Suppose the 100 people in society C all know the same 10 facts, but the people in society D specialize slightly, so that there are nine facts that they all know, but each person also knows one unique fact. What is the minimum number of people that must live in society D in order for there to be twice as many facts known in society D as are known in society C?

Answer: 11

Explanation:

Society C

Number of people = 100

Number of facts = 10

Fact per person = 10 : 100 = 0.1

Society D

Unique fact = 1

Common fact = 9

Number of people = y

minimum number of people that must live in society D in order for there to be twice as many facts known in society D as are known in society C;

Mathematically,

(y (1) + 9) = 2 (10)

(y + 9) = 20

y + 9 = 20

y = 20 - 9

y = 11

There are 10 facts known in society C and 100 people, which results in an average of 0.1 facts per person. In society D, there are five common facts and 50 specialized facts. That is 55 total facts, which results in an average of 5.5 per person.