Which of the following numbers is divisible by 11?

Concept Used:

To determine if a number is divisible by 11, you can use the following rule:

Starting from the rightmost digit, add every other digit (i.e. the ones in the odd positions)

and subtract the sum of the other digits (i.e. the ones in the even positions).
If the result is divisible by 11, then the original number is also divisible by 11.

Calculation:
-The rule for divisibility by 11 can be extended to larger numbers as well.

For example, let's take the number 2378965.

The sum of the digits in the odd positions is 2 + 7 + 9 + 5 = 23.

The sum of the digits in the even positions is 3 + 8 + 6 = 17.

The difference between these sums is 23 - 17 = 6,

which is not a multiple of 11. Therefore, 2378965 is not divisible by 11.
However, for the number 6598321,

- the sum of the digits in the odd positions is 6 + 9 + 3 + 1 = 19.

The sum of the digits in the even positions is 5 + 8 + 2 = 15.

The difference between these sums is 19 - 15 = 4, which is not a multiple of 11.

Therefore, 6598321 is not divisible by 11.

-let's take the number 5648741.

The sum of the digits in the odd positions is 5 + 4 + 7 + 1 = 17.

The sum of the digits in the even positions is 6 + 8 + 4 = 18.

The difference between these sums is 18 - 17 = 1,

which is not a multiple of 11.

Therefore, 5648741 is not divisible by 11.

Let's apply this rule to the number 5214341:

The sum of the digits at odd places is 5 + 1 + 3 + 1 = 10.
The sum of the digits at even places is 2 + 4 + 4 = 10.
The difference between the sum of the digits at odd places and the sum of the digits at even places is 10 - 10 = 0.
Since the difference between the sums is 0, we can conclude that 5214341 is divisible by 11.

Therefore, Option 1 is correct.