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

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

Problem: in a ratio which is equal to 4 : 6 , if the antecedent is 20 , then the consequent is ? 
Options: a ) 72 , b ) 85 , c ) 30 , d ) 51 , e ) 45
c

Problem: if both 5 ^ 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 ) 80 , b ) 120 , c ) 150 , d ) 225 , e ) 300

d