A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13?
- A11Correct
- B9
- C7
- D1
Explanation
To solve this, we first look for a pattern in the remainders when a sequence of 9s is divided by 13.
When we divide 999,999 by 13, the remainder is 0. This means any block of six 9s is exactly divisible by 13.
The number N consists of 99 nines. Since 96 is the largest multiple of 6 less than 99, we can divide the 99 nines into 16 groups of six nines each, leaving three nines remaining at the end.
The 16 groups of six nines will all give a remainder of 0 when divided by 13. Therefore, the remainder of the entire number N is the same as the remainder of the last three digits, which are 999.
Dividing 999 by 13: 999 divided by 13 equals 76 with a remainder of 11.
Thus, the remainder is 11. The correct option is A.
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