CAT 2021 Slot 1 · DILR · Set 3: Friends, Acquaintances and Strangers

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.

This question

From the relationship table, Gowtham's acquaintances are Dhinesh, Ezhil and Fani.

Hence, the answer is option 1.

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.

This question

• (Amudha, Gowtham) strangers vs (Ezhil, Fani) friends – different.

• (Bharatan, Chandran) strangers vs (Dhinesh, Ezhil) friends – different.

• (Chandran, Ezhil) strangers vs (Dhinesh, Gowtham) acquaintances – different.

• (Bharatan, Ezhil) acquaintances vs (Fani, Gowtham) acquaintances – same.

Hence, the answer is option 4.

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.

This question

From Step 4, Amudha's acquaintance is Dhinesh.

Hence, the answer is option 1.

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.

This question

From the relationship table, Chandran's acquaintance is Fani.

Hence, the answer is option 2.

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.

This question

Ezhil's friends are Amudha, Dhinesh and Fani – 3 friends.

Hence, the answer is 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.

This question

Friends of Ezhil: Amudha, Dhinesh, Fani. Friends of these (excluding Ezhil): Amudha – none else; Dhinesh – Bharatan; Fani – none else. People who are a friend or friend-of-a-friend: Amudha, Dhinesh, Fani, Bharatan = 4.

Hence, the answer is 4.