor. Amit knows the following information:
a) Mr Mehra’s office is above the Clearance office
b) The Archives dept office is above the Administration dept office
c) The Technical dept office is above the Accounts department
d) The Accounts department is situated between the Administration department on the left and Mr Kulkarni’s office on the right
e) Mr Jain’s office is above Mr Sharma’s office
f) Mr Mukherjee’s office is above the Administration Department

Question 16: Who is the head clerk of the Main Department?

a) Mr Sharma

b) Mr Verma

c) Mr Mehra

d) Mr Mukherjee

a) Mr Sharma

b) Mr Verma

c) Mr Mehra

d) Mr Mukherjee

Question 18: Which department is situated to the right of Mr Sharma’s office?

a) Archives

c) Main

d) Clearance

Question 19: Whose office is not adjacent (not beside/above/below) to Mr Sharma’s office?

a) Mr Verma

b) Mr Kulkarni

c) Mr Mehra

d) Mr Jain

Question 20: Which department is in the top right corner of the building?

a) Mr Mehra

b) Mr Verma

c) Mr Sharma

d) Mr Mukherjee

Instructions: 3 teams have to be selected from a group of 84 students – aerobics team, hockey team and football team. All the students are part of at least one of the three teams. The following information is known:

Football team has the maximum number of students.
There are 42 students in the aerobics team.
The number of students who were part of only the aerobics team was 4 less than the number of students who were part of only the hockey team.
30 members who belonged to the aerobics team were also part of at least one of the other two teams.
The number of students who were part of only the hockey team was double the number of students who were part of all the three teams.
In the football team, the number of students who were also part of the hockey team was 2 less than the number of students who were part of only the football team.

Question 21: What can be the minimum number of students who are part of both the aerobics team and the football teams, but not the hockey team?

a) 10

b) 11

c) 12

d) 9

Question 22: The number of students in any of the three teams in not less than

a) 30

b) 32

c) 36

d) 38

Question 23: Which of the following pieces of information is sufficient to determine the exact number of students in each team?

a) 18 students belong to only football team

b) 16 students belong to only hockey team

c) 8 students belong to all the three teams

d) 40 students belong to the hockey team

Question 24: If the number of students in the football team who are also in the aerobics team but not in the hockey team is minimum, what is the difference between this value and the number of students in the aerobics team who are also in the hockey team but not in the football team?

a) 0

b) 2

c) 4

d) 3

Question 25: It was decided that no student should be a part of all three teams. So, among those who were part of all three teams, 2 of them withdrew from the aerobics team, 2 of them withdrew from the hockey team and the rest withdrew from the football team. After this rearrangement, which of the following statements is true?

a) Hockey team has the maximum number of students

b) Football team has the maximum number of students

c) Aerobics team has the maximum number of students

d) Either a) or b)

The only possible combination after the first two rounds is:

India beat Australia 1-0
Australia beat NZ 5-1
India beat Zimbabwe 2-1
Sri Lanka beat NZ 1-0
Sri Lanka beat South Africa 1-0
South Africa beat Zimbabwe 2-0

The matches played in the third round are:

Australia vs South Africa
Sri Lanka vs India
NZ vs Zimbabwe

All three matches end in a draw. The points table after the 3rd round is as follows:

India- 7 points, Goal difference = 2
Sri Lanka – 7 points, Goal difference = 2
Australia – 4 points, Goal difference = 3
South Africa -4 points, Goal difference = 1
NZ – 1 point, Goal difference = -5
Zimbabwe – 1 point, Goal difference = -3

The remaining matches are:
Australia vs Sri Lanka
South Africa vs India
Australia vs Zimbabwe
South Africa vs NZ
India vs NZ
Sri Lanka vs Zimbabwe

Since South Africa and Australia won both their 4th and 5th round matches, and India and Sri Lanka won both their 5th round matches, the only possibility is:

4th round matches: Australia vs Sri Lanka and South Africa vs India
5th round matches: Australia vs Zimbabwe; South Africa vs NZ; India vs NZ; Sri Lanka vs Zimbabwe

The points table at the end of the 5th round is as follows:
South Africa – 10 points with a goal difference of 3
Australia – 10 points with a goal difference of >= 5
India – 10 points with a goal difference of 4
Sri Lanka – 10 points with a goal difference <= 3
NZ and Zimbabwe with 1 point each.

The only possible combination after the first two rounds is:

India beat Australia 1-0
Australia beat NZ 5-1
India beat Zimbabwe 2-1
Sri Lanka beat NZ 1-0
Sri Lanka beat South Africa 1-0
South Africa beat Zimbabwe 2-0

The matches played in the third round are:

Australia vs South Africa
Sri Lanka vs India
NZ vs Zimbabwe

All three matches end in a draw. The points table after the 3rd round is as follows:

India- 7 points, Goal difference = 2
Sri Lanka – 7 points, Goal difference = 2
Australia – 4 points, Goal difference = 3
South Africa -4 points, Goal difference = 1
NZ – 1 point, Goal difference = -5
Zimbabwe – 1 point, Goal difference = -3

The remaining matches are:
Australia vs Sri Lanka
South Africa vs India
Australia vs Zimbabwe
South Africa vs NZ
India vs NZ
Sri Lanka vs Zimbabwe

Since South Africa and Australia won both their 4th and 5th round matches, and India and Sri Lanka won both their 5th round matches, the only possibility is:

4th round matches: Australia vs Sri Lanka and South Africa vs India
5th round matches: Australia vs Zimbabwe; South Africa vs NZ; India vs NZ; Sri Lanka vs Zimbabwe

The points table at the end of the 5th round is as follows:
South Africa – 10 points with a goal difference of 3
Australia – 10 points with a goal difference of >= 5
India – 10 points with a goal difference of 4
Sri Lanka – 10 points with a goal difference <= 3
NZ and Zimbabwe with 1 point each.

Sri Lanka beat South Africa by 1 goal to 0.

The only possible combination after the first two rounds is:

India beat Australia 1-0
Australia beat NZ 5-1
India beat Zimbabwe 2-1
Sri Lanka beat NZ 1-0
Sri Lanka beat South Africa 1-0
South Africa beat Zimbabwe 2-0

The matches played in the third round are:

Australia vs South Africa
Sri Lanka vs India
NZ vs Zimbabwe

All three matches end in a draw. The points table after the 3rd round is as follows:

India- 7 points, Goal difference = 2
Sri Lanka – 7 points, Goal difference = 2
Australia – 4 points, Goal difference = 3
South Africa -4 points, Goal difference = 1
NZ – 1 point, Goal difference = -5
Zimbabwe – 1 point, Goal difference = -3

The remaining matches are:
Australia vs Sri Lanka
South Africa vs India
Australia vs Zimbabwe
South Africa vs NZ
India vs NZ
Sri Lanka vs Zimbabwe

Since South Africa and Australia won both their 4th and 5th round matches, and India and Sri Lanka won both their 5th round matches, the only possibility is:

4th round matches: Australia vs Sri Lanka and South Africa vs India
5th round matches: Australia vs Zimbabwe; South Africa vs NZ; India vs NZ; Sri Lanka vs Zimbabwe

The points table at the end of the 5th round is as follows:
South Africa – 10 points with a goal difference of 3
Australia – 10 points with a goal difference of >= 5
India – 10 points with a goal difference of 4
Sri Lanka – 10 points with a goal difference <= 3
NZ and Zimbabwe with 1 point each.

Australia finished at the top of the table.

The only possible combination after the first two rounds is:

India beat Australia 1-0
Australia beat NZ 5-1
India beat Zimbabwe 2-1
Sri Lanka beat NZ 1-0
Sri Lanka beat South Africa 1-0
South Africa beat Zimbabwe 2-0

The matches played in the third round are:

Australia vs South Africa
Sri Lanka vs India
NZ vs Zimbabwe

All three matches end in a draw. The points table after the 3rd round is as follows:

India- 7 points, Goal difference = 2
Sri Lanka – 7 points, Goal difference = 2
Australia – 4 points, Goal difference = 3
South Africa -4 points, Goal difference = 1
NZ – 1 point, Goal difference = -5
Zimbabwe – 1 point, Goal difference = -3

The remaining matches are:
Australia vs Sri Lanka
South Africa vs India
Australia vs Zimbabwe
South Africa vs NZ
India vs NZ
Sri Lanka vs Zimbabwe

Since South Africa and Australia won both their 4th and 5th round matches, and India and Sri Lanka won both their 5th round matches, the only possibility is:

4th round matches: Australia vs Sri Lanka and South Africa vs India
5th round matches: Australia vs Zimbabwe; South Africa vs NZ; India vs NZ; Sri Lanka vs Zimbabwe

The points table at the end of the 5th round is as follows:
South Africa – 10 points with a goal difference of 3
Australia – 10 points with a goal difference of >= 5
India – 10 points with a goal difference of 4
Sri Lanka – 10 points with a goal difference <= 3
NZ and Zimbabwe with 1 point each.

India finished second.

The only possible combination after the first two rounds is:

India beat Australia 1-0
Australia beat NZ 5-1
India beat Zimbabwe 2-1
Sri Lanka beat NZ 1-0
Sri Lanka beat South Africa 1-0
South Africa beat Zimbabwe 2-0

The matches played in the third round are:

Australia vs South Africa
Sri Lanka vs India
NZ vs Zimbabwe

All three matches end in a draw. The points table after the 3rd round is as follows:

India- 7 points, Goal difference = 2
Sri Lanka – 7 points, Goal difference = 2
Australia – 4 points, Goal difference = 3
South Africa -4 points, Goal difference = 1
NZ – 1 point, Goal difference = -5
Zimbabwe – 1 point, Goal difference = -3

The remaining matches are:
Australia vs Sri Lanka
South Africa vs India
Australia vs Zimbabwe
South Africa vs NZ
India vs NZ
Sri Lanka vs Zimbabwe

Since South Africa and Australia won both their 4th and 5th round matches, and India and Sri Lanka won both their 5th round matches, the only possibility is:

4th round matches: Australia vs Sri Lanka and South Africa vs India
5th round matches: Australia vs Zimbabwe; South Africa vs NZ; India vs NZ; Sri Lanka vs Zimbabwe

The points table at the end of the 5th round is as follows:
South Africa – 10 points with a goal difference of 3
Australia – 10 points with a goal difference of >= 5
India – 10 points with a goal difference of 4
Sri Lanka – 10 points with a goal difference <= 3
NZ and Zimbabwe with 1 point each.

4 matches were played in the 5th round.

We know that Ila came in just after the IAS and just before the Doctor and that the Doctor came in last. Hence, the order is A-B-C-IAS – Ila – Doctor. From 4, Mum – B – C – IAS- Ila-Doctor. Seema, a lawyer reached just before dentist. As she is not from Mumbai, she could not have reached first. The only space available then for Lawyer – Dentist is B-C. Hence, Mumbai – Seema(Lawyer) – Dentist – IAS – Ila – Doctor. Now Aarti came in just after Janaki. The only place for them to be together is if Janaki is the Dentist and Aarti is IAS. Hence, we have Mum – Seema(Lawyer) – Janaki(Dentist) – Aarti(IAS) – Ila – Doctor. Thus, the profession of the person who arrived third is Dentist.

We know that Ila came in just after the IAS and just before the Doctor and that the Doctor came in last. Hence, the order is A-B-C-IAS – Ila – Doctor. From 4, Mum – B – C – IAS- Ila-Doctor. Seema, a lawyer reached just before dentist. As she is not from Mumbai, she could not have reached first. The only space available then for Lawyer – Dentist is B-C. Hence, Mumbai – Seema(Lawyer) – Dentist – IAS – Ila – Doctor. Now Aarti came in just after Janaki. The only place for them to be together is if Janaki is the Dentist and Aarti is IAS. Hence, we have Mum – Seema(Lawyer) – Janaki(Dentist) – Aarti(IAS) – Ila – Doctor. From 5, Divya must be the doctor who arrived last. That means Gayatri arrived first and is from Mumbai. Hence, Gayatri(Mumbai) – Seema(Lawyer) – Janaki(Dentist) – Aarti(IAS, Pune) – Ila – Divya(Doctor,Chennai). Hence, we know the professions of Seema, Janaki, Aarti and Divya. Hence, option C.

We know that Ila came in just after the IAS and just before the Doctor and that the Doctor came in last. Hence, the order is A-B-C-IAS – Ila – Doctor. From 4, Mum – B – C – IAS- Ila-Doctor. Seema, a lawyer reached just before dentist. As she is not from Mumbai, she could not have reached first. The only space available then for Lawyer – Dentist is B-C. Hence, Mumbai – Seema(Lawyer) – Dentist – IAS – Ila – Doctor. Now Aarti came in just after Janaki. The only place for them to be together is if Janaki is the Dentist and Aarti is IAS. Hence, we have Mum – Seema(Lawyer) – Janaki(Dentist) – Aarti(IAS) – Ila – Doctor. From 5, Divya must be the doctor who arrived last. That means Gayatri arrived first and is from Mumbai. Hence, Gayatri(Mumbai) – Seema(Lawyer) – Janaki(Dentist) – Aarti(IAS, Pune) – Ila – Divya(Doctor,Chennai).

Thus, we know the location of Gayatri, Aarti and Divya. Hence, option B.

We know that Ila came in just after the IAS and just before the Doctor and that the Doctor came in last. Hence, the order is A-B-C-IAS – Ila – Doctor. From 4, Mum – B – C – IAS- Ila-Doctor. Seema, a lawyer reached just before dentist. As she is not from Mumbai, she could not have reached first. The only space available then for Lawyer – Dentist is B-C. Hence, Mumbai – Seema(Lawyer) – Dentist – IAS – Ila – Doctor. Now Aarti came in just after Janaki. The only place for them to be together is if Janaki is the Dentist and Aarti is IAS. Hence, we have Mum – Seema(Lawyer) – Janaki(Dentist) – Aarti(IAS) – Ila – Doctor. From 5, Divya must be the doctor who arrived last. That means Gayatri arrived first and is from Mumbai. Hence, Gayatri(Mumbai) – Seema(Lawyer) – Janaki(Dentist) – Aarti(IAS, Pune) – Ila – Divya(Doctor,Chennai).

If Ila is an Interior Designer then Gayatri must be the Engineer.

Three cities and 2 professions have not been assigned. If Ila is not from Hyderabad, the number of combinations of person – place is 3!-2 = 4. The number of combinations of person – profession is 2. Hence, the total number of combinations are 2*4 = 8.

The tallest person is given #1 and the shortest person #8.
From the first statement, we know that Sachin played Tennis and Cricket and is #8. From the second statement, Saurav is #3 and played Rugby. From 3, Srinath is #2 and Ishant is #1. Dhoni is taller than Dravid, who is taller than Kumble, who in turn is taller than Sehwag. So Dhoni is #4, Dravid is #5, Kumble is #6 and Sehwag is #7. Since Sehwag played Cricket and Kabaddi, Ishant played Tennis and Kabaddi. Kumble played Tennis and Srinath played Cricket. Since two guys played Table-Tennis, the sport played by Dravid and Dhoni is Table-Tennis.

The arrangement is as follows:

Sachin – Tennis, Cricket – #8

Saurav – Rugby – #3

Dravid – Table-Tennis – #5

Kumble – Tennis – #6

Dhoni – Table-tennis – #4

Ishant – Tennis, Kabaddi – #1

Srinath – Cricket – #2

Sehwag – Cricket, Kabaddi – #7

The people who play table-tennis are Dravid and Dhoni.

The tallest person is given #1 and the shortest person #8.
From the first statement, we know that Sachin played Tennis and Cricket and is #8. From the second statement, Saurav is #3 and played Rugby. From 3, Srinath is #2 and Ishant is #1. Dhoni is taller than Dravid, who is taller than Kumble, who in turn is taller than Sehwag. So Dhoni is #4, Dravid is #5, Kumble is #6 and Sehwag is #7. Since Sehwag played Cricket and Kabaddi, Ishant played Tennis and Kabaddi. Kumble played Tennis and Srinath played Cricket. Since two guys played Table-Tennis, the sport played by Dravid and Dhoni is Table-Tennis.

The arrangement is as follows:

Sachin – Tennis, Cricket – #8

Saurav – Rugby – #3

Dravid – Table-Tennis – #5

Kumble – Tennis – #6

Dhoni – Table-tennis – #4

Ishant – Tennis, Kabaddi – #1

Srinath – Cricket – #2

Sehwag – Cricket, Kabaddi – #7

The sports played by Ishant are Tennis and Kabaddi.

The tallest person is given #1 and the shortest person #8.
From the first statement, we know that Sachin played Tennis and Cricket and is #8. From the second statement, Saurav is #3 and played Rugby. From 3, Srinath is #2 and Ishant is #1. Dhoni is taller than Dravid, who is taller than Kumble, who in turn is taller than Sehwag. So Dhoni is #4, Dravid is #5, Kumble is #6 and Sehwag is #7. Since Sehwag played Cricket and Kabaddi, Ishant played Tennis and Kabaddi. Kumble played Tennis and Srinath played Cricket. Since two guys played Table-Tennis, the sport played by Dravid and Dhoni is Table-Tennis.

The arrangement is as follows:

Sachin – Tennis, Cricket – #8

Saurav – Rugby – #3

Dravid – Table-Tennis – #5

Kumble – Tennis – #6

Dhoni – Table-tennis – #4

Ishant – Tennis, Kabaddi – #1

Srinath – Cricket – #2

Sehwag – Cricket, Kabaddi – #7

The correct combination is Dhoni – Table-tennis – #4.

The tallest person is given #1 and the shortest person #8.
From the first statement, we know that Sachin played Tennis and Cricket and is #8. From the second statement, Saurav is #3 and played Rugby. From 3, Srinath is #2 and Ishant is #1. Dhoni is taller than Dravid, who is taller than Kumble, who in turn is taller than Sehwag. So Dhoni is #4, Dravid is #5, Kumble is #6 and Sehwag is #7. Since Sehwag played Cricket and Kabaddi, Ishant played Tennis and Kabaddi. Kumble played Tennis and Srinath played Cricket. Since two guys played Table-Tennis, the sport played by Dravid and Dhoni is Table-Tennis.

The arrangement is as follows:

Sachin – Tennis, Cricket – #8

Saurav – Rugby – #3

Dravid – Table-Tennis – #5

Kumble – Tennis – #6

Dhoni – Table-tennis – #4

Ishant – Tennis, Kabaddi – #1

Srinath – Cricket – #2

Sehwag – Cricket, Kabaddi – #7

It can be seen that statements 1 and 2 are correct whereas 3 is wrong.

The tallest person is given #1 and the shortest person #8.
From the first statement, we know that Sachin played Tennis and Cricket and is #8. From the second statement, Saurav is #3 and played Rugby. From 3, Srinath is #2 and Ishant is #1. Dhoni is taller than Dravid, who is taller than Kumble, who in turn is taller than Sehwag. So Dhoni is #4, Dravid is #5, Kumble is #6 and Sehwag is #7. Since Sehwag played Cricket and Kabaddi, Ishant played Tennis and Kabaddi. Kumble played Tennis and Srinath played Cricket. Since two guys played Table-Tennis, the sport played by Dravid and Dhoni is Table-Tennis.

The arrangement is as follows:

Sachin – Tennis, Cricket – #8

Saurav – Rugby – #3

Dravid – Table-Tennis – #5

Kumble – Tennis – #6

Dhoni – Table-tennis – #4

Ishant – Tennis, Kabaddi – #1

Srinath – Cricket – #2

Sehwag – Cricket, Kabaddi – #7

If the last condition is not given, the sports played by Dravid, Dhoni and Ishant cannot be exactly determined.

From c and d we know that the Accounts dept is in the middle on the lower floor with admin on the left and Kulkarni on the right. Hence from b and f, Mukherjee is in the top left corner and the head clerk of Archives department. The technical dept is in top middle office. From a, we know that Clearance must be on the bottom floor and hence is Mr Kulkarni’s office on the right which is the only remaining office. Thus, Mr Mehra is in the top right corner. The only column where both names are missing is the middle column. Hence, Mr Jain and Mr Sharma’s offices must be in the middle column. Hence, Mr Jain is in charge of the Technical Dept and Mr Sharma is in charge of the Accounts department. This leaves Mr Verma who must be in charge of the Admin office in the bottom left corner. Hence, Mr Mehra must be in charge of the Main office.

From c and d we know that the Accounts dept is in the middle on the lower floor with admin on the left and Kulkarni on the right. Hence from b and f, Mukherjee is in the top left corner and the head clerk of Archives department. The technical dept is in top middle office. From a, we know that Clearance must be on the bottom floor and hence is Mr Kulkarni’s office on the right which is the only remaining office. Thus, Mr Mehra is in the top right corner. The only column where both names are missing is the middle column. Hence, Mr Jain and Mr Sharma’s offices must be in the middle column. Hence, Mr Jain is in charge of the Technical Dept and Mr Sharma is in charge of the Accounts department. This leaves Mr Verma who must be in charge of the Admin office in the bottom left corner.

From c and d we know that the Accounts dept is in the middle on the lower floor with admin on the left and Kulkarni on the right. Hence from b and f, Mukherjee is in the top left corner and the head clerk of Archives department. The technical dept is in top middle office. From a, we know that Clearance must be on the bottom floor and hence is Mr Kulkarni’s office on the right which is the only remaining office. Thus, Mr Mehra is in the top right corner. The only column where both names are missing is the middle column. Hence, Mr Jain and Mr Sharma’s offices must be in the middle column. Hence, Mr Jain is in charge of the Technical Dept and Mr Sharma is in charge of the Accounts department. Thus Mr Kulkarni’s Clearance Department is to his right.

From c and d we know that the Accounts dept is in the middle on the lower floor with admin on the left and Kulkarni on the right. Hence from b and f, Mukherjee is in the top left corner and the head clerk of Archives department. The technical dept is in top middle office. From a, we know that Clearance must be on the bottom floor and hence is Mr Kulkarni’s office on the right which is the only remaining office. Thus, Mr Mehra is in the top right corner. The only column where both names are missing is the middle column. Hence, Mr Jain and Mr Sharma’s offices must be in the middle column. Hence, Mr Jain is in charge of the Technical Dept and Mr Sharma is in charge of the Accounts department. This leaves Mr Verma who must be in charge of the Admin office in the bottom left corner. Hence, Mr Mehra must be in charge of the Main office. Hence, Mr Mehra’s office is not adjacent.

From c and d we know that the Accounts dept is in the middle on the lower floor with admin on the left and Kulkarni on the right. Hence from b and f, Mukherjee is in the top left corner and the head clerk of Archives department. The technical dept is in top middle office. From a, we know that Clearance must be on the bottom floor and hence is Mr Kulkarni’s office on the right which is the only remaining office. Thus, Mr Mehra is in the top right corner. The only column where both names are missing is the middle column. Hence, Mr Jain and Mr Sharma’s offices must be in the middle column. Hence, Mr Jain is in charge of the Technical Dept and Mr Sharma is in charge of the Accounts department. This leaves Mr Verma who must be in charge of the Admin office in the bottom left corner. Hence, Mr Mehra must be in charge of the Main office.

From the given information,

d+e+f+g = 42

a+b+c+d+e+f+g = 84

g = c – 4

d+e+f = 30

c = 2e

b+e = a-2

Solving these equations, we get, a=18, b=8, c=16, e=8, g=12 and d+f = 22

Since Football team has the maximum number of students,

a+b+d+e >= 43 => d >= 9 and

a+b+d+e >= b+c+e+f+1

=> d >= f-1

d+f = 22.

Therefore, min. value of d = 11, in which case f = 11.

From the given information,

d+e+f+g = 42

a+b+c+d+e+f+g = 84

g = c – 4

d+e+f = 30

c = 2e

b+e = a-2

Solving these equations, we get, a=18, b=8, c=16, e=8, g=12 and d+f = 22

Since Football team has the maximum number of students, a+b+d+e >= 43 => d >= 9

and a+b+d+e >= b+c+e+f+1

=> d >= f-1

d+f = 22.

Therefore, min. value of d = 11, in which case f = 11.

The number of students in Hockey team = 32+f. f can be 0. Therefore, the minimum number of students = 32.

From the given information,

d+e+f+g = 42

a+b+c+d+e+f+g = 84

g = c – 4

d+e+f = 30

c = 2e

b+e = a-2

Solving these equations, we get, a=18, b=8, c=16, e=8, g=12 and d+f = 22

Since Football team has the maximum number of students, a+b+d+e >= 43

=> d >= 9

and a+b+d+e >= b+c+e+f+1

=> d >= f-1

d+f = 22.

Therefore, min. value of d = 11, in which case f = 11.

Information in a), b) and c) is already known. d) is required.

From the given information,

d+e+f+g = 42

a+b+c+d+e+f+g = 84

g = c – 4

d+e+f = 30

c = 2e

b+e = a-2

Solving these equations, we get, a=18, b=8, c=16, e=8, g=12 and d+f = 22

Since Football team has the maximum number of students, a+b+d+e >= 43

=> d >= 9 and a+b+d+e >= b+c+e+f+1

=> d >= f-1

d+f = 22.

Therefore, min. value of d = 11, in which case f = 11.

When d is minimum, value of f = 11 and d = 11. Difference = 0.

From the given information,

d+e+f+g = 42

a+b+c+d+e+f+g = 84

g = c – 4

d+e+f = 30

c = 2e

b+e = a-2

Solving these equations, we get, a=18, b=8, c=16, e=8, g=12 and d+f = 22

Since Football team has the maximum number of students,

a+b+d+e >= 43 => d >= 9

and a+b+d+e >= b+c+e+f+1

=> d >= f-1

d+f = 22.

Therefore, min. value of d = 11, in which case f = 11.

After the rearrangement, the number of students in each of the teams becomes: Aerobics = 40, Hockey = 34+f, Football = 30+d.
The additional six will be redistributed between d and f. Hence,

d+f = 28.

For any values of d and f, either 34+f or 30 +d > 40. Therefore, Hockey team or Football team has the maximum number of students.