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Which of the following is divisible by 99?
1. 2776149
2. 2767149
3. 2767419
4. 2776419

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Correct Answer - Option 2 : 2767149

Concept:

To check the divisibility of a number by 99, we need to check if that number is divisible by 9 and 11.

Divisibility by 9:

If the sum of the digits of the given number is divisible by 9, then that number is divisible by 9.

Eg. 756 is divisible by 9 because the sum of digits of 756 = 7 + 5 + 6 = 18 is divisible by 9.

Divisibility by 11:

If the difference between "Sum of digits at the even place" and "Sum of digits at odd place" is divisible by 11 or it is 0, then the whole number is divisible by 11.

Such as, 9174.

(9 + 7) - (4 + 1) = 16 - 5 = 11 is divisible by 11. So, 9174 is also divisible by 11.

Calculation:

By checking through options,

Number 2767149 is divisible by both 9 and 11.

Sum of digits of 2767149 

= 2 + 7 + 6 + 7 + 1 + 4 + 9 = 36 which is divisible by 9.

∴ 2767149 is divisible by 9.

(Sum of digits at even place) - (Sum of digits at odd place) = (7 + 7 + 4) - (2 + 6 + 1 + 9)

= 18 - 18

= 0

∴ 2767149 is also divisible by 11.

∵ 2767149 is divisible by both 9 and 11.

∴ 2767149 is divisible by 99.

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