i came across 2 similar type of problem but the method for solving each is lil vague so please help me

Question 1
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

Answer is E.

Explanation says:

When we divide s by t we can always write:

s/t = q + r/t

where q is the 'quotient', and r is the 'remainder', where 0 <= r < t (so 0 <= r/t < 1). That's essentially the definition of the remainder, so is quite important to understand- many remainder questions will be difficult to answer otherwise. If

s/t = 64.12 = 64 + 12/100

then 64 is the quotient, while the fractional part, 12/100, is equal to r/t (compare with the other equation above). This doesn't mean 12 is the remainder, however- that would only be true if t was equal to 100. Still, we can find what values r might take. Rewriting:

r/t = 12/100
r/t = 3/25
25r = 3t

and if r and t are integers, the primes that divide the right side of this equation must also divide the left- in particular r must be divisible by 3. Only one answer choice is divisible by 3- E, or 45- so it's the only possible value of r among the answer choices.

There are many other possible values for r- any multiple of 3 would have been a possible answer, in fact.

Question 2
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96
B. 75
C. 48
D. 25
E. 12

So x = y * A + 9 (A is integer quotient we get when we perform x / y).
x / y = 96.12 <=> x = y * 96.12 <=> x = y * 96 + .12 * y
A = 96 and 9 = .12 * y <=> y = 9 / .12 <=> y = 75

Remember this: When dividing X by Y, a is the quotient and b is the remainder, we get X = a * Y + b




Ok!!!!! so in the first one we divde the remainder by the divsor and the second question multiplies. YYYYYYYYYYYYYY???????