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: John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 45 mph to reach his destination. How many miles did John drive?

 Option A: 235 miles.

 Option B: 245 miles.

 Option C: 225 miles.

 Option D: 265 miles.

 Option E: 275 miles.
[A]: Option C


[Q]: Question: For any positive integer Y, the sum of the first Y positive integers equals Y(Y+1)/2 . If X and Y are positive integers and X > Y, what is the sum of all the integers between X and Y, inclusive?

 Option A:  X(X+1

 Option B:  X(X+1

 Option C:  X(X+1

 Option D:  X(X+1

 Option E:  X(Y+1
[A]: Option B


[Q]: Question: As x increases from 169 to 155, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)

 Option A:  I only

 Option B:  III only

 Option C:  I and II

 Option D:  I and III

 Option E:  II and III
[A]:
Option B