GMAT Practice Question: When the positive integer k is divided by the positive integer n, the remainder is 11 . If...
Question
When the positive integer k is divided by the positive integer n, the remainder is 11 . If \frac{k}{n}= 81.2 , what is the value of n ?
- 9
- 20
- 55
- 70
- 81
Topics: divisibility, remainders, decimals
Solution
Step 1
We translate the statement about the remainder when k is divided by n into an equation using a quotient q and remainder r.
k = n \times q + 11
Step 2
We interpret the decimal result of the division to identify its integer part (the quotient) and fractional part (the remainder over the divisor).
\frac{k}{n} = 81.2 = 81 + 0.2
Step 3
We convert the fractional part 0.2 into a common fraction. This will match the form remainder over divisor.
0.2 = \frac{2}{10} = \frac{1}{5}
Step 4
We set the fraction representing the remainder over the divisor equal to \frac{1}{5} and solve for n.
\frac{11}{n} = \frac{1}{5} n = 11 \times 5 = 55
Answer
55
