Find the how many two-digit numbers are divisible by 6? (CBSE 2011)

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

Here, First term = a = 12

Common difference d = 18 – 12 = 6,

Last term = a_n = 96

Since, n^th term is given by:

a_n = a + (n - 1)d

96 = 12 + (n – 1)6

96 – 12 = (n – 1)6

84 = 6n – 6

84 + 6 = 6n

90 = 6n

n = 15

There are 15 two-digit numbers divisible by 6.