Which of the following numbers is divisible by 99 ?

Key idea: A number is divisible by 99 if and only if it is divisible by both 9 and 11.

Divisibility rules used:

• Divisible by 9: the sum of the digits is divisible by 9.

• Divisible by 11: the difference between the sum of digits in odd positions and the sum in even positions (counting from the right) is a multiple of 11 (including 0).

Check each given number:

• 3572406: Sum of digits = 3+5+7+2+4+0+6 = 27 → divisible by 9. Alternating-position difference = (6+4+7+3) − (0+2+5) = 20 − 7 = 13 → not a multiple of 11. Therefore not divisible by 99.

• 913462: Sum of digits = 9+1+3+4+6+2 = 25 → not divisible by 9. Therefore not divisible by 99.

• 135792: Sum of digits = 1+3+5+7+9+2 = 27 → divisible by 9. Alternating-position difference = (2+7+3) − (9+5+1) = 12 − 15 = −3 → not a multiple of 11. Therefore not divisible by 99.

• 114345: Sum of digits = 1+1+4+3+4+5 = 18 → divisible by 9. Alternating-position difference = (5+3+1) − (4+4+1) = 9 − 9 = 0 → a multiple of 11. Therefore divisible by both 9 and 11, so divisible by 99.

Conclusion: 114345 is divisible by 99.