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If s and t are positive integers such that s/t = 64.12 which [#permalink]
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26 Nov 2010, 08:17
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If s and t are positive intergers such 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
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Re: Remainders [#permalink]
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26 Nov 2010, 08:34
Wayxi wrote: 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 nonnegative 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. Answer: E.
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Re: Remainders [#permalink]
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26 Nov 2010, 20:45
Wayxi wrote: 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.
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Re: Remainders [#permalink]
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26 Nov 2010, 23:35
Thanks, i understand this now. I solved it down to 64 3/25 and i didn't see a 3 in any of the choices so i didn't know where to go from there.
Can we also say that t = some multiple of 25 ? ie. And therefore s = 64 * some multiple of 25 + some multiple of 3 ?



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Re: Remainders [#permalink]
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27 Nov 2010, 07:05
Wayxi wrote: Thanks, i understand this now. I solved it down to 64 3/25 and i didn't see a 3 in any of the choices so i didn't know where to go from there.
Can we also say that t = some multiple of 25 ? ie. And therefore s = 64 * some multiple of 25 + some multiple of 3 ? You are right. If remainder is 45 (3*15), then t must be 25*15 and s must be 64*(25*15) + 45.
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Re: Remainders [#permalink]
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27 Nov 2010, 08:14
Cool, thanks a lot Karishma.



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anshumishra wrote: ajit257 wrote: thanks guys....
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. Regards, Murali. Kudos?



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Re: Remainders [#permalink]
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21 Dec 2010, 18:59
VeritasPrepKarishma wrote: Wayxi wrote: 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. Thanks always cristal clear
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Re: Remainders [#permalink]
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16 Aug 2013, 23:02
VeritasPrepKarishma wrote: Wayxi wrote: 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? regrds, Rrsnatha.



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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
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17 Aug 2013, 12:04
Wayxi wrote: If s and t are positive intergers such 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 12/100 = remainder/quotient = 3/25 = 45/(25*15) so remainder = 45
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If s and t are positive integers such that s/t = 64.12 which [#permalink]
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07 Jan 2018, 18:02
Wayxi wrote: If s and t are positive intergers such 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 .12=12/100=9/75=6/50=3/25 note all numerators are multiples of 3 45 is only multiple of 3 E




If s and t are positive integers such that s/t = 64.12 which
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