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

Positive Example 1 -
Input: Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 6 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ? 
Options: a ) 5 : 1 , b ) 30 : 2 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Output: b

Positive Example 2 -
Input: Problem: if 6 and 8 are factors of 60 n , what is the minimum value of n ? 
Options: a ) 2 , b ) 4 , c ) 7 , d ) 14 , e ) 56
Output: b

Negative Example 1 -
Input: Problem: 100 people are attending a newspaper conference . 40 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ? 
Options: a ) 21 , b ) 24 , c ) 28 , d ) 30 , e ) 32
Output: d

Negative Example 2 -
Input: Problem: sachin is younger than rahul by 7 years . if the ratio of their ages is 5 : 12 , find the age of sachin 
Options: a ) 9 , b ) 24.8 , c ) 2 , d ) 3 , e ) 5
Output: b

Now complete the following example -
Input: Problem: a king has 1000 bottles of wine , a queen wants to kill the king and sends a servant to poison the wine . fortunately the king ' s guard ' s catch d servant after he has only poisoned one bottle and the guard do n ' t know which bottle is poisoned . furthermore it takes one month to have an effect , and there is an anniversary party coming up in 5 weeks time ! the king decides he will get some of the prisoners in his vast dungeons to drink the wine . how many minimum prisoners does it required to sample the wine to find out the poisoned bottle so that the guests will still be able to drink the rest of the wine at his anniversary party in 5 weeks time ? 
Options: a ) 1 , b ) 499 , c ) 500 , d ) 999 , e ) 10
Output: 


Output: e