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.
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Question: Question: A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 8 miles per day and it will take them two days, how many miles long is the route down the mountain?

 Option A: 18

 Option B: 20

 Option C: 22

 Option D: 24

 Option E: 25

Answer: Option D


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: The average of 11 results is 50, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?

 Option A: 55

 Option B: 56

 Option C: 57

 Option D: 58

 Option E: 59

Answer:
Option E