If a and b are positive integers, which of the following cannot be an integer? Choose the correct choice:
A) (2b)/(4a+1)
B) (2b)/(3a+1)
C) (2a+1)/(4b)
D) (2a+1)/(4b+1)
E) (2a·b)/(4b+2)
I'd first look for an option which gives odd/even for any values of a and b, because odd/even is not an integer.   Option C fits: 2a+1/4b=even+odd/even=odd/even≠integer   To discard other A consider a=5 and b=1.   To discard other B consider a=2 and b=1.   To discard other D consider a=2 and b=1.   To discard other E consider a=3 and b=1.   Answer: (2a+1)/(4b).
<result>C</result>
If a and b are positive integers, which of the following cannot be an integer?