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: each factor of 210 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ? 
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4

Output: c


Input: Consider Input: Problem: a dog takes 3 leaps for every 7 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is : 
Options: a ) 9 : 7 , b ) 9 : 9 , c ) 9 : 6 , d ) 9 : 1 , e ) 9 : 2


Output: a