Question

By which number is ${10}^{1000}-1$ divisible?

• A. 9
• B. 3
• C. 11
• D. 6

Answer 1

Answer: (A), (B), (C)

The correct options are
A 9
B 3
C 11

${10}^{1000}-1$ = 999 .... 999 (1000 times)

The digits in all places are 9.
Hence, it is divisible by 3 and 9.
There are 1000 digits and their sum of digits in odd places and sum digits even places are same. Their difference is 0.
Hence, it is divisible by 11.