The number 611611611611 is: (a)divisible by both 6 and 11 (b)neither divisible by 6 nor by 11 (c)divisible by 6 only (d)divisible by 11 only

Given:

The number is 611611611611.

Formula used:

Divisibility Rules:

1. A number is divisible by 6 if it is divisible by both 2 and 3.

2. A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11.

Calculation:

Check for divisibility by 6:

1. Divisibility by 2: The last digit is 1, which is not even. Hence, 611611611611 is not divisible by 2.

2. Divisibility by 3: Sum of the digits = 6 + 1 + 1 + 6 + 1 + 1 + 6 + 1 + 1 + 6 + 1 + 1 = 32. Since 32 is not divisible by 3, 611611611611 is not divisible by 3.

Since the number is not divisible by both 2 and 3, it is not divisible by 6.

Check for divisibility by 11:

Sum of digits in odd positions = 6 + 1 + 1 + 6 + 1 + 1 = 16

Sum of digits in even positions = 1 + 6 + 1 + 1 + 6 + 1 = 16

Difference = 16 - 16 = 0

Since the difference is 0, 611611611611 is divisible by 11.

⇒ 611611611611 is divisible by 11 only.

∴ The correct answer is option (3).