Question

The total number of $4 -$ digit numbers whose greatest common divisor with $18$ is $3$ , ___

Answer 1

Let $N$ be the four digit number $\operatorname{gcd}( N , 18)=3$
Hence $N$ is an odd integer which is divisible by $3$ but not by $9$ .
$4$ digit odd multiples of 3 $1005,1011, \ldots \ldots, 9999 \rightarrow 1500$
$4$ digit odd multiples of 9 $1017,1035, \ldots \ldots, 9999 \rightarrow 500$
Hence number of such $N =1000$