Q43 of 178 Page 526

How many two - digit numbers are divisible by 3?

The two digit numbers divisible by 3 are 12, 15, 18, 21, …., 99.

This forms an AP with first term a = 12


and common difference = d = 3


Last term is 99.


Now, number of terms in this AP are given as:


99 = a + (n - 1)d


⇒ 99 = 12 + (n - 1)3


⇒ 99 - 12 = 3n - 3


⇒ 87 + 3 = 3n


⇒ 90 = 3n


⇒ n = 30


There are 30 two - digit numbers that are divisible by 3.


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