Question

How many numbers of two digits are divisible by 3

Answer 1

Lowest two digit number divisible by 3 is 12 Highest two digit number divisible by 3 We know that 99/3 = 33 ∴ Highest two digit number divisible by 3 is 99 So the series starts with 12 and ends with 99. Difference between numbers is 3..

Answer 2

Let two digit numbers are 10, 11, 12 , -------------99

which are divisible by 3 are 12, 15 ...............,99.

Here a = 12 and common difference = 3 , an = l = 99

nth term (tn) = a + ( n - 1) d

⇒ 99 = 12 + ( n - 1) 3

⇒ (n - 1)3 = 99 - 12 = 87

⇒ ( n -1) = 87 / 3

⇒ n - 1 = 29

∴ n = 30

∴ 30 two digit numbers which are divisible by 3.