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'.

Ex Input:
Problem: the sum of the numbers is 220 . if the first number be twice the second and third number be one - third of the first , then the second number is : 
Options: a ) 48 , b ) 54 , c ) 72 , d ) 60 , e ) 27

Ex Output:
d


Ex Input:
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units x digit of ( a + 2 ) ^ 2 ? 
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14

Ex Output:
a


Ex Input:
Problem: let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 24 , what is the maximum value of y for which f ( x , y ) = 0 ? 
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 21

Ex Output:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
d


