Need help with bash. What is wrong in this code?

Question

bash

k=$(cat $1 | wc -l)
if (($k<10) && ($k>1)); then
 echo $1
fi

What is wrong in this code? It doesn't work, which is very strange for me.
It should display text file names that have more than one line of text and less than 10.

Answer 1

k=$(cat $1 | wc -l)

if [ $k -lt 10 ] && [ $k -gt 1 ]
then
 echo $1
fi

Answer 2

as option
#! /bin/bash
k=$(cat $1 | wc -l)
if (( $k > 1 && $k < 10 )); then
echo $1
fi