instruction:
In this task, you need to provide the correct option for a given problem from the provided options.
question:
Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 5 : 9 . what is the ratio of the smaller number to the larger number ? 
Options: a ) 1 : 5 , b ) 1 : 6 , c ) 1 : 7 , d ) 1 : 8 , e ) 1 : 9
answer:
e


question:
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
answer:
d


question:
Problem: two family reunions are happening at the park avenue hotel , the oates reunion and the hall reunion . all 100 guests at the hotel attend at least one of the reunions . if 40 people attend the oates reunion and 70 people attend the hall reunion , how many people attend both reunions 
Options: a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 22
answer:

c