CAT 2021 Slot 1 · DILR · Question 15
CAT 2021 Slot 1 previous year question on Caselet DI, with the answer and a step-by-step solution.
Set 3: Friends, Acquaintances and Strangers — this question belongs to a set. Read the full set with all 6 questions →
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 Friends | No. of Acquaintances | No. of Strangers | |
Amudha | 1 | 4 | |
Bharatan | |||
Chandran | 1 | ||
Dhinesh | 2 | ||
Ezhil | 1 | ||
Fani | 1 | ||
Gowtham | 3 | 2 |
The following additional facts are also known.
1. Amudha, Bharatan, and Chandran are mutual strangers.
2. Amudha, Dhinesh, and Fani are Ezil'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.
Answer & solution
Answer: 3
Solving the set
Step 1 – Amudha, Bharatan and Chandran are mutual strangers (fact 1). Amudha has 4 strangers, so besides Bharatan and Chandran she has 2 more strangers, 1 acquaintance and 1 friend (6 relations). Ezhil is her friend (fact 2).
Step 2 – Facts 4 and 5: Amudha's friends = Bharatan's acquaintances, and Amudha's acquaintances = Bharatan's friends. So Ezhil is Bharatan's acquaintance, and Bharatan has exactly one friend (Amudha's single acquaintance).
Step 3 – Chandran–Gowtham are friends (fact 3). Gowtham has 3 acquaintances and 2 strangers, so his only friend is Chandran. Fani has only one friend – Ezhil (fact 2). Ezhil has only one stranger.
Step 4 – Testing who can be Amudha's acquaintance (= Bharatan's friend) among Dhinesh, Fani and Gowtham: Fani's only friend is Ezhil and Gowtham's only friend is Chandran, so it must be Dhinesh. Then Amudha's strangers are Bharatan, Chandran, Fani, Gowtham, and the remaining relations follow from the counts in the table.
Person | Friends | Acquaintances | Strangers |
Amudha | Ezhil | Dhinesh | Bharatan, Chandran, Fani, Gowtham |
Bharatan | Dhinesh | Ezhil | Amudha, Chandran, Fani, Gowtham |
Chandran | Gowtham | Fani | Amudha, Bharatan, Dhinesh, Ezhil |
Dhinesh | Bharatan, Ezhil | Amudha, Gowtham | Chandran, Fani |
Ezhil | Amudha, Dhinesh, Fani | Bharatan, Gowtham | Chandran |
Fani | Ezhil | Chandran, Gowtham | Amudha, Bharatan, Dhinesh |
Gowtham | Chandran | Dhinesh, Ezhil, Fani | Amudha, Bharatan |
This question
Ezhil's friends are Amudha, Dhinesh and Fani – 3 friends.
Hence, the answer is 3.
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