Question

Which of the following numbers is divisible by 99?

• A. 913462
• B. 114345
• C. 135792
• D. 3572406

Answer 1

The correct option is B

114345

99 = 9 $\times$ 11
In order to check the divisibility by 99, the divisibility by 9 and 11 are to be checked.

913462 is not divisible by 9 since the sum of digits is 25 which is not a multiple of 9.

135792 is divisible by 9 since the sum of digits is 27 which is a multiple of 9.
The sum of digits at odd places is
1 + 5 + 9 = 15
The sum of digits at even places is 3 + 7 + 2 = 12
Difference = 15 - 12 = 3 which is not 0 or the multiple of 11.

3572406 is divisible by 9 since the sum of digits is 27 which is a multiple of 9.
The sum of digits at odd places is 3 + 7 + 4 + 6 = 20
The sum of digits at even places is 5 + 2 + 0 = 7
Difference = 20 – 7 = 13 which is not equal to 0 or the multiple of 11. Therefore, the number 3572406 is not divisible by 11.

114345 is divisible by 9 since the sum of its digits is 18.
The sum of digits at odd places is 1 + 4 + 4 = 9
The sum of digits at even places is 1 + 3 + 5 = 9
Difference = 9 - 9 = 0. So, 114345 is divisible by 11.