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

Example Input: Problem: if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) , what is the smallest possible positive value of n ? 
Options: a ) 15 , b ) 45 , c ) 75 , d ) 125 , e ) 150
Example Output: a

Example Input: Problem: at a supermarket , the ratio of the number of shampoos to the number of soaps is 8 to 5 , and the ratio of the number of drinks to the number of shampoos is 3 to 4 . if the ratio of the soaps to the number of cereals is 9 to 2 , what is the ratio of the number of drinks to the number of cereals ? 
Options: a ) 4 : 3 , b ) 15 : 6 , c ) 45 : 16 , d ) 15 : 4 , e ) 27 : 5
Example Output: e

Example Input: Problem: the compound ratio of 1 : 4 , 3 : 2 and 4 : 5 ? 
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 3 : 10 , e ) 1 : 4
Example Output:
d