Home Question How many two digit numbers are divisible by 3 ?

How many two digit numbers are divisible by 3 ?

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[Note: Two digit number are- 10, 11, 12, 13…………….98, 99]

Solution:

First two digit number divisible by 3 = 12

Last two digit number divisible by 3 = 99

An Arithmetic Progression is a progression in which the difference between two consecutive terms is constant.

A.P (Arithmetic Progression) = 12, 15, 18, 24…,99

Here,

First term (a) = 12

Common difference (d) = 3

Let us consider there are n numbers then-

an = 99

a + (n – 1)d = 99

12 + (n – 1)3 = 99

12 + 3n – 3 = 99

3n + 9 = 99

3n = 99-9

3n = 90

n = 90/3

n = 30

∴ Two digit numbers are divisible by 3 = 30.

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