If \(s\) and \(t\) are positive integers such that \(\dfrac{s}{t} = 64.12,\) which of the following could be the remaind

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If \(s\) and \(t\) are positive integers such that \(\dfrac{s}{t} = 64.12,\) which of the following could be the remainder when \(s\) is divided by \(t ?\)

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

[spoiler]OA=E[/spoiler]

Source: Official Guide

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Vincen wrote:
Tue Jun 30, 2020 7:30 am
If \(s\) and \(t\) are positive integers such that \(\dfrac{s}{t} = 64.12,\) which of the following could be the remainder when \(s\) is divided by \(t ?\)

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

[spoiler]OA=E[/spoiler]

Source: Official Guide
So we have \(\dfrac{s}{t} = 64.12.\)

\(\dfrac{s}{t} = 64.12, = \dfrac{6,412}{100} = 64 + \dfrac{12}{100}\)

We see that the remainder is 12, but there is no option as 12.

Let's analyze the question further. Note that I did not reduce the fraction \(\dfrac{6,412}{100}\) in its shortest form.

Let's do it.

\(\dfrac{s}{t} = 64.12, = \dfrac{6,412}{100} = \dfrac{1,603}{25} = 64 + \dfrac{3}{25}\)

We see that the remainder is 3, but there is no option as 3, too.

Note that when the divisor was 100, the quotient was 64, and the remainder was 12, and when the divisor was 25, the quotient was 64, and the remainder is 3. There can be many divisors such as 50, 200, etc. But in each case, the remainder would be a multiple of 3. There's only option, which is a multiple of 3, and that is option E = 45, the correct answer.

Correct answer: E

Hope this helps!

-Jay
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