instruction:
In this task, you need to provide the correct option for a given problem from the provided options.
question:
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 8 and the other one , that is cheaper , costs $ 3 . the factory holds a $ 100 worth stock of 25 modules . how many of the modules in the stock are of the cheaper kind ? 
Options: a ) 21 , b ) 20 , c ) 22 , d ) 23 , e ) 24
answer:
b


question:
Problem: a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ? 
Options: a ) 42 , b ) 70 , c ) 140 , d ) 180 , e ) 315
answer:
d


question:
Problem: among 400 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 42 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ? 
Options: a ) 30 , b ) 90 , c ) 120 , d ) 168 , e ) 188
answer:

d