When the positive integer k is divided by the positive integ : GMAT Problem Solving (PS)
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# When the positive integer k is divided by the positive integ

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When the positive integer k is divided by the positive integ [#permalink]

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12 Aug 2014, 04:00
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When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n?

A. 9
B. 20
C. 55
D. 70
E. 81

Can someone break this down for me please?

Here is a response from Beat The GMAT (/tricky-remainder-problem-t270176.html)

Before I past the question, I am confused with how the user came up with K = 81n +11. Where did the .2 go for this representation?

"If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k:
xn + 11 = k

If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.

k = 81.2n

and

k = 81n + 11

Now, we can simply set these expressions equal to each other, since they're both equal to k:

81.2n = 81n + 11
0.2n = 11
n = 55"

Thank you for your help!!
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2014, 04:18, edited 1 time in total.
RENAMED THE TOPIC.
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Re: When the positive integer k is divided by the positive integ [#permalink]

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12 Aug 2014, 04:44
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joaomario wrote:
When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n?

A. 9
B. 20
C. 55
D. 70
E. 81

Can someone break this down for me please?

Here is a response from Beat The GMAT (/tricky-remainder-problem-t270176.html)

Before I past the question, I am confused with how the user came up with K = 81n +11. Where did the .2 go for this representation?

"If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k:
xn + 11 = k

If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.

k = 81.2n

and

k = 81n + 11

Now, we can simply set these expressions equal to each other, since they're both equal to k:

81.2n = 81n + 11
0.2n = 11
n = 55"

Thank you for your help!!

If $$x$$ and $$y$$ are positive integers, there exist unique integers $$q$$ and $$r$$, called the quotient and remainder, respectively, such that $$y =divisor*quotient+remainder= xq + r$$ and $$0\leq{r}<x$$.

For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since $$15 = 6*2 + 3$$.

Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n.

We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, q, is 81 and 11/n is 0.2: 11/n = 0.2 --> n = 55.

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Theory on remainders problems: remainders-144665.html
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Re: When the positive integer k is divided by the positive integ [#permalink]

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13 Aug 2014, 03:59
Bunuel wrote:
If $$x$$ and $$y$$ are positive integers, there exist unique integers $$q$$ and $$r$$, called the quotient and remainder, respectively, such that $$y =divisor*quotient+remainder= xq + r$$ and $$0\leq{r}<x$$.

For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since $$15 = 6*2 + 3$$.

Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n.

We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, q, is 81 and 11/n is 0.2: 11/n = 0.2 --> n = 55.

How did you know to create K = 81n + 11? How did you know to leave out the 0.2? I am confused as heck by this!
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Re: When the positive integer k is divided by the positive integ [#permalink]

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13 Aug 2014, 05:39
joaomario wrote:
Bunuel wrote:
If $$x$$ and $$y$$ are positive integers, there exist unique integers $$q$$ and $$r$$, called the quotient and remainder, respectively, such that $$y =divisor*quotient+remainder= xq + r$$ and $$0\leq{r}<x$$.

For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since $$15 = 6*2 + 3$$.

Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n.

We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, q, is 81 and 11/n is 0.2: 11/n = 0.2 --> n = 55.

How did you know to create K = 81n + 11? How did you know to leave out the 0.2? I am confused as heck by this!

Please follow the links given in my post. You need to brush up fundamentals.
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Re: When the positive integer k is divided by the positive integ [#permalink]

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17 Dec 2014, 03:36
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joaomario wrote:
When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n?

A. 9
B. 20
C. 55
D. 70
E. 81

Can someone break this down for me please?

Here is a response from Beat The GMAT (/tricky-remainder-problem-t270176.html)

Before I past the question, I am confused with how the user came up with K = 81n +11. Where did the .2 go for this representation?

"If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k:
xn + 11 = k

If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.

k = 81.2n

and

k = 81n + 11

Now, we can simply set these expressions equal to each other, since they're both equal to k:

81.2n = 81n + 11
0.2n = 11
n = 55"

Thank you for your help!!

If K/N is 81,2 and the remainder is 11 we can say that 11=0,2n
11/0,2=55
N=55

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Re: When the positive integer k is divided by the positive integ [#permalink]

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21 Dec 2014, 19:09
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Hi joaomario,

Here's an approach that's based on Number Properties and a bit of "brute force" math:

We're told that K and N are both INTEGERS.

Since K/N = 81.2, we can say that K = 81.2(N)

N has to "multiply out" the .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.

With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)

Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH
Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.

[Reveal] Spoiler:
C

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Re: When the positive integer k is divided by the positive integ [#permalink]

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29 Dec 2014, 16:18
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Yes, I am aware that my answer goes after the 800-scorer Rich, but I´ll try my best!

Once you really understood the pattern in which Gmat works with this type of problem, it all boils down to a very simple system of 3 equations and 3 variables. That´s the "trick" you should know.

Here is my reasoning:

The System of Equations
1st Equation: k = nq + 11 --> k/n = q + 11/n
2nd Equation: k/n = 81.2 --> k/n = 81 + 1/5
3rd Equation: q = 81

Plug in q (from equation 3) in equation 1
k/n = 81 + 11/n

Rewrite Equations 1 and 2
k/n – 81 = 11/n
k/n – 81 = 1/5

Set Equalities in Equations 1 and 2
11/n = 1/5
n = 55

There are many ways to find the system of equations. I just found this approach "elegant".

Hope it helps!
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Re: When the positive integer k is divided by the positive integ   [#permalink] 31 May 2016, 04:10
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# When the positive integer k is divided by the positive integ

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