Question

The number 311311311311311311311 is

• A. divisible by 3 but not by 11
• B. divisible by 11 but not by 3
• C. divisible by both 3 and 11
• D. neither divisible by 3 nor by 11

Answer 1

The Correct Option is D

To determine whether the number 311311311311311311311 is divisible by 3 or 11, we apply the rules of divisibility for each number.

Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. 

Let's calculate the sum:

Digit	3	1	1	3	1	1	3	1	1	3	1	1	3	1	1	3	1	1
Sum	60

The sum of the digits is 60, which is divisible by 3. Therefore, the number is divisible by 3.

Divisibility by 11: A number is divisible by 11 if the difference between the sum of its digits at odd positions and the sum of its digits at even positions is divisible by 11.

Odd Positions	3	1	3	3	3	3	3	1 (Sum: 18)
Even Positions	1	1	1	1	1	1	1 (Sum: 9)

Difference = 18 - 9 = 9, which is not divisible by 11. Therefore, the number is not divisible by 11.

Conclusion: The number 311311311311311311311 is divisible by 3 but not by 11, making the correct assertion that it is neither divisible by 3 nor by 11 incorrect based on the original statement. Apologies for any confusion; the correct conclusion is that it is divisible by 3 but not by 11 based on our calculation, despite the initial statement suggesting otherwise.