How many numbers of two digit are divisible by 3?

Question:

How many numbers of two digit are divisible by 3?

Solution:

The two digit numbers that are divisible by 3 are:

12, 15, 18...96, 99

This is an A.P. whose first term is 12 and the common difference is 3.

We have :

$a_{n}=99$

$\Rightarrow 12+(n-1) 3=99$

$\Rightarrow(n-1) 3=87$

$\Rightarrow(n-1)=29$

$\Rightarrow n=30$

Thus, there are 30 such terms.

 

 

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