When the positive integer k is divided by the positive integer n

Question

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

Bunuel · Accepted Answer

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} n = 55. Answer: C. Similar questions to practice: https://gmatclub.com/forum/when-positiv ... 06493.html https://gmatclub.com/forum/if-s-and-t-a ... 35190.html Theory on remainders problems: https://gmatclub.com/forum/remainders-144665.html Tips on Remainders: https://gmatclub.com/forum/remainders-t ... s#p1376126 Units digits, exponents, remainders problems: https://gmatclub.com/forum/new-units-di ... 68569.html All DS remainders problems to practice: https://gmatclub.com/forum/search.php?s ... tag_id=198 All PS remainders problems to practice: https://gmatclub.com/forum/search.php?s ... tag_id=199

minwoswoh · Answer

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!

pierferraro · Answer

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

Answer C

EMPOWERgmatRichC · Answer

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.

Final Answer:  C

GMAT assassins aren't born, they're made, 
Rich

pra1785 · Answer

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 ?

Bunuel · Answer

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.

JeffTargetTestPrep · Answer

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

Answer: C

davidbeckham · Answer

could someone please explain the logic behind writing 81.2 in form 81 + 0.2 or 81 + 1/5?

EMPOWERgmatRichC · Answer

Hi davidbeckham,

GMAT questions can almost always be solved in more than one way (including how you might choose to work through the 'math steps' involved). Sometimes 'converting' information from one format to another can make it easier for you to answer the given question (depending on how you like to "see" your math work).

Some of the explanations in this thread 'convert' 81.2 in the way that you describe, but that is NOT a necessary step to answering this question. Working in that way is just one option for dealing with the fact that both K and N must be INTEGERS and K/N has a remainder of 11.
 
GMAT assassins aren't born, they're made,
Rich

IanStewart · Answer

Everything you learn about remainders will be about integers, so you generally would always want to rewrite a question like this using integers instead of decimals. From the definition of a quotient and a remainder, then when we divide integer n by integer d,

n = qd + r

where integer q is the quotient, and integer r is the remainder. The remainder must be between 0 and d-1 inclusive, so r < d is always true. If you divide by d on both sides, you get

n/d = q + (r/d)

Since r < d, then r/d must be between 0 and 1. So when you divide n by d, the quotient q is the whole number part of the result, and r/d is the decimal or fractional part of the result. If we use that for this question (and I'm going to change the letters, because whoever designed this question did something profoundly annoying -- they're using "n" where "d" is normally used in a quotient/remainder definition, and using "k" where "n" would normally be used) :

When the positive integer n is divided by the positive integer d , the remainder is 11. If n/d = 81.2 , what is the value of d?

then 81 is the whole number part of the result, so is the quotient, and 0.2 = 1/5 is the decimal part of the result, so equals r/d. Since r = 11, and r/d = 1/5, we have 11/d = 1/5 and d = 55.

So if you replace 0.2 with a fraction of integers, and you know how to use the definition of a remainder, it's a one-line solution. It's true that you can solve this question in other ways, as the post above mine suggests, but if you're doing something like testing answers here, you're spending far more time on this question than you need to.

Nikhil30 · Answer

this question is not difficult but ya , a bit tricky to understand when you see this question at first. 
so ,
 K/N = 11 i.e. K= NQ+11
K/N =81.2= K=N*81+0.2 for example : 16/3= 3*5+1 
 now , 
K= 81N+11
81.2N=81N+11
N=55.

Basshead · Answer

We're told  \frac{k}{n} = 81.2

We can rewrite 81.2 as  81 \frac{1}{5}

That 1/5 represents a remainder of 11.

Therefore, 5/5 = 55.

Answer is C.

avigutman · Answer

Video solution from Quant Reasoning starts at 5:45: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=OyREEhNJcDY

BrenCraw · Answer

I don't understand how you Multiply the .2 out and why N has to be a multiple of 5? If you multiply the .2 out, are you not left with 81 which is NOT a multiple of 5? I understand every step after this point! I am not an assassin! lol

Bunuel · Answer

Because 0.2 = 1/5. For K = 81.2 * N to be an integer, N must cancel the denominator 5. That is why N has to be a multiple of 5. You are not “left with 81”, you are making the entire product an integer.

When the positive integer k is divided by the positive integer n

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When the positive integer k is divided by the positive integer n

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