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: if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability w that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) w = 1 / 6

Output: e


Input: Consider Input: Problem: if - 3 x + 2 y = 28 and 3 x + 6 y = 84 , what is the product of x and y ? 
Options: a ) 264 . , b ) 428 , c ) 0 , d ) 462 , e ) 642

Output: c


Input: Consider Input: Problem: how many positive integers less than 5,000 are evenly divisible by neither 15 nor 23 ? 
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349


Output: c