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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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New post 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

Answer: Option 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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New post 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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New post 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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New post 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.

Answer: 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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New post 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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New post 08 Apr 2018, 06:51
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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.

Answer: E
Re: If s and t are positive integers such that s/t = 64.12 which   [#permalink] 08 Apr 2018, 06:51

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