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CAT 2021 Slot 1 DILR · Set 4 of 4Logical ReasoningModerate DifficultyQ15–Q20 · 4 MCQ + 2 TITA

CAT 2021 Slot 1 DILR Set 4: Arrangements (6 Questions) with Solutions

The Arrangements set from the official CAT 2021 Slot 1 DILR paper: the caselet, all 6 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2021 Slot 1 DILR · Questions 15–20
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.
No. of FriendsNo. of AcquaintancesNo. of Strangers
Amudha14
Bharatan
Chandran1
Dhinesh2
Ezhil1
Fani1
Gowtham32
The following additional facts are also known.
1
Amudha, Bharatan, and Chandran are mutual strangers.
2
Amudha, Dhinesh, and Fani are Ezhil's friends.
3
Chandran and Gowtham are friends.
4
Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.
5
Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q15. Arrangements

MCQ · +3 / −1
Who are Gowtham's acquaintances?
  1. A) Bharatan, Dhinesh and Ezhil
  2. B) Dhinesh, Ezhil and Fani
  3. C) Amudha, Dhinesh and Fani
  4. D) Amudha, Bharatan and Fani
Correct Answer
B) Dhinesh, Ezhil and Fani
Step-by-step solution
📌 Core Concept
The relationships are fixed by combining the row totals (each person has 6 relationships) with the two "every friend is an acquaintance" rules, which swap Amudha's and Bharatan's friend and acquaintance sets.
🔢 Step-by-Step Solution
1
Amudha has 1 acquaintance and 4 strangers, so 1 friend. Fact 2 makes that friend Ezhil. Fact 4 then says Bharatan's acquaintances are exactly {Ezhil}.
2
Amudha has exactly one acquaintance. By Fact 5 that person is Bharatan's only friend.
3
Gowtham has 2 strangers and 3 acquaintances, so 1 friend. Fact 3 makes that friend Chandran, so Gowtham is not a friend of Bharatan.
4
Fani has only 1 friend, Ezhil (Fact 2). So Fani is not a friend of Bharatan either.
5
Ezhil is Bharatan's acquaintance, so Ezhil is not his friend. Chandran is a stranger to Bharatan (Fact 1). Amudha is also a stranger to Bharatan (Fact 1). The only candidate left for Bharatan's friend is Dhinesh. So Dhinesh is Amudha's acquaintance.
6
Amudha's strangers are therefore Bharatan, Chandran, Fani and Gowtham. Bharatan's strangers are Amudha, Chandran, Fani and Gowtham.
7
Gowtham's 6 relationships: strangers Amudha and Bharatan, friend Chandran. The other three (Dhinesh, Ezhil, Fani) must be his 3 acquaintances.
Why Not the Others
A: Bharatan is a stranger to Gowtham.
C: Amudha is a stranger to Gowtham.
D: Amudha and Bharatan are both strangers to Gowtham.
Correct Answer: B

Q16. Arrangements

MCQ · +3 / −1
Which of these pairs share the same type of relationship?
  1. A) (Bharatan, Ezhil) and (Fani, Gowtham)
  2. B) (Amudha, Gowtham) and (Ezhil, Fani)
  3. C) (Chandran, Ezhil) and (Dhinesh, Gowtham)
  4. D) (Bharatan, Chandran) and (Dhinesh, Ezhil)
Correct Answer
A) (Bharatan, Ezhil) and (Fani, Gowtham)
Step-by-step solution
📌 Core Concept
Build the full relationship table from the row totals and the swap rules in Facts 4 and 5, then compare the pairs.
🔢 Step-by-Step Solution
1
Amudha has 1 friend (Ezhil, Fact 2), 1 acquaintance and 4 strangers. Fact 4 makes Bharatan's acquaintances exactly {Ezhil}.
2
Gowtham has exactly 1 friend, Chandran (Fact 3). Fani has exactly 1 friend, Ezhil. So neither of them can be Bharatan's friend.
3
Bharatan's one friend is Amudha's one acquaintance (Fact 5). It cannot be Amudha, Chandran (Fact 1), Ezhil, Fani or Gowtham, so it is Dhinesh.
4
Gowtham has 3 acquaintances. He is a stranger to Amudha and Bharatan and a friend of Chandran, so Dhinesh, Ezhil and Fani are his acquaintances.
5
Ezhil has 1 stranger. Her relationships so far are: friends Amudha, Dhinesh and Fani; acquaintances Bharatan and Gowtham. So Chandran is the stranger.
6
Dhinesh has 2 strangers. He is a friend of Ezhil and Bharatan, and an acquaintance of Amudha and Gowtham. So Chandran and Fani are his 2 strangers.
7
Chandran has 1 acquaintance. He is a stranger to Amudha, Bharatan, Dhinesh and Ezhil, and a friend of Gowtham. So Fani is his acquaintance.
8
Check the pairs:
(Bharatan, Ezhil) is acquaintance and (Fani, Gowtham) is acquaintance, so they match.
(Amudha, Gowtham) is stranger and (Ezhil, Fani) is friend.
(Chandran, Ezhil) is stranger and (Dhinesh, Gowtham) is acquaintance.
(Bharatan, Chandran) is stranger and (Dhinesh, Ezhil) is friend.
Why Not the Others
B, C and D each pair two different relationship types.
Correct Answer: A

Q17. Arrangements

MCQ · +3 / −1
Who is an acquaintance of Amudha?
  1. A) Fani
  2. B) Ezhil
  3. C) Dhinesh
  4. D) Gowtham
Correct Answer
C) Dhinesh
Step-by-step solution
📌 Core Concept
Amudha has exactly one acquaintance. Fact 5 says that person is Bharatan's only friend, so finding Bharatan's friend identifies the answer.
🔢 Step-by-Step Solution
1
Amudha has 1 acquaintance and 4 strangers, so 1 friend. Fact 2 makes that friend Ezhil.
2
Fact 5: every acquaintance of Amudha is a friend of Bharatan, and every friend of Bharatan is an acquaintance of Amudha. So Bharatan has exactly 1 friend, who is Amudha's acquaintance.
3
Fact 1 makes Amudha and Chandran strangers to Bharatan, so neither is his friend.
4
Fact 4 makes Ezhil, Amudha's friend, an acquaintance of Bharatan, so Ezhil is not his friend.
5
Fani's only friend is Ezhil, and Gowtham's only friend is Chandran (Fact 3). So neither can be Bharatan's friend.
6
That leaves Dhinesh as Bharatan's friend, and therefore as Amudha's acquaintance.
7
This fits Dhinesh's total: he has 2 strangers (Chandran and Fani).
Why Not the Others
A: Fani's only friend is Ezhil, and Amudha is a stranger to Fani.
B: Ezhil is Amudha's friend (Fact 2).
D: Gowtham has only one friend, Chandran, and he is Amudha's stranger.
Correct Answer: C

Q18. Arrangements

MCQ · +3 / −1
Who is an acquaintance of Chandran?
  1. A) Fani
  2. B) Ezhil
  3. C) Dhinesh
  4. D) Bharatan
Correct Answer
A) Fani
Step-by-step solution
📌 Core Concept
Once every other relationship of Chandran is fixed, his single acquaintance is the person left over.
🔢 Step-by-Step Solution
1
Chandran has exactly 1 acquaintance. Fact 3 makes Gowtham his friend, and Fact 1 makes Amudha and Bharatan his strangers.
2
Ezhil has exactly 1 stranger. Her friends are Amudha, Dhinesh and Fani (Fact 2), and Bharatan is her acquaintance (Fact 4). Gowtham, with 3 acquaintances, is her acquaintance, so Chandran is her stranger.
3
Dhinesh is Bharatan's only friend (Fani and Gowtham each have only one friend, and Ezhil is Bharatan's acquaintance). Dhinesh's relationships are friends Ezhil and Bharatan, and acquaintances Amudha and Gowtham. His 2 strangers must then be Chandran and Fani.
4
So Chandran's strangers are Amudha, Bharatan, Dhinesh and Ezhil, and his friend is Gowtham. That leaves Fani as his one acquaintance.
5
Fani's row confirms this: friend Ezhil, acquaintances Chandran and Gowtham, and the rest are strangers.
Why Not the Others
B: Ezhil is Chandran's stranger.
C: Dhinesh is Chandran's stranger.
D: Fact 1 makes Bharatan a stranger.
Correct Answer: A

Q19. Arrangements

TITA · +3 / 0
How many friends does Ezhil have?
Correct Answer
3
Step-by-step solution
📌 Core Concept
The totals in each row (6 relationships per person) combined with Facts 4 and 5 pin down Bharatan's only friend. That fixes Gowtham's relationships, and Ezhil's relationship with Chandran follows.
🔢 Step-by-Step Solution
1
Fact 2 makes Amudha, Dhinesh and Fani friends of Ezhil. Amudha has 6 - 1 - 4 = 1 friend, so Ezhil is Amudha's only friend.
2
Fact 4: Bharatan's acquaintances are exactly Amudha's friends, so Ezhil is Bharatan's only acquaintance.
3
Fact 5: Bharatan's friends are exactly Amudha's acquaintances. Amudha has 1 acquaintance, so Bharatan has exactly one friend, call them X. Bharatan's other 4 relationships are strangers, and Amudha is one of them (Fact 1).
4
X cannot be Amudha or Chandran (Fact 1) or Ezhil (an acquaintance). X is Dhinesh, Fani or Gowtham.
5
Fani has only 1 friend, and Ezhil is already that friend. So X is not Fani.
6
Gowtham has 6 - 3 - 2 = 1 friend, and Fact 3 makes Chandran that friend. So X is not Gowtham.
7
Hence X = Dhinesh. Dhinesh is Bharatan's friend and Amudha's acquaintance.
8
Amudha's 4 strangers are Bharatan, Chandran, Fani and Gowtham. Bharatan's 4 strangers are Amudha, Chandran, Fani and Gowtham.
9
Gowtham has exactly 2 strangers, Amudha and Bharatan. His friend is Chandran. His remaining 3 relationships (Dhinesh, Ezhil, Fani) must be the 3 acquaintances. So Gowtham is Ezhil's acquaintance, not a friend.
10
Ezhil's relationships so far: friends Amudha, Dhinesh and Fani; acquaintances Bharatan and Gowtham. Ezhil has exactly 1 stranger, and only Chandran is left, so Chandran is Ezhil's stranger.
11
Ezhil has 3 friends, 2 acquaintances and 1 stranger.
Quick Check
3 + 2 + 1 = 6, which matches the six other people. Ezhil's single stranger (Chandran) agrees with the table.
Correct Answer: 3

Q20. Arrangements

TITA · +3 / 0
How many people are either a friend or a friend-of-a-friend of Ezhil?
Correct Answer
4
Step-by-step solution
📌 Core Concept
List Ezhil's friends, then add the friends of those friends, leaving out Ezhil herself and anyone already counted.
🔢 Step-by-Step Solution
1
Ezhil's friends are Amudha, Dhinesh and Fani (Fact 2). She has no other friends, since Bharatan and Gowtham are her acquaintances and Chandran is her stranger.
2
Amudha's only friend is Ezhil, because Amudha has 1 acquaintance and 4 strangers.
3
Fani's only friend is Ezhil (the table gives Fani 1 friend).
4
Dhinesh is Bharatan's only friend, as Amudha's one acquaintance is Bharatan's one friend (Fact 5). Dhinesh is also Ezhil's friend. So Dhinesh's friends are Ezhil and Bharatan.
5
The only new person reached is Bharatan, a friend of a friend.
6
The count is 3 friends (Amudha, Dhinesh, Fani) plus 1 friend-of-a-friend (Bharatan), which is 3+1=43 + 1 = 4.
Quick Check
Chandran and Gowtham are linked only to each other as friends, so neither is reached through Ezhil's friends.
Correct Answer: 4
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CAT 2021 Slot 1 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Ahmedabad

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