Check if my thinking is correct -OG12 Diagnostic

[mdavidm_531]

Hi, Experts,

Here's the question:

Source: OG12 Diagnostic test #13

"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

Here's my thought process:

1. We know that s = (quotient)(t) + remainder
2. We divide both sides by t. We have s/t = quotient + remainder/t
3. We know that s/t = 64.12
4. We know that s/t = 64.00 + 12/100
5. As such remainder/t = 12/100
6. Isolate t, we have (remainder)(100)/(12) = t
7. Now here's where I got it wrong. I forgot that t should be integer!
8. There could only be one value of r that could make t an integer. That is 45 (we will be able to reduce 12 to 1 when there's 45 in the numerator)
9. Answer: E

I think the lesson here is that WE SHOULD NOT FORGET THE CONDITIONS. This also applies to data sufficiency, where many errors are made because of not satisfying the statements condition.

[aneesh.kg]

Absolutely correct and very methodical. And I liked the way you wrote down your thought-process.

However, you could reduced your effort a little bit.

If you notice: The decimal part of any number is contributed by the remainder.
The decimal part is the Remainder divided by the Divisor. This is what you found at Step 4.
(You can also take a few numbers to digest this better)
And now what you get is your Step5.

0.12 = Remainder/t
or
Remainder = 0.12t

[GMATGuruNY]

I posted a solution here:

https://www.beatthegmat.com/remainder-t111428.html

[LalaB]

s/t = 64+ 12/100

Remainder/t=12/100=3/25

it means that Remainder must be divisible by 3

among answer choices only 45 is divisible by 3