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'.

Problem: if a and b are positive numbers , and a ^ 3 + b ^ 3 = 100 , then the greatest possible value of a is between : 
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
c

Problem: if there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 30 % of the total . what fraction of the total is men who own cars ? 
Options: a ) 3 ⁄ 20 , b ) 31 ⁄ 60 , c ) 9 ⁄ 40 , d ) 1 ⁄ 3 , e ) 11 ⁄ 20
b

Problem: if the average of 5 positive integers is 70 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ? 
Options: a ) 50 , b ) 52 , c ) 69 , d ) 78 , e ) 84

d