Question

How many two digit numbers are divisible by 3?

Answer 1

Two digits numbers divisible by 3 are
12, 15, 18, 21, …, 99
Here, a = 13, d = 15 – 12 = 3 and l = 99
Let number divisible by 3 and n
∴ T_n = l = a + (n – 1)d
99 = 12 + (n – 1) x 3
⇒ 99 – 12 = 3(n – 1)
⇒ 3(n –1) = 87
⇒ n – 1 = `(87)/(3)` = 29
∴ n = 29 + 1
= 30.