In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Ex Input:
Problem: a circular rim a having a diameter of 45 inches is rotating at the rate of x inches / min . another circular rim b with a diameter of 30 inches is rotating at the rate of y inches / min . what is the value of y in terms of x , if both the rims reach their starting positions at the same time after every rotation . 
Options: ['a ) 3 x / 2', 'b ) 4 x / 5', 'c ) 7 x / 5', 'd ) 5 x / 7', 'e ) 3 x / 4']

Ex Output:
a


Ex Input:
Problem: the number 70 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ? 
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13

Ex Output:
d


Ex Input:
Problem: 20 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? 
Options: a ) 144 , b ) 131 , c ) 330 , d ) 390 , e ) 445

Ex Output:

c