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: a large field of 900 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ? 
Options: a ) 435 hectares . , b ) 425 hectares . , c ) 445 hectares . , d ) 415 hectares . , e ) 405 hectares .
Example Output: e

Example Input: Problem: if a - b = 5 and a 2 + b 2 = 31 , find the value of ab . 
Options: a ) 9 , b ) 2 , c ) 3 , d ) 7 , e ) 12
Example Output: c

Example Input: Problem: a batsman in his 12 th innings makes a score of 75 and thereby increases his average by 1 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ? 
Options: a ) 42 , b ) 43 , c ) 44 , d ) 64 , e ) 46
Example Output:
d