Section C: Quantitative Ability

 

64.  Sara has just joined Facebook. She has 5 friends. Each of her five friends has twenty five friends. It is found that at least two of Sara’s friends are connected with each other. One her birthday, Sara decides to invite her friends and the friends of her friends. How many people did she invite for her birthday party?

A.    ³105    

B.    £123

C.   <125            

D.   ³100 and £125 

E.    ³105 and £123

      

Solution:

For the minimum number, we can assume that each of Sara’s 5 friends (F1 to F5) are mutual friends and they also share all their other friends, a set of 20 friends (say G1 to G20).

       (The 25 friends of F1 are Sara, F2 to F5 and G1 to G20. Similarly, we can provide 25 friends for each of F2 to F5). \ The minimum number of who could have been invited is 25 (F1 to F5 and G1 and G20).

 

For the maximum number, we assume minimum overlap. Say only F1 and F2 are friends. F1 would have Sara, F2 and 23 other friends. F2 would have Sara, F1 and 23 other friends. Each of F3 to F5 could have her set of 24 distinct friends and each would have Sara as the only common friend. \ The maximum number of people who could have been invited is 1(F1) + 23 + 1(F2) + 23 + 3[1 + 24] = 123.

       \ If n is the number of people invited (and not present which would include Sara), then 25 £ n £ 123. choice B is the best option.  

                                                                                                                                                                                                                                   Choice (B)