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.

Input: Consider Input: Question: If x is positive and y is negative, which of the following must be true?

 Option A: The product of x and y is positive

 Option B: The sum of x and y is positive

 Option C: The sum of x and y is negative

 Option D: The difference of x and y is positive

 Option E: The sum of x^2 and y^2 is positive

Output: Option E


Input: Consider Input: Question: A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates Z apply to what fraction of a week?

 Option A:  1/2

 Option B:  5/8

 Option C:  9/14

 Option D:  16/21

 Option E:  9/10

Output: Option C


Input: Consider Input: Question: A certain cricket team played seven games and scored an average of 180 runs per game. If, in the team’s first five games, it scored 175, 169, 181, 190, and 173 points, what was the average (arithmetic mean) number of points scored over the last two games?

 Option A: 165

 Option B: 181

 Option C: 182

 Option D: 186

 Option E: Cannot be determined from the information given.


Output: Option D