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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

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

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We can rewrite the given equality as \(s = 64t + 0.12t\). The divider is t, the quotient is 64. The remainder is \(0.12t\) (it is less than t) and it is an integer, being equal to \(s-64t\). Since \(0.12t=\frac{3}{25} t\), it follows that t should be a multiple of 25, so \(t=25n\), for some positive integer n. Therefore, the remainder is \(3n\), or a multiple of 3. The only answer that is a multiple of 3 is 45.

Answer: E
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]

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02 Jul 2012, 02:55

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i dont know if this method is correct or not, would need expert check s/t = 64.12 = 64+12/100 = 64+3/25 i got 3, and in the options the multiple of is 45

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

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

If s and t are positive integers such that s/t = 64.12 which [#permalink]

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18 Aug 2012, 05:50

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Shortcut for this question:- 64.12 = 64 + 12/100 Now focus on remainder part which is 12/100= 3/25 Because 3 represents some fraction (ratio) of remainder , the remainder must be a multiple of 3. only 45 is a multiple of 3.

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which of the following could be the remainder when s is divided by t?

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

s/t = 64.12, => s = t*64.12 => s = 64t + t*.12 So, when s is divided by t then we will get t*.12 as reminder (as t*.12 will be less than t) Now t is an integer and .12 is 12*.01 which means it is 3*something So, only answer choices which are multiple of 3 are contenders.

If s and t are positive integers such that s/t = 64.12, which of [#permalink]

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26 Dec 2012, 23:15

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\(\frac{S}{t} = 64 + .12\) \(S = 64t + .12t\)

The remainder is equal to .12t.

R = .12t R/.12 = t

We have to look for R where R/.12 is an integer.

A)2/.12 = 200/12 is not an integer B)4/.12 = 400/12 = 100/3 is not an integer C) 8/.12 = 800/12 = 400/6 = 200/3 is not an integer D) also not E) 45/12 = 4500/12 = 1500/4 = 15*25 is an integer

If s and t are positive integers such that s/t = 64.12 which [#permalink]

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23 Jun 2014, 03:25

Bunuel wrote:

SOLUTION

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

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

I did not understand why r must be a multiple of 3? From answer choice E 45 is 15 times 3 (a multiple of 3) does that mean t will be 15 times 25?

If s and t are positive integers such that s/t = 64.12 which [#permalink]

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23 Jun 2014, 03:41

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nehamodak wrote:

Bunuel wrote:

SOLUTION

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

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

I did not understand why r must be a multiple of 3? From answer choice E 45 is 15 times 3 (a multiple of 3) does that mean t will be 15 times 25?

Because \(\frac{3}{25}\)cannot be simplified further (say factorised further)

\(\frac{3}{25}= \frac{3*15}{25*15}= \frac{45}{25*15}\) ... That is possible
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]

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01 Mar 2015, 00:31

Bunuel wrote:

SOLUTION

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

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

If the question had been which of the following cannot be the remainder. Then can we use the propertry that Remainder must be divisibe by 25 as well???

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

\(s\) divided by \(t\) yields the remainder of \(r\) can always be expressed as: \(\frac{s}{t}=q+\frac{r}{t}\) (which is the same as \(s=qt+r\)), where \(q\) is the quotient and \(r\) is the remainder.

Given that \(\frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}\), so according to the above \(\frac{r}{t}=\frac{3}{25}\), which means that \(r\) must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

If the question had been which of the following cannot be the remainder. Then can we use the propertry that Remainder must be divisibe by 25 as well???

Dear Ankush

Good to see you here on GC!

Here's the answer to your question:

It is not necessary for the remainder to be divisible by 25.

Let's look at this in terms of constraints:

Constraint 1: The remainder is always a non-negative integer.

From the equation

\(\frac{r}{t}=\frac{3}{25}\), we get that

r=\(\frac{3t}{25}\)

From constraint 1, we see that

\(\frac{3t}{25}\) must be a non-negative integer.

This means either t = 0 or t is a multiple of 25.

But t cannot be equal to 0 because then the expression \(\frac{s}{t}\) becomes undefined

This means, t is a multiple of 25.

Constraint 2: The question states that t is a positive integer.

As explained in the post I made just above, this means \(\frac{25r}{3}\) is a positive integer, which leads you to the inference that r is a multiple of 3.

So, the bottom-line is that the only 2 inferences that we can conclusively draw from the given information is that:

i) t is a multiple of 25 and ii) r is a multiple of 3

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