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

Input: Consider Input: 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

Output: d


Input: Consider Input: Problem: a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ? 
Options: a ) 6000 , b ) 9000 , c ) 9500 , d ) 12000 , e ) none

Output: b


Input: Consider Input: Problem: if the radii of umbra and penumbra cast by an object on a wall are of the ratio 2 : 6 , what is the area of the penumbra ring around the umbra of the latter ’ s radius is 40 cms ? 
Options: ['a ) 40288.57 cm ^ 2', 'b ) 40388.57 cm ^ 2', 'c ) 40488.57 cm ^ 2', 'd ) 40588.57 cm ^ 2', 'e ) 40688.57 cm ^ 2']


Output: a