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'.

[Q]: 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
[A]: d


[Q]: Problem: of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 30 grades are d ' s . what is the number of students in the course ? 
Options: a ) 80 , b ) 110 , c ) 160 , d ) 600 , e ) 400
[A]: d


[Q]: Problem: if the product of 2 integers is negative , at most how many of the integers can be negative ? 
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
[A]:
a