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
Answer: E
Source: Official Guide
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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 remaind
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Solution:
We see that s = 64.12t = 64t + 0.12t. Therefore, 0.12t = 12t/100 = 3t/25 must be the remainder. Since 3 is not a multiple of 25, t must be a multiple of 25 (so that 3t/25 will be an integer). In that case, t/25 is an integer, and 3t/25 = 3 * t/25 must be a multiple of 3. Because the only multiple of 3 in the given choices is 45, then 45 could be the remainder when s is divided by t.
Answer: E
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Here, we have
\(\dfrac{s}{t} = 64.12\)
\(s = t\cdot 64.12\)
\(s = 64t + t\cdot 0.12\)
So, when \(s\) is divided by \(t\) then we will get \(t\cdot 0.12\) as reminder (as \(t\cdot 0.12\) will be less than \(t\))
Now \(t\) is an integer and \(0.12\) is \(12\cdot 0.01\) which means it is \(3\cdot\)something
So, only answer choices which are multiple of \(3\) are contenders.
Therefore, E
