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

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Intern
Joined: 13 Oct 2009
Posts: 48
Location: New York, NY
Schools: Columbia, Johnson, Tuck, Stern
If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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26 Nov 2010, 07:17
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25% (medium)

Question Stats:

75% (01:26) correct 25% (02:02) wrong based on 292 sessions

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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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8665
Location: Pune, India

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26 Nov 2010, 19:45
6
3
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
Veritas Prep GMAT Instructor

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Math Expert
Joined: 02 Sep 2009
Posts: 51121

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26 Nov 2010, 07:34
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 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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Joined: 13 Oct 2009
Posts: 48
Location: New York, NY
Schools: Columbia, Johnson, Tuck, Stern

### Show Tags

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 ?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8665
Location: Pune, India

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27 Nov 2010, 06:05
1
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

Intern
Joined: 13 Oct 2009
Posts: 48
Location: New York, NY
Schools: Columbia, Johnson, Tuck, Stern

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27 Nov 2010, 07:14
Cool, thanks a lot Karishma.
Manager
Joined: 30 Aug 2010
Posts: 88
Location: Bangalore, India

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20 Dec 2010, 04:11
1
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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Joined: 01 Sep 2010
Posts: 3292

### Show Tags

21 Dec 2010, 17:59
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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Manager
Joined: 30 May 2013
Posts: 158
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82

### Show Tags

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.
Senior Manager
Joined: 10 Jul 2013
Posts: 315
Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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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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Asif vai.....

VP
Joined: 07 Dec 2014
Posts: 1128
If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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07 Jan 2018, 17:02
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 &nbs [#permalink] 07 Jan 2018, 17:02
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