Q42 of 178 Page 526

How many two - digit numbers are divisible by 6?

The two digit numbers divisible by 6 are 12, 18, 24, 30,…96.

This forms an AP with first term a = 12


and common difference = d = 6


Last term is 96.


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


96 = a + (n - 1)d


⇒ 96 = 12 + (n - 1)6


⇒ 96 - 12 = 6n - 6


⇒ 84 + 6 = 6n


⇒ 90 = 6n


⇒ n = 15


There are 15 two - digit numbers that are divisible by 6.


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