When the positive integer K is divided by 18, the remainder is 9. What is the remainder when K is divided by 6?

Correct option is B

Given:

When the positive integer K is divided by 18, the remainder is 9.
We are asked to find the remainder when K is divided by 6.

Solution:

From the given information:

K = 18n + 9    , 

Where n = 1,2,3....

This means that when K is divided by 18, the quotient is n, and the remainder is 9.

Now, divide K = 18n + 9 by 6:

K = 18n + 9 = 6(3n) + 9

We can see that 18n is divisible by 6 (since 18 is a multiple of 6), so we are left with the term 9. Now, divide 9 by 6:

9 ÷ 6 = 1 remainder 3

The remainder when K is divided by 6 is 3.