In this task, you need to provide the correct option for a given problem from the provided options.

Ex Input:
Problem: what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ? 
Options: a ) e = 5 , b ) e = 9 , c ) e = 10 , d ) e = 20 , e ) 30

Ex Output:
d


Ex Input:
Problem: a garrison of 400 men had a provision for 31 days . after 26 days 275 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ? 
Options: a ) 16 days , b ) 45 days , c ) 10 days , d ) 17 days , e ) 18 days

Ex Output:
a


Ex Input:
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 16 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ? 
Options: a ) 1 / 10 , b ) 13 / 50 , c ) 1 / 2 , d ) 7 / 10 , e ) 9 / 10

Ex Output:

b