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

Example Input: Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 4 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ? 
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Example Output: d

Example Input: Problem: set a consists of the integers from 4 to 15 , inclusive , while set b consists of the integers from 7 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ? 
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Example Output: d

Example Input: Problem: if both 5 ^ 2 and 3 ^ 3 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ? 
Options: a ) 49 , b ) 75 , c ) 150 , d ) 225 , e ) 343
Example Output:
b