Which of the following numbers is divisible by 99

For a number to be divisible by 99 it should be divisible by both 11 and 9.

Option (a) ⇒ Divisibility by 9: sum of digits = 9 + 1 + 3 + 4 + 6 + 2 = 25 and we know that 25 is not divisible by 9. Therefore the number 913462 is not divisible by 9. Hence it is not divisible by 99.

Option (b) ⇒ Divisibility by 9: sum of digits = 1 + 1 + 4 + 3 + 4 + 5 = 18. And 18 is divisible by 9 .Hence the number 114345 is divisible by 9.

Divisibility by 11 : difference of the sum of alternate digits = (1 + 4 + 4) – (1 + 3 + 5) = 9 – 9 = 0 .And 0 is multiple of 11 (11 x 0 = 0) .Therefore the number 114345 is divisible by 11

Since the number is divisible by both 11 and 9

∴ The number is divisible by 99.

Option (c) ⇒ Divisibility by 9: sum of digits = 1 + 3 + 5 + 7 + 9 + 2 = 27. And 27 is divisible by 9 .Hence the number 114345 is divisible by 9.

Divisibility by 11 : difference of the sum of alternate digits = (1 + 5 + 9) – (3 + 7 + 2) = 15-12 = 3. And 3 is not a multiple of 11.Therefore the number 114345 is not divisible by 11.

∴ the number 135792 is not divisible by 99.

Option (d) ⇒ Divisibility by 9: sum of digits = 3 + 5 + 7 + 2 + 4 + 0 + 6 = 27. And 27 is divisible by 9 .Hence the number 114345 is divisible by 9.

Divisibility by 11 : difference of the sum of alternate digits = (3 + 7 + 4 + 6) – (5 + 2 + 0) = 20-7 = 13. And 13 is not a multiple of 11.Therefore the number 114345 is not divisible by 11.

∴ the number 3572406is not divisible by 99.