How many two - digit numbers are divisible by 6?

Question

Philoid · Accepted Answer

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.