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.

[Q]: 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
[A]: c


[Q]: Problem: if the range q of the 6 numbers 4, 314, 710 and x is 12, what is the difference between the greatest possible value of x and least possible value of x ?
Options: a. 0, b. 2, c. 12, d. 13, e. 15
[A]: d


[Q]: Problem: a rectangle having length 89 cm and width 34 cm. if the length of the rectangle is increased by eighty percent then how much percent the breadth should be decreased so as to maintain the same area.
Options: a. 25 %, b. 33.33 %, c. 47.33 %, d. 75 %, e. none of these
[A]:
c