Question

How many two-digit numbers are divisible by 6?

Answer 1

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

Clearly, these number are in AP.

Here, a = 12 and d = 18 – 12 = 6

Let this AP contain n terms. Then,

a_n = 96

⇒ 12 + (n – 1) × 6 = 96   ...[a_n = a + (n – 1)d]

⇒ 6n + 6 = 96 

⇒ 6n = 96 – 6 = 90 

⇒ n = 15 

Hence, these are 15 two-digit numbers divisible by 6.