instruction:
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.
question:
Question: A six-character password consists of three letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?

 Option A: 5,040

 Option B: 2,228,720

 Option C: 22,226,000

 Option D: 22,237,440

 Option E: 22,464,000
answer:
Option E


question:
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
answer:
Option E


question:
Question: Two trains 190 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?

 Option A: 10.7

 Option B: 10.9

 Option C: 10.6

 Option D: 12.6

 Option E: 18.8
answer:

Option D