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# When the positive integer k is divided by the positive integ

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Joined: 11 Aug 2014
Posts: 3
When the positive integer k is divided by the positive integ  [#permalink]

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Updated on: 20 Sep 2017, 05:43
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Question Stats:

85% (01:31) correct 15% (01:59) wrong based on 480 sessions

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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"

Originally posted by joaomario on 12 Aug 2014, 05:00.
Last edited by abhimahna on 20 Sep 2017, 05:43, edited 2 times in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 50007
Re: When the positive integer k is divided by the positive integ  [#permalink]

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12 Aug 2014, 05:44
10
14
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"

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.

Similar questions to practice:
when-positive-integer-x-is-divided-by-positive-integer-y-106493.html
if-s-and-t-are-positive-integers-such-that-s-t-64-12-which-135190.html

Theory on remainders problems: remainders-144665.html
Tips on Remainders: remainders-tips-and-hints-175000.html?hilit=remainders%20tips#p1376126

Units digits, exponents, remainders problems: new-units-digits-exponents-remainders-problems-168569.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199

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

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17 Dec 2014, 04:36
1
1
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"

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, 20:09
3
1
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.

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

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29 Dec 2014, 17:18
1
2
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]

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28 Sep 2017, 04:00
Bunuel wrote:
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"

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.

Similar questions to practice:
http://gmatclub.com/forum/when-positive ... 06493.html
http://gmatclub.com/forum/if-s-and-t-ar ... 35190.html

Theory on remainders problems: http://gmatclub.com/forum/remainders-144665.html
Tips on Remainders: http://gmatclub.com/forum/remainders-ti ... s#p1376126

Units digits, exponents, remainders problems: http://gmatclub.com/forum/new-units-dig ... 68569.html

All DS remainders problems to practice: http://gmatclub.com/forum/search.php?se ... tag_id=198
All PS remainders problems to practice: http://gmatclub.com/forum/search.php?se ... tag_id=199

P.S. Please read carefully and follow: http://gmatclub.com/forum/rules-for-pos ... 33935.html Pay attention to rule 3. Thank you.

Hi Bunuel,

"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."

I was wondering, why can't q = 0.2 and 81=11/n ?
Math Expert
Joined: 02 Sep 2009
Posts: 50007
Re: When the positive integer k is divided by the positive integ  [#permalink]

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28 Sep 2017, 04:20
pra1785 wrote:
Bunuel wrote:
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"

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.

Similar questions to practice:
http://gmatclub.com/forum/when-positive ... 06493.html
http://gmatclub.com/forum/if-s-and-t-ar ... 35190.html

Theory on remainders problems: http://gmatclub.com/forum/remainders-144665.html
Tips on Remainders: http://gmatclub.com/forum/remainders-ti ... s#p1376126

Units digits, exponents, remainders problems: http://gmatclub.com/forum/new-units-dig ... 68569.html

All DS remainders problems to practice: http://gmatclub.com/forum/search.php?se ... tag_id=198
All PS remainders problems to practice: http://gmatclub.com/forum/search.php?se ... tag_id=199

P.S. Please read carefully and follow: http://gmatclub.com/forum/rules-for-pos ... 33935.html Pay attention to rule 3. Thank you.

Hi Bunuel,

"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."

I was wondering, why can't q = 0.2 and 81=11/n ?

The point is that the quotient must be an integer.

For example, 15 divided by 6 gives the quotient of 2 and the remainder of 3: 15 = 2*6 + 3. The quotient (2 in our case) is the greatest whole number of times a divisor (6 in our case) may be subtracted from a dividend (15) without the remainder becoming negative.
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Re: When the positive integer k is divided by the positive integ  [#permalink]

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03 Oct 2017, 09:30
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

We can create two remainder equations:

k/n = 81 + 2/10

k/n = 81 + 1/5

and

k/n = 81 + 11/n

Thus:

1/5 = 11/n

n = 55

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Re: When the positive integer k is divided by the positive integ &nbs [#permalink] 03 Oct 2017, 09:30
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