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.

[Q]: Question: If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?

 Option A: one

 Option B: two

 Option C: three

 Option D: four

 Option E: five
[A]: Option B


[Q]: Question: How many numbers are divisible by 4 between 1 and 100.

 Option A: 24

 Option B: 23

 Option C: 22

 Option D: 21

 Option E: 25
[A]: Option A


[Q]: Question: John must arrange 3 different physics books and 4 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?

 Option A: 6

 Option B: 9

 Option C: 36

 Option D: 120

 Option E: 144
[A]:
Option E