How Many Two-Digit Numbers are Divisible by 3

Answer: The foremost two-digit number in the number system that is divisible by 3 is 12.

99 is the last number that is divisible by 3, provided we’re only considering two-digit numbers.

In arithmetic progression, the numerical interval between two successive terms is constant. 

Hence, arithmetic progression = 12, 15, 18, 21 … 99

We can see that the first term (x) = 12

Common difference = 3

Let’s say the common difference as d.

If we assume that n numbers exist, then xn = 99

Or, x + (n-1) d = 99

⇒ 12 + 3(n-1) = 99

⇒ 12 – 3 + 3n = 99

⇒ n = 99 – (12 – 3) / 3

⇒ n = 30

Therefore 30 two digit figures can be divided by 3.