Question

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

Answer 1

Answer: 1000

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