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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.
