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 the average (arithmetic mean) of x, x + 2, and x + 4 is 33, what is the value of x?

 Option A: 30

 Option B: 31

 Option C: 32

 Option D: 32

 Option E: 37
[A]: Option B


[Q]: Question: If x is to be chosen at random from the set {1, 2, 3} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?

 Option A:  1/6

 Option B:  1/3

 Option C:  1/2

 Option D:  2/3

 Option E:  5/6
[A]: Option E


[Q]: Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 32.5 meters. How many times did the ball bounce?

 Option A: 2

 Option B: 6

 Option C: 7

 Option D: 8

 Option E: 9
[A]:
Option A