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: 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: In a photography exhibition, some photographs were taken by Octavia the photographer, and some photographs were framed by Jack the framer. Jack had framed 24 photographs taken by Octavia, and 12 photographs taken by other photographers. If 36 of the photographs in the exhibition were taken by Octavia, how many photographs were either framed by Jack or taken by Octavia?

 Option A: 36

 Option B: 48

 Option C: 72

 Option D: 96

 Option E: 108

Output: Option B


Input: Consider Input: Question: If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24?

 Option A: 101

 Option B: 187

 Option C: 191

 Option D: 201

 Option E: 287


Output: Option E