instruction:
In this task, you need to provide the correct option for a given problem from the provided options.
question:
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 19 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ? 
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 7 / 10 , e ) 29 / 100
answer:
e


question:
Problem: if 75 percent of a class answered the first question on a certain test correctly , 35 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ? 
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
answer:
c


question:
Problem: the duplicate ratio of 2 : 6 is ? 
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 9 , d ) 1 : 18 , e ) 1 : 13
answer:

c