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'.

Example Input: Problem: gold is 10 times as heavy as water and copper is 6 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ? 
Options: a ) 3 : 2 , b ) 1 : 1 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Example Output: b

Example Input: Problem: village x has a population of 68000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ? 
Options: a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13
Example Output: e

Example Input: Problem: if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 4 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ? 
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 4
Example Output:
e