Question

The number of all-digit numbers divisible by 6 is

(a) 12
(b) 15
(c) 16
(d) 18

Answer 1

(b) 15
All 2 − digit numbers divisible by 6, are
12, 18, 24, 30........96
This is an AP, in which a = 12, d = (18 − 12) = 6 and l = 96
Let the number of these terms be n.
Then, T_n = 96
⇒ a + (n − 1)d = 96
⇒ 12 + (n − 1) × 6 = 96
⇒ (n − 1) × 6 = 84
⇒ (n − 1) = 14 ⇒ n = 15