# LR - Puzzles - Previous Year CAT/MBA Questions

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Here we bring you all previous year LR - Puzzles CAT questions along with detailed solutions.

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

A visa processing office (VPO) accepts visa applications in four categories – US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.

There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.

On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.

Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.

The following additional information is known about that day.

1. All slots were full.

2. The number of US applications was the same in all the slots. The same was true for the other three categories.

3. 50% of the applications were US applications.

4. All applicants except Ira, Vijay and Nandini arrived on time.

5. Vijay was called to a counter at 9:25 am.

**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

How many UK applications were scheduled on that day?

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**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

What is the maximum possible value of the total time (in minutes, nearest to its integer value) required to process all applications in the Others category on that day?

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**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

Which of the following is the closest to the time when Nandini’s application process got over?

- (a)
9:35 am

- (b)
9:37 am

- (c)
9:45 am

- (d)
9:50 am

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**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

Which of the following statements is false?

- (a)
The application process of Mahira started after Nandini’s.

- (b)
The application process of Osman was completed before Vijay’s.

- (c)
The application process of Osman was completed before 9:45 am.

- (d)
The application process of Mahira was completed before Nandini’s.

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**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

When did the application processing for all US applicants get over on that day?

- (a)
3:40 pm

- (b)
2:05 pm

- (c)
2:25 pm

- (d)
2:00 pm

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

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.

**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

Which two candidates can belong to the same department?

- (a)
Prof. Pakrasi and Prof. Qureshi

- (b)
Prof. Qureshi and Prof. Ramaswamy

- (c)
Prof. Pakrasi and Prof. Samuel

- (d)
Prof. Ramaswamy and Prof. Samuel

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**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

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

- (a)
7

- (b)
9

- (c)
6

- (d)
8

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**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

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.

- (a)
Only statement A

- (b)
Only statement B

- (c)
Neither statement A not statement B

- (d)
Both statements A and B

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**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

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

- (a)
It was Prof. Samuel.

- (b)
It was either Prof. Ramaswamy or Prof. Samuel.

- (c)
It was Prof. Ramaswamy.

- (d)
It was either Prof. Pakrasi or Prof. Qureshi.

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**CAT 2023 LRDI Slot 1 | LR - Puzzles CAT Question**

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.

- (a)
Neither statement A nor statement B

- (b)
Only statement A

- (c)
Only statement B

- (d)
Both statements A and B

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

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly.

The following information is also known.

- Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).
- Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited.
- Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm.
- The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.

**CAT 2023 LRDI Slot 2 | LR - Puzzles CAT Question**

What was the total amount spent on tickets (in Rs.) by Bipasha?

- (a)
110

- (b)
100

- (c)
90

- (d)
120

Answer: Option A

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**Text Explanation** :

We get the following chart for the rides taken by the three visitors.

Bipasha took rides 1, 2 and 4.

Her total cost for tickets = 20 + 50 + 40 = Rs. 110.

Hence, option (a).

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**CAT 2023 LRDI Slot 2 | LR - Puzzles CAT Question**

Which were all the rides that Anjali completed by 2:00 pm?

- (a)
Ride-1 and Ride-3

- (b)
Ride-1, Ride-2, and Ride-4

- (c)
Ride-1 and Ride-4

- (d)
Ride-1, Ride-2, and Ride-3

Answer: Option D

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**Text Explanation** :

We get the following chart for the rides taken by the three visitors.

By 2 pm Anjali took rides 1, 2 and 3.

Hence, option (d).

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**CAT 2023 LRDI Slot 2 | LR - Puzzles CAT Question**

Which ride was taken by all three visitors?

- (a)
Ride-1

- (b)
Ride-3

- (c)
Ride-2

- (d)
Ride-4

Answer: Option A

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**Text Explanation** :

We get the following chart for the rides taken by the three visitors.

Ride 1 was taken by all thee visitors.

Hence, option (a).

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**CAT 2023 LRDI Slot 2 | LR - Puzzles CAT Question**

How many rides did Anjali and Chitra take in total?

Answer: 6

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**Text Explanation** :

We get the following chart for the rides taken by the three visitors.

Anajli took rides 1, 2, 3 and 4 i.e., 4 rides

Chitra took rides 1 and 3 i.e., 2 rides

Anjali and Chitra together took 4 + 2 = 6 rides.

Hence, 6.

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**CAT 2023 LRDI Slot 2 | LR - Puzzles CAT Question**

What was the total amount spent on tickets (in Rs.) by Anjali?

Answer: 140

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**Text Explanation** :

We get the following chart for the rides visited by the three persons.

Anjali took all 4 rides hence spent 20 + 50 + 30 + 40 = Rs. 140.

Hence, 140.

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**CAT 2023 LRDI Slot 2 | LR - Puzzles CAT Question**

If the total score of Bimal is a multiple of 3, what is the score of Akhil on Day 2?

- (a)
Cannot be determined

- (b)
5

- (c)
6

- (d)
4

Answer: Option D

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**Text Explanation** :

We get the following table for their score on each of the 5 days.

If Bimal's total score is a multiple of 3, it means Bimals get a total score of 27 hence Akhil gets a total score of 23.

This is possible when Akhil get 4 on Day 2 and 4 on Day 5.

Hence, option (d).

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**Answer the next 6 questions based on the information given **

Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.

Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.

The following additional facts are also known.

- Amudha, Bharatan, and Chandran are mutual strangers.
- Amudha, Dhinesh, and Fani are Ezil's friends.
- Chandran and Gowtham are friends.
- Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.
- Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.

**CAT 2021 LRDI Slot 1 | LR - Puzzles CAT Question**

Who are Gowtham’s acquaintances?

- (a)
Bharatan, Dhinesh and Ezhil

- (b)
Amudha, Dhinesh and Fani

- (c)
Dhinesh, Ezhil and Fani

- (d)
Amudha, Bharatan and Fani

Answer: Option C

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**Text Explanation** :

Amudha, Bharatan, and Chandran are mutual strangers.

Amudha, Dhinesh, and Fani are Ezil's friends.

Chandran and Gowtham are friends.

Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha. And every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.

Since Ezil is Amudha’s friend Ezil will be Bharatan’s acquaintance

Gautam has 3 acquaintances and 2 strangers hence Gautam will have 1 friend.

Fani also has 1 friend.

We can see from the table that Fani and Gautam already have one friend and the remaining people will be either acquaintances or strangers.

Now, if Fani is an acquaintance of Amudha/Bharatan, he will be a friend of Bharatan/Amudha. Thus Fani will have 2 friends which is not possible. Hence, Fani will be a stranger to both Amudha and Bharatan

We can use the same logic for Gautam and conclude that Gautam will be a stranger to both Amudha and Bharatan.

Now, Gautam has 3 acquaintances, these will be Dhinesh, Ezhil and Fani.

Amudha has 1 acquaintance, this can only be Dhinesh. Since Dhinesh is Amudha’s acquaintance, he will be Bharatan’s friend.

Dhinesh has two strangers, hence Chandran and Fani will be strangers to Dhinesh.

Ezil has one stranger, this can only be Chandran.

Chandran has one acquaintance and this will be Fani.

Hence, we get the final table for all relationships.

Gautham’s acquaintances are Dhinesh, Ezil and Fani.

Hence, option (c).

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**CAT 2021 LRDI Slot 1 | LR - Puzzles CAT Question**

Which of these pairs share the same type of relationship?

- (a)
(Bharatan, Ezhil) and (Fani, Gowtham)

- (b)
(Bharatan, Chandran) and (Dhinesh, Ezhil)

- (c)
(Chandran, Ezhil) and (Dhinesh, Gowtham)

- (d)
(Amudha, Gowtham) and (Ezhil, Fani)

Answer: Option A

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**Text Explanation** :

Consider the solution to first question of this set.

Bharatan and Chandran are acquaintances while Dhinesh and Ezhil are also acquaintances.

Hence, option (a).

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**CAT 2021 LRDI Slot 1 | LR - Puzzles CAT Question**

Who is an acquaintance of Amudha?

- (a)
Ezhil

- (b)
Dhinesh

- (c)
Fani

- (d)
Gowtham

Answer: Option B

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**Text Explanation** :

Consider the solution to first question of this set.

Dhinesh is an acquaintance of Amudha.

Hence, option (b).

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**CAT 2021 LRDI Slot 1 | LR - Puzzles CAT Question**

Who is an acquaintance of Chandran?

- (a)
Dhinesh

- (b)
Bharatan

- (c)
Fani

- (d)
Ezhil

Answer: Option C

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**Text Explanation** :

Consider the solution to first question of this set.

Fani is an acquaintance of Chandran.

Hence, option (c).

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**CAT 2021 LRDI Slot 1 | LR - Puzzles CAT Question**

How many friends does Ezhil have?

Answer: 3

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**Text Explanation** :

Consider the solution to first question of this set.

Ezil has 3 friends, i.e., Amudha, Dhinesh and Fani.

Hence, 3.

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**CAT 2021 LRDI Slot 1 | LR - Puzzles CAT Question**

How many people are either a friend or a friend-of-a-friend of Ezhil?

Answer: 4

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**Text Explanation** :

Consider the solution to first question of this set.

Ezil’s direct friends are Amudha, Dhinesh and Fani while friends of friends is Bharatan (Dhinesh’s friend).

Hence, 4.

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**Answer the next 6 questions based on the information given **

Ten objects o1, o2, …, o10 were distributed among Amar, Barat, Charles, Disha, and Elise. Each item went to exactly one person. Each person got exactly two of the items, and this pair of objects is called her/his bundle.

The following table shows how each person values each object.

The value of any bundle by a person is the sum of that person’s values of the objects in that

bundle. A person X envies another person Y if X values Y’s bundle more than X’s own bundle.

For example, hypothetically suppose Amar’s bundle consists of o1 and o2, and Barat’s bundle consists of o3 and o4. Then Amar values his own bundle at 4 + 9 = 13 and Barat’s bundle at 9 + 3 = 12. Hence Amar does not envy Barat. On the other hand, Barat values his own bundle at 7 + 5 = 12 and Amar’s bundle at 5 + 9 = 14. Hence Barat envies Amar.

The following facts are known about the actual distribution of the objects among the five

people.

- If someone’s value for an object is 10, then she/he received that object.
- Objects o1, o2, and o3 were given to three different people.
- Objects o1 and o8 were given to different people.
- Three people value their own bundles at 16. No one values her/his own bundle at a number higher than 16.
- Disha values her own bundle at an odd number. All others value their own bundles at an even number.
- Some people who value their own bundles less than 16 envy some other people who value their own bundle at 16. No one else envies others

**CAT 2021 LRDI Slot 2 | LR - Puzzles CAT Question**

What BEST can be said about object o8?

- (a)
o8 was given to Disha

- (b)
o8 was given to Charles

- (c)
o8 was given to Charles or Disha

- (d)
o8 was given to Amar, Charles, or Disha

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**CAT 2021 LRDI Slot 2 | LR - Puzzles CAT Question**

Who among the following envies someone else?

- (a)
Charles

- (b)
Elise

- (c)
Barat

- (d)
Amar

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**CAT 2021 LRDI Slot 2 | LR - Puzzles CAT Question**

Object o4 was given to

- (a)
Barat

- (b)
Elise

- (c)
Charles

- (d)
Disha

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