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: in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many q eggs does the plant process per day ? 
Options: a ) 100 , b ) 300 , c ) 400 , d ) 3000 , e ) 4000
c

Problem: if x + y = 250 , x - y = 200 , for integers of x and y , y = ? 
Options: a ) 200 , b ) 225 , c ) 50 , d ) 115 , e ) 150

b