well if you put it in equation form:
s/t = Qt + R

s = Q + r/t

64 + 12/100 = s

R/T = 12/100 = 3/25.

The remainder is some multiple of 3, the only answer choice which is a multiple of 3 is E. (45)

you can also do it as s/t = 6142/100 = 1603/25

which has a remainder of 3, so from this as well, you can tell the remainder has to be some sort of a multiple to 3.

IMO E.

I like Sams answer but the title says it was a tricky questions and this was easy to solve....

Whats the answer OP

I don't know why its called a tricky question , but all the question measure is the ability to understand decimals

lets look at the answers

A)2
B)4
C)8
D)20
E)45

We observe that it cannot be A , why ? because if it were A then the decimal part should me either 0 or 0.5

It cannot be B Y ? if B then decimal should be 0,0.25,0.50,0.75

Similarly it cannot be C or D

which leaves only E

Is the answer E?

I reasoned it this way. 64.12 can be expressed as 64 + 3/25 and 3/25 can be 6/50,9/75 12/100 ... has to be a multiple of 3 and among the numbers only 45 is a multiple of 3. Hence E.

Answer is 45:

s/t = 64.12 => s = 64.12 * t
s = 64t + .12t, .12t is reminder r, by definition a positive integer.

r = .12t, hence t = r / .12 = r * 100 / 12 = r * 25 / 3