instruction:
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.
question:
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
answer:
Option D


question:
Question: The ages of two persons differ by 16 years. If 6 years ago , the elder one be 3 times as old as the younger one, find their present ages .

 Option A: 10 years and 18 years

 Option B: 18 years and 26 years

 Option C: 20 years and 28 years

 Option D: 14 years and 30 years

 Option E: 16 years and 25 years
answer:
Option D


question:
Question: Of the sixteen participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?

 Option A: 3

 Option B: 4

 Option C: 36

 Option D: 9

 Option E: 20
answer:

Option C