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 bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?

 Option A: 89.33 km/h

 Option B: 85.34 km/h

 Option C: 87.67 km/h

 Option D: 90.25 km/h

 Option E: 90.64 km/h
[A]: Option A


[Q]: Question: Two pipes P and Q can fill a cistern in 12 and 14 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?

 Option A: 11 1/2 min

 Option B: 11 1/4 min

 Option C: 11 2/4 min

 Option D: 11 1/5 min

 Option E: 10 1/2 min
[A]: Option E


[Q]: Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 66°, what fraction of the wheel’s area is represented by the smallest sector?

 Option A: 1/24

 Option B: 1/20

 Option C: 1/15

 Option D: 1/12

 Option E: 1/10
[A]:
Option C