Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.

Ex Input:
Problem: on a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. on the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. on both days, all the orangeade that was made was sold. if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.30 per glass on the first day, what was the price per glass on the second day ?
Options: a. $ 0.15, b. $ 0.20, c. $ 0.30, d. $ 0.40, e. $ 0.45

Ex Output:
b

Ex Input:
Problem: two trains of equal length are running on parallel lines in the same directions at 46 km / hr. and 36 km / hr. the faster trains pass the slower train in 72 seconds. the length of each train is :
Options: a. 82 m, b. 50 m, c. 72 m, d. 100 m, e. none of these

Ex Output:
d

Ex Input:
Problem: in the x - y plane, there are 4 points ( 0,0 ), ( 0,4 ), ( 8,4 ), and ( 8,0 ). if these 4 points makes a rectangle, what is the probability that x + y < 4 ?
Options: a. 1 / 2, b. 1 / 3, c. 2 / 3, d. 1 / 4, e. 2 / 5

Ex Output:
d