# LR - Puzzles - Previous Year CAT/MBA Questions

You can practice all previous year CAT questions from the topic LR - Puzzles. This will help you understand the type of questions asked in CAT. It would be best if you clear your concepts before you practice previous year CAT questions.

**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**

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

**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).

Workspace:

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

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

**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).

Workspace:

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

Who is an acquaintance of Amudha?

- A.
Ezhil

- B.
Dhinesh

- C.
Fani

- D.
Gowtham

Answer: Option B

**Explanation** :

Consider the solution to first question of this set.

Dhinesh is an acquaintance of Amudha.

Hence, option (b).

Workspace:

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

Who is an acquaintance of Chandran?

- A.
Dhinesh

- B.
Bharatan

- C.
Fani

- D.
Ezhil

Answer: Option C

**Explanation** :

Consider the solution to first question of this set.

Fani is an acquaintance of Chandran.

Hence, option (c).

Workspace:

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

How many friends does Ezhil have?

Answer: 3

**Explanation** :

Consider the solution to first question of this set.

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

Hence, 3.

Workspace:

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

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

Answer: 4

**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.

Workspace:

**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**

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

Answer: Option B

**Explanation** :

Workspace:

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

Who among the following envies someone else?

- A.
Charles

- B.
Elise

- C.
Barat

- D.
Amar

Answer: Option D

**Explanation** :

Workspace:

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

Object o4 was given to

- A.
Barat

- B.
Elise

- C.
Charles

- D.
Disha

Answer: Option D

**Explanation** :

Workspace:

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

What is Amar’s value for his own bundle?

Answer: 12

**Explanation** :

Workspace:

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

Object o5 was given to

- A.
Amar

- B.
Elise

- C.
Disha

- D.
Charles

Answer: Option B

**Explanation** :

Workspace:

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

What BEST can be said about the distribution of object o1?

- A.
o1 was given to Charles

- B.
o1 was given to Charles, Disha, or Elise

- C.
o1 was given to Disha

- D.
o1 was given to Charles or Disha

Answer: Option C

**Explanation** :

Workspace:

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

10 players – P1, P2, … , P10 - competed in an international javelin throw event. The number (after P) of a player reflects his rank at the beginning of the event, with rank 1 going to the topmost player. There were two phases in the event with the first phase consisting of rounds 1, 2, and 3, and the second phase consisting of rounds 4, 5, and 6. A throw is measured in terms of the distance it covers (in meters, up to one decimal point accuracy), only if the throw is a ‘valid’ one. For an invalid throw, the distance is taken as zero. A player’s score at the end of a round is the maximum distance of all his throws up to that round. Players are re-ranked after every round based on their current scores. In case of a tie in scores, the player with a prevailing higher rank retains the higher rank. This ranking determines the order in which the players go for their throws in the next round.

In each of the rounds in the first phase, the players throw in increasing order of their latest rank, i.e. the player ranked 1 at that point throws first, followed by the player ranked 2 at that point and so on. The top six players at the end of the first phase qualify for the second phase. In each of the rounds in the second phase, the players throw in decreasing order of their latest rank i.e. the player ranked 6 at that point throws first, followed by the player ranked 5 at that point and so on. The players ranked 1, 2, and 3 at the end of the sixth round receive gold, silver, and bronze medals respectively.

All the valid throws of the event were of distinct distances (as per stated measurement accuracy). The tables below show distances (in meters) covered by all valid throws in the first and the third round in the event.

Distances covered by all the valid throws in the first round

The following facts are also known.

- Among the throws in the second round, only the last two were valid. Both the throws enabled these players to qualify for the second phase, with one of them qualifying with the least score. None of these players won any medal.
- If a player throws first in a round AND he was also the last (among the players in the current round) to throw in the previous round, then the player is said to get a double. Two players got a double.
- In each round of the second phase, exactly one player improved his score. Each of these improvements was by the same amount.
- The gold and bronze medalists improved their scores in the fifth and the sixth rounds respectively. One medal winner improved his score in the fourth round.
- The difference between the final scores of the gold medalist and the silver medalist, as well as the difference between the final scores of the silver medalist and the bronze medalist was 1.0 m.

**CAT 2021 LRDI Slot 3 | LR - Puzzles**

Which two players got the double?

- A.
P1, P8

- B.
P2, P4

- C.
P1, P10

- D.
P8, P10

Answer: Option D

**Explanation** :

Workspace:

**CAT 2021 LRDI Slot 3 | LR - Puzzles**

Who won the silver medal?

- A.
P9

- B.
P7

- C.
P5

- D.
P1

Answer: Option D

**Explanation** :

Workspace:

**CAT 2021 LRDI Slot 3 | LR - Puzzles**

Who threw the last javelin in the event?

- A.
P7

- B.
P9

- C.
P10

- D.
P1

Answer: Option A

**Explanation** :

Workspace:

**CAT 2021 LRDI Slot 3 | LR - Puzzles**

What was the final score (in m) of the silver-medalist?

- A.
89.6

- B.
87.2

- C.
88.6

- D.
88.4

Answer: Option C

**Explanation** :

Workspace:

**CAT 2021 LRDI Slot 3 | LR - Puzzles**

Which of the following can be the final score (in m) of P8?

- A.
81.9

- B.
0

- C.
85.1

- D.
82.7

Answer: Option D

**Explanation** :

Workspace:

**CAT 2021 LRDI Slot 3 | LR - Puzzles**

By how much did the gold medalist improve his score (in m) in the second phase?

- A.
1.0

- B.
1.2

- C.
2.0

- D.
2.4

Answer: Option D

**Explanation** :

Workspace:

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

In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations.

The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations.

- If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for.
- If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for.
- The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.

The following facts are also known.

- Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.
- The student who missed the Mathematics examination did not miss any other examination.
- One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.

**CAT 2020 LRDI Slot 1 | LR - Puzzles**

Who among the following did not appear for the Mathematics examination?

- A.
Carl

- B.
Esha

- C.
Foni

- D.
Alva

Answer: Option A

**Explanation** :

For the subjects missed, the student gets average of top 2 or 3 scores.

∴ Among the six students given, no students would’ve missed that subject where they get highest of the lowest marks.

Also, in the missed subject(s) the student cannot get 2nd lowest marks.

∴ For the missed subject(s), the student will get 2nd highest or 3rd highest marks.

English is missed by 2 students. These two students can only be Esha and Foni.

(For Esha and Foni English is neither highest nor lowest)

**Solving for Esha:**

Esha has missed English.

∴ Marks in English should be average of top three of the remaining subjects.

Average of remaining top three marks = (95 + 85 + 60)/3 = 80 (which is equal to Esha’s marks in English).

One of the students missed only Mathematics. Carl is the only one who could’ve missed Mathematics.

**Solving for Carl**

∴ Carl will not miss any other exam.

One of the students missed Hindi and Science. This can be either Alva or Deep since they both have same marks in Hindi and Science.

One of the students missed only Hindi. This can be either Alva, Deep since their marks in Hindi is same as average of the remaining top 3 scores.

∴ One of Alva or Deep missed only Hind and the other missed Hindi and Science.

So far we have

Alva missed ⇒ only Hindi or Hindi and Science

Carl ⇒ only Mathematics

Deep missed ⇒ only Hindi or Hindi and Science

Esha missed ⇒ only English

Alva and Deep definitely missed Hindi

Esha and Foni definitely missed English

One of Alva or Deep missed Science

We need to find one more person who missed Science and two more people who missed Social Science.

One more person who could’ve missed Science is Bithi and two more people who could’ve missed Social Science are Bithi and Foni

∴ We finally have

**Alva **missed ⇒ only Hindi or Hindi and Science

**Carl **missed ⇒ only Mathematics

**Bithi **missed ⇒ Science and Social Science

**Deep **missed ⇒ Hindi and Science or only Hindi

**Esha **missed ⇒ only English

**Foni **missed ⇒ English and Social Science

∴ Carl missed the Mathematics exam.

Hence, option (a).

Workspace:

**CAT 2020 LRDI Slot 1 | LR - Puzzles**

Which students did not appear for the English examination?

- A.
Cannot be determined

- B.
Esha and Foni

- C.
Carl and Deep

- D.
Alva and Bithi

Answer: Option B

**Explanation** :

Consider the solution the first question of this set.

Esha and Foni did not appear for English.

Hence, option (b).

Workspace:

**CAT 2020 LRDI Slot 1 | LR - Puzzles**

What BEST can be concluded about the students who did not appear for the Hindi examination?

- A.
Alva and Esha

- B.
Two among Alva, Deep and Esha

- C.
Deep and Esha

- D.
Alva and Deep

Answer: Option D

**Explanation** :

Consider the solution the first question of this set.

Alva and Deep both missed Hindi exam.

Hence, option (d).

Workspace:

**CAT 2020 LRDI Slot 1 | LR - Puzzles**

What BEST can be concluded about the students who missed the Science examination?

- A.
Bithi and one out of Alva and Deep

- B.
Alva and Deep

- C.
Deep and Bithi

- D.
Alva and Bithi

Answer: Option A

**Explanation** :

Consider the solution the first question of this set.

Bithi definitely missed Science exam. One of Alva or Deep also missed Science.

Hence, option (a).

Workspace:

**CAT 2020 LRDI Slot 1 | LR - Puzzles**

How many out of these six students missed exactly one examination?

Answer: 3

**Explanation** :

Consider the solution the first question of this set.

Esha, Carl and one of Alva or Deep missed only one exam.

Hence, 3.

Workspace:

**CAT 2020 LRDI Slot 1 | LR - Puzzles**

For how many students can we be definite about which examinations they missed?

Answer: 4

**Explanation** :

Consider the solution the first question of this set.

Except for Alva and Deep we can determine number of exams missed for other 4 students.

Hence, 4.

Workspace:

**Answer the next 4 questions based on the information given below.**

A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit.

For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.

For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.

Answer the following questions INDEPENDENTLY of each other.

**CAT 2020 LRDI Slot 2 | LR - Puzzles**

Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car) arrive. At this moment, which among the following numbered car is parked next to car 3?

- A.
6

- B.
7

- C.
5

- D.
8

Answer: Option B

**Explanation** :

Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars.

∴ The configuration is

| 1 | 1 | 2 | 3 | 4 | 4 |

Here each cell represents a single parking slot.

Now, Car 1 leaves. The configuration will be:

| V | V | 2 | 3 | 4 | 4 |

Car 5 (a compact car) and car 6 (an SUV) arrive. The configuration will be:

| 5 | V | 2 | 3 | 4 | 4 | 6 | 6 |

Car 4 leaves. The configuration will be:

| 5 | V | 2 | 3 | V | V | 6 | 6 |

Car 7 (an SUV) and car 8 (a compact car) arrive. The configuration will be:

| 5 | 8 | 2 | 3 | 7 | 7 | 6 | 6 |

At this point cars that are parked next to car 3 are car 2 and car 7.

Hence, option (b).

Workspace:

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