[150] How many 3 digit numbers are divisible by 6 in all ?

For Competitive Exams

How many 3 digit numbers are divisible by 6 in all ?

149

150

151

166

Explanation:

Required numbers are 102, 108, 114, ... , 996

This is an A.P. in which $ a $ = 102, $ d $ = 6 and $ l $ = 996

Let the number of terms be $ n $. Then,

$ a $ + $\left( n - 1\right)$ d = 996

$\Rightarrow$ 102 + $\left( n - 1\right)$ x 6 = 996

$\Rightarrow$ 6 x $\left( n - 1\right)$ = 894

$\Rightarrow$ $\left( n - 1\right)$ = 149

$\Rightarrow$ $ n $ = 150.

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