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

Input: Consider Input: Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 5 : 7 . what is the ratio of the smaller number to the larger number ?
Options: a ) 2 : 3 , b ) 2 : 5 , c ) 3 : 7 , d ) 4 : 9 , e ) 5 : 6

Output: c

Input: Consider Input: Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 28 !
Options: a ) 13 , b ) 10 , c ) 12 , d ) 14 , e ) 16

Output: a

Input: Consider Input: Problem: a bag holds 2 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Output: a