Question

How many natural numbers are there between 23 and 100 which are exactly divisible by 6?
(a) 13
(b) 12
(c) 11
(d) 16

Answer 1

(a) 13

The required numbers are 24, 30, 36, 42, ..., 96.
This is an AP in which a = 24, d = (30 - 24) = 6.
Let the number of terms be n.
Then T_n = 96
⇒ a + (n - 1)d = 96
⇒ 24 + (n -1) ⨯ ​6 = 96
⇒ 6n = 78
⇒ n = 13

Hence, 13 numbers which are exactly divisible by 6 lie in between 23 and 100.