In this task, you need to provide the correct option for a given problem from the provided options.

[EX Q]: Problem: in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3200 circuit boards where 64 fail inspection ? 
Options: a ) 72 , b ) 192 , c ) 456 , d ) 256 , e ) 264
[EX A]: c

[EX Q]: Problem: in a group of 22 boys , 13 play basketball and 15 play football . 3 of the boys play neither . how many play both ? 
Options: a ) 18 , b ) 20 , c ) 21 , d ) 22 , e ) 25
[EX A]: a

[EX Q]: Problem: if both 2 ^ 2 and 3 ^ 4 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ? 
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
[EX A]:
b