You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.

Input: Consider Input: Question: If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. ab + b^2
II. (a + b)^2
III. a + b

 Option A: I only

 Option B: II only

 Option C: III only

 Option D: I and II only

 Option E: I, II, and III

Output: Option B


Input: Consider Input: Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 9 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

 Option A: 23 years

 Option B: 24 years

 Option C: 25 years

 Option D: 26 years

 Option E: 27 years

Output: Option D


Input: Consider Input: Question: A certain deck of cards contains 2 black cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not black?

 Option A: 15/28

 Option B: 1/4

 Option C: 9/16

 Option D: 1/32

 Option E: 1/16


Output: Option A