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: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 41 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?

 Option A: 140

 Option B: 175

 Option C: 210

 Option D: 245

 Option E: 280
[A]: Option D


[Q]: Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1260. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?

 Option A:  2480

 Option B:  3490

 Option C:  6785

 Option D:  8235

 Option E:  9255
[A]:
Option D