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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
02 Jul 2012, 01:08

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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

s divided by t yields the remainder of r can always be expressed as: \frac{s}{t}=q+\frac{r}{t} (which is the same as s=qt+r), where q is the quotient and r is the remainder.

Given that \frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}, so according to the above \frac{r}{t}=\frac{3}{25}, which means that r must be a multiple of 3. Only option E offers answer which is a multiple of 3

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We can rewrite the given equality as s = 64t + 0.12t. The divider is t, the quotient is 64. The remainder is 0.12t (it is less than t) and it is an integer, being equal to s-64t. Since 0.12t=\frac{3}{25} t, it follows that t should be a multiple of 25, so t=25n, for some positive integer n. Therefore, the remainder is 3n, or a multiple of 3. The only answer that is a multiple of 3 is 45.

Answer: E

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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
02 Jul 2012, 01:55

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i dont know if this method is correct or not, would need expert check s/t = 64.12 = 64+12/100 = 64+3/25 i got 3, and in the options the multiple of is 45

Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
06 Jul 2012, 01:57

2

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Expert's post

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

s divided by t yields the remainder of r can always be expressed as: \frac{s}{t}=q+\frac{r}{t} (which is the same as s=qt+r), where q is the quotient and r is the remainder.

Given that \frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}, so according to the above \frac{r}{t}=\frac{3}{25}, which means that r must be a multiple of 3. Only option E offers answer which is a multiple of 3

If s and t are positive integers such that s/t = 64.12 which [#permalink]
18 Aug 2012, 04:50

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Shortcut for this question:- 64.12 = 64 + 12/100 Now focus on remainder part which is 12/100= 3/25 Because 3 represents some fraction (ratio) of remainder , the remainder must be a multiple of 3. only 45 is a multiple of 3.

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Re: Divisibility / Remainder problem [#permalink]
28 Aug 2012, 01:32

1

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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

s/t = 64.12, => s = t*64.12 => s = 64t + t*.12 So, when s is divided by t then we will get t*.12 as reminder (as t*.12 will be less than t) Now t is an integer and .12 is 12*.01 which means it is 3*something So, only answer choices which are multiple of 3 are contenders.

If s and t are positive integers such that s/t = 64.12, which of [#permalink]
26 Dec 2012, 22:15

3

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\frac{S}{t} = 64 + .12 S = 64t + .12t

The remainder is equal to .12t.

R = .12t R/.12 = t

We have to look for R where R/.12 is an integer.

A)2/.12 = 200/12 is not an integer B)4/.12 = 400/12 = 100/3 is not an integer C) 8/.12 = 800/12 = 400/6 = 200/3 is not an integer D) also not E) 45/12 = 4500/12 = 1500/4 = 15*25 is an integer

If s and t are positive integers such that s/t = 64.12 which [#permalink]
23 Jun 2014, 02:25

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

s divided by t yields the remainder of r can always be expressed as: \frac{s}{t}=q+\frac{r}{t} (which is the same as s=qt+r), where q is the quotient and r is the remainder.

Given that \frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}, so according to the above \frac{r}{t}=\frac{3}{25}, which means that r must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

I did not understand why r must be a multiple of 3? From answer choice E 45 is 15 times 3 (a multiple of 3) does that mean t will be 15 times 25?

If s and t are positive integers such that s/t = 64.12 which [#permalink]
23 Jun 2014, 02:41

nehamodak wrote:

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

s divided by t yields the remainder of r can always be expressed as: \frac{s}{t}=q+\frac{r}{t} (which is the same as s=qt+r), where q is the quotient and r is the remainder.

Given that \frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}, so according to the above \frac{r}{t}=\frac{3}{25}, which means that r must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.

I did not understand why r must be a multiple of 3? From answer choice E 45 is 15 times 3 (a multiple of 3) does that mean t will be 15 times 25?

Because \frac{3}{25}cannot be simplified further (say factorised further)

\frac{3}{25}= \frac{3*15}{25*15}= \frac{45}{25*15} ... That is possible