Question : If 7 divides the integer n, then the remainder is 2. What will be the remainder if 9n is divided by 7?
Option 1: 3
Option 2: 5
Option 3: 1
Option 4: 4
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Correct Answer: 4
Solution :
Let $x$ be the quotient when n is divided by 7.
$n = 7x+2$
When $9n$ is divided by $7$,
$\frac{9n}{7} =\frac{9(7x+2)}{7} = \frac{63x+18}{7} = (9x+2)+\frac{4}{7}$
So, the remainder when $9n$ is divided by $7$ is $4$.
Hence, the correct answer is 4.
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