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

Input: Consider Input: Problem: the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people b who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500

Output: d

Input: Consider Input: Problem: the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 350

Output: e

Input: Consider Input: Problem: the ratio of pens to pencils is 5 to 6 . there are 9 more pencils than pens . how many pencils are there ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Output: d