What are the possible committee sizes?

Question

An organization with 110 people will be divided into smaller committees. What are the possible committee sizes if the organization wants to have some large committees (each the same size) and some smaller committees (each the same size), and the larger committees must be twice the size of the smaller ones? (Enter your answers as ordered pairs of the form (n, 2n). Separate each ordered pair with a comma.)

Answer 1

The committees have two sizes and one size is twice the other, but the number of committees for each size do not have to be equal. We can think of it as integer or whole number division with a remainder equal to the size of a committee or a multiple of same.

 

ordered pair       example(s where the sum = 110

 

(1, 2)                36 1 person, 37 2 person committees (assuming 1 person committees make sense)

(2, 4)                19 and 18 (2 and 4 person committees respectively ), 33 and 11, etc.

(5, 10)              8 and 7

(10, 20)            3 and 4

(11, 22)            4 and 3

(22, 44)            1 and 2

 

Can you think of more?