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

Input: Consider Input: Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 150 ? 
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900

Output: c


Input: Consider Input: Problem: two vessels contains equal number of mixtures milk and water in the ratio 4 : 2 and 5 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ? 
Options: a ) 3 : 1 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4

Output: a


Input: Consider Input: Problem: two mixtures of a and b have a and b in the ratio 3 : 2 and 3 : 4 . in what proportion should these two mixtures be mixed to get a new mixture in which the ration of a to b is 5 : 4 ? 
Options: a ) 6 : 1 , b ) 5 : 4 , c ) 20 : 7 , d ) 10 : 9 , e ) 14 : 11


Output: c