GMAT Divisibility: If k/n= 81.2, what is the value of n?

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 ?

divisibilityremaindersdecimals

Explanation	Calculations	Help
$We translate the statement about the remainder when k is divided by n into an equation using a quotient q and remainder r .$	$k = n \times q + 11$
$We interpret the decimal result of the division to identify its integer part (the quotient) and fractional part (the remainder over the divisor).$	$\frac{k}{n} = 81.2 = 81 + 0.2$
$We convert the fractional part into a common fraction. This will match the form remainder over divisor.$	$0.2 = \frac{2}{10} = \frac{1}{5}$
$We set the fraction representing the remainder over the divisor equal to and solve for .$	$\frac{11}{n} = \frac{1}{5} n = 11 \times 5 = 55$

55 (C)

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