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

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

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Difficulty: 650
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 02 Jul 2012, 01:08
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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 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.
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 02 Jul 2012, 01:27
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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

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Difficulty: 650


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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] New post 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

Answer - E
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 02 Jul 2012, 02:11
Hi,

Difficulty level: 600

s/t = 64.12
or s/t = 64 + 0.12 = 64 + 12/100 = 64 + 3/25; 3/25 will give the remainder.
Thus, the reminder should be multiple of 3.

Answer (E)

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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 06 Jul 2012, 01:57
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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 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.
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If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 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: If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 18 Aug 2012, 09:00
+1 E

0.12 = 12/100 = 3/25, the remainder must be a multiple of 3.
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Re: Divisibility / Remainder problem [#permalink] New post 28 Aug 2012, 01:32
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.

Only possbility is E!

Hope it helps!
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Re: Divisibility / Remainder problem [#permalink] New post 28 Aug 2012, 01:57
Answer is E

S/T = 64.12 or you can write it as 6412/100 or 1603/25

So, If we divide 1603 by 25 we will get remainder of 3.

From the five options, only 45 is divisible by 3 So, The answer should be 45.
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 28 Aug 2012, 07:20
its E...

i think diffculty level is 650.. i knw we can do it in 20 sec..but very few ppl knw this trick to solve this question..
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If s and t are positive integers such that s/t = 64.12, which of [#permalink] New post 26 Dec 2012, 22:15
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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

Answer: E
C)
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Which could be the remained when "s" is divided by "t"? [#permalink] New post 19 Jun 2013, 03:32
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
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Re: Which could be the remained when "s" is divided by "t"? [#permalink] New post 19 Jun 2013, 03:36
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Rs1991 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


Merging similar topics. Please refer to the solutions above.

All OG13 questions with solutions: the-official-guide-quantitative-question-directory-143450.html
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 27 Jun 2013, 09:18
Bunuel wrote:
which means that r must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.


out of the answer explanation, but can we also say that t must be a multiple of 25 using the same fraction?
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 27 Jun 2013, 09:48
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Bunuel wrote:
which means that r must be a multiple of 3. Only option E offers answer which is a multiple of 3

Answer. E.


out of the answer explanation, but can we also say that t must be a multiple of 25 using the same fraction?


Yes, t must be a multiple of 25: s/t = 1603/25 = 3206/50 = 6412/100 = ... = 64.12 --> the remainders 3, 6, 12, ..., respectively.
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If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 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?
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If s and t are positive integers such that s/t = 64.12 which [#permalink] New post 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
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If s and t are positive integers such that s/t = 64.12 which   [#permalink] 23 Jun 2014, 02:41
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