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Raja Harish Chandra Club Friendship Graph

XAT 2011 · Decision Making · Hard · Logical Reasoning

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Answer question based on the following information

Every Saturday, the members of Raja Harish Chandra Club meet in the evening. All the member of the club are honest and never lie. Last Saturday, the following conversation was heard at one of the table with five members sitting around it.

Satya Sadhan: In this club not all members are friends with each other. Satyabrata: None of the pair of friends in this club has any common friend. Satyajit: Every pair of member who are not friends has exactly two common friends in this club. Satya Pramod: There are fewer than 22 people in this club.

Question 1 of 2

How many members are there in the club?

  1. A.

    5

  2. B.

    7

  3. C.

    15

  4. D.

    16

  5. E.

    20

Answer

D

Explanation

Modeling as a strongly regular graph with parameters (n,m)(n, m), where no adjacent pair shares a common neighbor and non-adjacent pairs share 2 common neighbors, n=1+m+∶m(m−1)/2n = 1 + m + ∶ m(m-1)/2. For m=5m=5, n=16<22n = 16 < 22.

Question 2 of 2

How many friends does Satya Sadhan have in the club?

  1. A.

    2

  2. B.

    3

  3. C.

    5

  4. D.

    7

  5. E.

    8

Answer

C

Explanation

From the graph symmetry where degree m=5m=5, Satya Sadhan has 5 friends.

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