Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.

Problem: set s consists of integers { 7, 8, 10, 12, 13 }. if integer n is included in the set, the average ( arithmetic mean ) of set s will increase by 10 %. what is the value of integer n ?
Options: a. 10, b. 12, c. 16, d. 22, e. 24
c

Problem: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 80, what is the value of c − a ?
Options: a. 25, b. 60, c. 90, d. 140, e. it can not be determined from the information given.
b

Problem: the average age of a family of 5 members is 20 years. if the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member ?
Options: a. 13.5, b. 14, c. 15, d. 12.5, e. none

d