When the positive integer k is divided by the positive integ

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:

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

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

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

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.

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.

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.

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.

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 ?

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

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

Partly a bit of fun. Hope it helps someone out there! This tutor is going old-school for this! (Gosh, his writing is terrible すみません!) *technically this topic was done yesterday - It's now past midnight where I am!

https://ibb.co/2K4Pckp

Video solution from Quant Reasoning starts at 5:45:
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basshead How did you get 5/5 is 55? I got the 1/5 is 11, but how the 5/5? I'm a bit lost & slow lol

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