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

Example Input: Problem: set a consists of the integers from 4 to 15 , inclusive , while set b consists of the integers from 7 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ? 
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Example Output: d

Example Input: Problem: there are 10 girls and 20 boys in a classroom . what is the ratio of girls to boys ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 10 / 30 , e ) 2 / 5
Example Output: a

Example Input: Problem: the present ratio of students to teachers at a certain school is 35 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ? 
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Example Output:
b