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

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

Example Input: Problem: the hcf of two numbers is 42 and the other two factors of their lcm are 10 and 20 . what is the largest number . 
Options: a ) 462 , b ) 450 , c ) 840 , d ) 504 , e ) 555
Example Output: c

Example Input: Problem: 200 college students were asked in a survey if they preferred windows or mac brand computers . 70 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 80 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ? 
Options: a ) 25 , b ) 50 , c ) 57 , d ) 60 , e ) 75
Example Output:
b