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

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Manager
Joined: 13 Oct 2009
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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
[Reveal] Spoiler: OA
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Kudos [?]: 106052 [0], given: 11607

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26 Nov 2010, 08:34
Expert's post
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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.

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26 Nov 2010, 20:45
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Expert's post
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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.
_________________

Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 13 Oct 2009 Posts: 55 Location: New York, NY Schools: Columbia, Johnson, Tuck, Stern Followers: 1 Kudos [?]: 65 [0], given: 2 Re: Remainders [#permalink] ### Show Tags 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 ? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7372 Location: Pune, India Followers: 2287 Kudos [?]: 15099 [1] , given: 224 Re: Remainders [#permalink] ### Show Tags 27 Nov 2010, 07:05 1 This post received KUDOS Expert's post 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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27 Nov 2010, 08:14
Cool, thanks a lot Karishma.
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20 Dec 2010, 05:11
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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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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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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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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]

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03 Sep 2014, 12:14
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]

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31 May 2016, 05:04
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Re: If s and t are positive integers such that s/t = 64.12 which   [#permalink] 31 May 2016, 05:04
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