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Hi, I was was not satisfied with the explanation given from the Official Guide for this question. Please let me know if there are alternative techniques to solve this:

If s and t are positive intergers sug that s/t = 64.12, which of the following could be the remainder when s is dividted by t ?

a. 2 b. 4 c. 8 d. 20 e. 45

Note: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, "s divided by t gives remainder r" can be expressed by the following formula: \(s=qt+r\), in or case as \(\frac{s}{t}=64.12\) then \(q=64\), --> \(s=64t+r\), divide both parts by \(t\) --> \(\frac{s}{t}=64+\frac{r}{t}\) --> \(64.12=64+\frac{r}{t}\) --> \(0.12=\frac{r}{t}\)--> \(\frac{3}{25}=\frac{r}{t}\) so \(r\) must be the multiple of 3. Only answer multiple of 3 is 45.

Or: \(\frac{s}{t}=64\frac{12}{100}=64\frac{3}{25}\), so if the divisor=t=25 then the remainder=r=3. Basically we get that divisor is a multiple of 25 and the remainder is a multiple of 3. Only answer multiple of 3 is 45.

Hi, I was was not satisfied with the explanation given from the Official Guide for this question. Please let me know if there are alternative techniques to solve this:

If s and t are positive intergers sug that s/t = 64.12, which of the following could be the remainder when s is dividted by t ?

a. 2 b. 4 c. 8 d. 20 e. 45

When we say \(\frac{s}{t} = 64.12 = 64 \frac{12}{100} = 64 \frac{3}{25}\) We get \(\frac{s}{t} = 64 \frac{3}{25}\) What does the mixed fraction of the right hand side signify? It signifies that s > t and when s is divided by t, we get 64 as quotient and 3 as remainder if t is 25.

e.g. \(\frac{13}{5} = 2 \frac{3}{5}\). Here, remainder is 3 \(\frac{130}{50} = 2 \frac{30}{50}\). Here remainder is 30. \(\frac{26}{10} = 2 \frac{6}{10}\). Here remainder is 6. So in our question, the remainder will be 3 or any multiple of 3. 45 is the only multiple of 3. _________________

anshumishra....thanks for the hint. i feel better now.

Great ! I am happy that it helped.

Here is another similar problem. Try to solve yourself first.

If s and t are positive integer 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

Ans: E 0.12 = 12/100 = r/t => t = 100*r/12 (where r & t are both integers) Only E has the integral soln.

Thanks

Let me put it in a better way.

reminder \(R = 12t/100\) ==> \(12t/100\) is an integer ==> \(3t/25\) is an integer ==> \(3t/5^2\) is an integer note that 3 and 5 are prime #s ==> t has to be a multiple of 5^2 for the reminder to be an integer and the reminder has to be a multiple of 3 as the prime # 3 presents in the numerator.

The only mupltiple of 3 in the answers choices is 45 i.e E.

Hi, I was was not satisfied with the explanation given from the Official Guide for this question. Please let me know if there are alternative techniques to solve this:

If s and t are positive intergers sug that s/t = 64.12, which of the following could be the remainder when s is dividted by t ?

a. 2 b. 4 c. 8 d. 20 e. 45

When we say \(\frac{s}{t} = 64.12 = 64 \frac{12}{100} = 64 \frac{3}{25}\) We get \(\frac{s}{t} = 64 \frac{3}{25}\) What does the mixed fraction of the right hand side signify? It signifies that s > t and when s is divided by t, we get 64 as quotient and 3 as remainder if t is 25.

e.g. \(\frac{13}{5} = 2 \frac{3}{5}\). Here, remainder is 3 \(\frac{130}{50} = 2 \frac{30}{50}\). Here remainder is 30. \(\frac{26}{10} = 2 \frac{6}{10}\). Here remainder is 6. So in our question, the remainder will be 3 or any multiple of 3. 45 is the only multiple of 3.

Hi, I was was not satisfied with the explanation given from the Official Guide for this question. Please let me know if there are alternative techniques to solve this:

If s and t are positive intergers sug that s/t = 64.12, which of the following could be the remainder when s is dividted by t ?

a. 2 b. 4 c. 8 d. 20 e. 45

When we say \(\frac{s}{t} = 64.12 = 64 \frac{12}{100} = 64 \frac{3}{25}\) We get \(\frac{s}{t} = 64 \frac{3}{25}\) What does the mixed fraction of the right hand side signify? It signifies that s > t and when s is divided by t, we get 64 as quotient and 3 as remainder if t is 25.

e.g. \(\frac{13}{5} = 2 \frac{3}{5}\). Here, remainder is 3 \(\frac{130}{50} = 2 \frac{30}{50}\). Here remainder is 30. \(\frac{26}{10} = 2 \frac{6}{10}\). Here remainder is 6. So in our question, the remainder will be 3 or any multiple of 3. 45 is the only multiple of 3.

Hi,

In this if the remainder is 45 then the Divisor will be 25*15 right?

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