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: There are n arithmetic means between 3 and 45 such that the sum of these arithmetic means is 552. find the value of n.

Option A: 11

Option B: 15

Option C: 17

Option D: 21

Option E: 23

Output: Option E

Input: Consider Input: Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

Option A: 3

Option B: 14

Option C: 30

Option D: 42

Option E: 70

Output: Option D

Input: Consider Input: Question: There are 10 books on a shelf: 5 English books, 5 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?

Option A: 1

Option B: 0

Option C: 1/3

Option D: 31/45

Option E: 28/90
Output: Option A