Question

What will be the remainder when 1212121212... (repeated 300 times) is divided by 99?

a. 18
b. 81
c. 54
d. 36

Answer 1

The remainder when 1212121212... (repeated 300 times) is divided by 99 is 18. Therefore, the correct option is: a. 18

Let's break down the solution step by step:

1. Express the repeating pattern 1212121212... (repeated 300 times) as (9N), where N is the quotient obtained when divided by 9.

1212121212... (300 times) = 9N

2. Recognize that N is divisible by 11.

13468013468...(repeated 50 times) = 11
`*` Q + 2

Here, Q represents the quotient.

3. Determine the remainder when 13468013468... (repeated 50 times) is divided by 11. Using the divisibility rule of 11 from the right-hand side, the remainder is found to be 2.

4. Multiply the remainder by 9 (as in the original expression 9N\.

`\[ 2 * 9 = 18 \]`

Therefore, the remainder when 1212121212... (repeated 300 times) is divided by 99 is 18.