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: 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

A: Option E
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Q: Question: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?

 Option A: 5

 Option B: 6

 Option C: 7

 Option D: 8

 Option E: 10

A: Option E
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Q: Question: If 4x+y=34, 2x-y=20, for integers of x and y, y^2=?

 Option A: 2

 Option B: 4

 Option C: 0

 Option D: 10

 Option E: 3

A:
Option B
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