Question

How many 3-digit numbers are completely divisible by $6$?

• A. $149$
• B. $150$
• C. $151$
• D. $166$

Answer 1

The correct option is B $150$

3-digit number divisible by $6$ are: $102,108,114,.....996$
This is an A.P. in which $a=102,d=6,l=996$
Let the number of terms be $n$. Then $t_n=996$
$\therefore$ $a+(n-1)d=996$
$\Rightarrow$ $102+(n-1)\times 6=996$
$\Rightarrow$ $6\times (n-1)=894$
$\Rightarrow$ $(n-1)=149$
$\Rightarrow$ $n=150$
$\therefore$ Number of terms $=150$