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

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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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14 Jul 2015, 08:44
Bunuel wrote:
If s and t are positive integers 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

Decimal part x Divisor = Remainder

i.e. o.12*t = remainder
i.e. Remainder = (12/100)*t = (3/25)*t

Since the Result has to be multiple of 3 so Option E is the only choice that fits the requirement

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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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08 Dec 2015, 11:47
Bunuel wrote:
If s and t are positive integers 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

Diagnostic Test
Question: 13
Page: 22
Difficulty: 650

r = .12t = 12/100 * t
r = 3/25 * t
t = 25/3 * r

now we know that t is a positive integer. Thus, r should be a value divisible by 3. Only 45 satisfies that. Thus r = 45, so t to be a positive integer.
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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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04 Dec 2016, 00:17
This is an Amazing official Question.
Here is what i did in this Question =>

S/T=64.12
Using the Basic Remainder theory =>Dividend =Divisor*Quotient +Remainder
Here Quotient =64.12
So S=64.12T
=> S=64T+0.12T

0.12T ≥0 and <T
Hence it must be the remainder.
So the remainder is 0.12T
T=Remainder/0.12=> 25*Remainder/3
As T is an integer => Remainder must be a multiple of 3
Only value that is multiple of 3 is 45 aka option E

Hence E

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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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11 Dec 2017, 18:31
Bunuel wrote:
If s and t are positive integers 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

This problem will be best solved using the remainder formula. Let’s first state the remainder formula:

When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.

In this problem we are given the following:

s/t = 64.12

We can simplify this to read as the remainder formula:

s/t = 64 + 0.12

s/t = 64 + 0.12

s/t = 64 + 12/100

s/t = 64 + 3/25

Because Q is always an integer, we see that Q must be 64, and thus the remainder r/y must be 3/25. We can now equate r/y to 3/25 and determine a possible value for r.

r/y = 3/25

Note that some equivalent values for r/y could be 6/50 or 9/75 or 12/100, and so forth. Note that in all cases, the value of r is a multiple of 3.

Of the answer choices, the only multiple of 3 is 45, so that is a possible value of r.

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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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06 Apr 2018, 10:09
we can use the formula $$s=tQ+R$$ so $$\frac{R}{t}=\frac{12}{100}=\frac{3}{25}$$
this means that R must be of the form $$R=3k$$.
the only multiple of 3 is E.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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08 Apr 2018, 06:51
1
The remainder is 0.12t0.12t (it is less than t) and it is an integer, being equal to s−64ts−64t.
Since 0.12t=325t0.12t=325t, it follows that t should be a multiple of 25, so t=25nt=25n, for some positive integer n.
Therefore, the remainder is 3n3n, or a multiple of 3. The only answer that is a multiple of 3 is 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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09 Aug 2018, 11:44
The article by Karishma really helped! Thanks a lot for putting in the link!
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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 2018, 22:44
VeritasKarishma Is it possible to solve this question by the method?-- http://www.veritasprep.com/blog/2011/04 ... unraveled/
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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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06 Dec 2018, 11:52
I looked at it a bit differently. Since s & t are positive integers, Remainder/0.12 or (Remainder*100)/(4*3) should be an integer. Since 100 isn't divisible by 3, the remainder should be. Option E (45) is the only one that fits the bill.
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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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14 Apr 2019, 15:43
If s/t = 64.12 then this means that t goes into s 64 times and .12 t is our remainder. From here plug in answer choices = .12t and see if we get an integer value for t. E) 45 = .12t ---> t =375, an integer therefore E
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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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11 May 2019, 23:46
Bunuel wrote:
If s and t are positive integers 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

Diagnostic Test
Question: 13
Page: 22
Difficulty: 650

Here,
r/t=.12 [remainder part]
=12/100=3/25
r:t=3:25
r is a multiple of 3

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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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06 Aug 2019, 21:46
luckyme17187 wrote:
Answered this question wrong but when i finished reading karishma's blog http://www.veritasprep.com/blog/2011/05/quarter-wit-quarter-wisdom-knocking-off-the-remaining-remainders/ . I am confident about these type of questions.

s/t=64.12

when we divide "s" by "t" then 64.12, Here .12 is a Remainder which we are representing in quotient. so to find the possible remainder...

0.12--12/100 -- 3/25 , so 25 or multiple of 25 has to be a "t" & 3 or multiple of 3 has to be remainder.

Thank you for the link. Her explanation is super easy and well expressed.
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Re: If s and t are positive integers such that s/t = 64.12 which  [#permalink]

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15 Aug 2019, 14:07
Bunuel wrote:
SOLUTION

If s and t are positive integers 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

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.

How did you conclude that q is 64? The rest makes sense except this..
Re: If s and t are positive integers such that s/t = 64.12 which   [#permalink] 15 Aug 2019, 14:07

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