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

The answer is C.

Hi mgm,

Ceilidh has shown an algebraic solution to this question. Here's a solution that's based more 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

mgm 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

Answer: C