The number 311311311311311311311 is

By looking into the option, we can see that we only need to check the divisibility of the given number by 3 and 11.

Divisibility test by 3 : The given number, 311311311311311311311 has seven 3s and fourteen 1s.

So, the sum of the digits in the number= (7*3)+(14*1)= 21+14=35.

Since, 35 is not divisible by 3, the given number is not divisible by 3.

Divisibility test by 11: The sum of digits at odd places= (1+3+1+1+3+1+1+3+1+1+3)= 19

The sum of digits at even places= Sum of all the digits- Sum of digits at odd places= 35-19= 16.

Since, the difference between the the sum of digits at odd places and the sum of digits at even places, i.e. 19-16 is not a multiple of 11.

So, the given number is also not divisible by 11.

Hence, option D