Question

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

Answer 1

Since, required number has G.C.D with $18$ as $3$. It must odd multiple of '$3$' but not a multiple of '$9$'
$\left(i\right)$ Now, $4$-digit number which are odd multiple of '$3$' are,
$1005,1011,1017,...,9999\to 1499$
$\left(ii\right)4$-digit number which are odd multiple of $9$ are,
$1017,1035,...,9999\to 499$
$\therefore$ Required numbers $=1499-499=1000$