Which of the following is divisible by 11?
1011011
1111111
22222222
3333333
Divisibility rule for 11 (simple):
Find the difference between:
• sum of digits in odd places
• sum of digits in even places
If this difference is \(0\) or a multiple of \(11\), the number is divisible by \(11\).
Check each option.
A) 1011011
Odd places digits: \(1,1,0,1\)
Odd sum: \(1+1+0+1 = 3\)
Even places digits: \(0,1,1\)
Even sum: \(0+1+1 = 2\)
Difference: \(3 - 2 = 1\) → not \(0\) or a multiple of \(11\). Not divisible.
B) 1111111
Odd places digits: \(1,1,1,1\)
Odd sum: \(1+1+1+1 = 4\)
Even places digits: \(1,1,1\)
Even sum: \(1+1+1 = 3\)
Difference: \(4 - 3 = 1\) → not \(0\) or a multiple of \(11\). Not divisible.
C) 22222222
Odd places digits: \(2,2,2,2\)
Odd sum: \(2+2+2+2 = 8\)
Even places digits: \(2,2,2,2\)
Even sum: \(2+2+2+2 = 8\)
Difference: \(8 - 8 = 0\) → this is \(0\). So it is divisible by \(11\).
D) 3333333
Odd places digits: \(3,3,3,3\)
Odd sum: \(3+3+3+3 = 12\)
Even places digits: \(3,3,3\)
Even sum: \(3+3+3 = 9\)
Difference: \(12 - 9 = 3\) → not \(0\) or a multiple of \(11\). Not divisible.
Answer: Option C (22222222).