Which of the following is exactly divisible by 11?

To determine if a number is exactly divisible by 11, we use the alternating sum of digits rule: subtract the sum of the digits in even positions from the sum of the digits in odd positions. If the result is 0 or a multiple of 11, the number is divisible by 11.

Step-by-Step Analysis
Let's apply this rule to each option:

Option 1: 456121

Sum of digits in odd positions (1st, 3rd, 5th from right): 1 + 1 + 5 = 7

Sum of digits in even positions (2nd, 4th, 6th from right): 2 + 6 + 4 = 12

Difference: 12 - 7 = 5. (Not divisible by 11)

Option 2: 466131

Sum of odd positions: 1 + 1 + 6 = 8

Sum of even positions: 3 + 6 + 4 = 13

Difference: 13 - 8 = 5. (Not divisible by 11)

Option 3: 415624

Sum of odd positions: 4 + 6 + 1 = 11

Sum of even positions: 2 + 5 + 4 = 11

Difference: 11 - 11 = 0. (Divisible by 11)

Option 4: 121021

Sum of odd positions: 1 + 0 + 2 = 3

Sum of even positions: 2 + 1 + 1 = 4

Difference: 4 - 3 = 1. (Not divisible by 11)