A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13?

(UPSC CSAT – 2023)

1. 11
2. 9
3. 7
4. 1

Solution: Ans.(1.)

As we know 1001 = 7×11×13, 1001 is divisible by 13

1001×999 = 999999 (6 times 9s) is also divisible by 13

Therefore number formed by writing 96 (multiple of 6) times 9s is also divisible by 13

Now, when remaining 3 times 9s (999) is divided by 13, the remainder is 11.

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