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

Example Input: Problem: a student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ? 
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Example Output: d

Example Input: Problem: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 12 people were made to stand in a column , how many columns could be formed ? 
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Example Output: c

Example Input: Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 18 white marbles . how many red marbles could be in bag a ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Example Output:
a