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

[EX Q]: 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
[EX A]: d

[EX Q]: Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ? 
Options: a ) 91 , b ) 59 , c ) 53 , d ) 47 , e ) 45
[EX A]: c

[EX Q]: Problem: if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by 
Options: a ) 330 , b ) 340 , c ) 350 , d ) 360 , e ) 370
[EX A]:
a