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CAT 2021 Slot 1 — DILR Question 15

Mixed PracticeEasy
Passage / Data

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.

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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.

Who are Gowtham’s acquaintances?

Answer & solution

  • A

    Bharatan, Dhinesh and Ezhil

  • B

    Amudha, Dhinesh and Fani

  • Dhinesh, Ezhil and Fani

  • D

    Amudha, Bharatan and Fani

Solution

Amudha, Bharatan, and Chandran are mutual strangers.

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

Chandran and Gowtham are friends.

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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

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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.

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

Ezil has one stranger, this can only be Chandran.

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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).

CAT 2021 Slot 1 DILR Q15: Who are Gowtham’s acquaintances? — Solution | TheCATExam