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 train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?

 Option A: 229

 Option B: 240

 Option C: 288

 Option D: 277

 Option E: 221
[A]: Option B


[Q]: Question: Two trains, each 100 m long, moving in opposite directions, cross other in 6 sec. If one is moving twice as fast the other, then the speed of the faster train is?

 Option A: 80 km/hr

 Option B: 66 km/hr

 Option C: 60 km/hr

 Option D: 67 km/hr

 Option E: 22 km/hr
[A]: Option A


[Q]: Question: The security gate at a storage facility requires a five-digit lock code. If the lock code
must consist only of digits from 1 through 7, inclusive, with no repeated digits, and
the first and last digits of the code must be odd, how many lock codes are possible?

 Option A: 120

 Option B: 240

 Option C: 360

 Option D: 720

 Option E: 1440
[A]:
Option D