Which of the following number is divisible by 11?

Correct option is A

Given:

The numbers are 6589, 9164, 8962, and 4857.
Concept Used: A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or divisible by 11.
Solution:
For 6589:
Sum of digits at odd places (6 and 8) = 6 + 8 = 14
Sum of digits at even places (5 and 9) = 5 + 9 = 14
Difference = 14 - 14 = 0
Since 0 is divisible by 11, 6589 is divisible by 11.
For 9164:
Sum of digits at odd places (9 and 6) = 9 + 6 = 15
Sum of digits at even places (1 and 4) = 1 + 4 = 5
Difference = 15 - 5 = 10
Since 10 is not divisible by 11, 9164 is not divisible by 11.
For 8962:
Sum of digits at odd places (8 and 6) = 8 + 6 = 14
Sum of digits at even places (9 and 2) = 9 + 2 = 11
Difference = 14 - 11 = 3
Since 3 is not divisible by 11, 8962 is not divisible by 11.
For 4857:
Sum of digits at odd places (4 and 5) = 4 + 5 = 9
Sum of digits at even places (8 and 7) = 8 + 7 = 15
Difference = 9 - 15 = -6
The absolute difference, 6, is not divisible by 11, so 4857 is not divisible by 11 either.