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: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 50 ? 
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 120
d

Problem: a number whose fifth part increased by 7 is equal to its fourth part diminished by 7 is ? 
Options: a ) 160 , b ) 180 , c ) 200 , d ) 280 , e ) none
d

Problem: if p represents the product of the first 16 positive integers , then p is not a multiple of 
Options: a ) 99 , b ) 84 , c ) 72 , d ) 65 , e ) 51

e