In this task, you need to answer the given multiple-choice question on the general math. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Input: Consider Input: Problem: the product of two positive integers is 1023 and their difference is 2 . what is the bigger number ? 
Options: a ) 29 , b ) 31 , c ) 33 , d ) 35 , e ) 37

Output: c


Input: Consider Input: Problem: a certain country is divided into 4 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 12 the total number of progressives in the entire country , what fraction of the country is traditionalist ? 
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4

Output: e


Input: Consider Input: Problem: if n is a positive integer , what is the remainder when ( 7 ^ ( 4 n + 3 ) ) ( 3 ^ n ) is divided by 10 ? 
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8


Output: b