Easy probability question from GMAT...?

Question

This was asked by the GMAT test makers, I have no clue what they're even saying, and I have degree in electrical engineering... Here it is, word for word:

If s and t are positive integers such that s / t = 64.12, which of the following could be the remainder when s is divided by t?

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

They indicate the correct answer as E

Answer 1

In this division the remainder, R, can be expressed as follows:

s = 64t + R where R = 0.12t

R has to be one of the values listed as possible answers. Since t is said to be a positive integer, the R / 0.12 must be a positive integer. By replacing R with all the possible answers you'll see that only 45 gives a t that is a positive integer.

Here is another way to look at this (and more in line with the previous response posted): R / 0.12 = R / (3 / 25) = 25R / 3 which is only an integer when R is a multiple of 3 (since 25 is not a multiple of 3).

Answer 2

64.12 is the same as 64 and 3/25. Thus when s is divided by t the remainder must be a mutiple of 3. Answer E is the only possibility because it is the only one that is a multiple of 3.