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

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If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 26 Nov 2010, 07:17
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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
[Reveal] Spoiler: OA
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Re: Remainders [#permalink] New post 26 Nov 2010, 07:34
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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 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.

Answer: E.
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Re: Remainders [#permalink] New post 26 Nov 2010, 19:45
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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] New post 26 Nov 2010, 22:35
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] New post 27 Nov 2010, 06:05
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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] New post 27 Nov 2010, 07:14
Cool, thanks a lot Karishma.
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new [#permalink] New post 20 Dec 2010, 04:11
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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

[Reveal] Spoiler:
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.
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Re: Remainders [#permalink] New post 21 Dec 2010, 17:59
Expert's post
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] New post 16 Aug 2013, 22:02
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] New post 17 Aug 2013, 11:04
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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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 03 Sep 2014, 11:14
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Re: If s and t are positive integers such that s/t = 64.12 which   [#permalink] 03 Sep 2014, 11:14
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