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

Ex Input:
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer q factors does 2 xy have ? 
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12

Ex Output:
d


Ex Input:
Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fourth widget , starting with the fourth , 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 ) 50 , b ) 52 , c ) 53 , d ) 55 , e ) 56

Ex Output:
c


Ex Input:
Problem: a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 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 ) 81 , b ) 82 , c ) 84 , d ) 86 , e ) 88

Ex Output:

c