If the five-digit number $235xy$ is divisible by $3$, $7$ and $11$, then what is the value of $(x-y)$?

Since the number is divisible by $3,7,$ and $11$, it must be divisible by their lowest common multiple ($\text{LCM}$):
$$\text{LCM}(3,7,11)=3\times 7\times 11=231$$
Let the largest possible value of the five-digit number matching the pattern be $23599$.Dividing $23599$ by $231$:
$$23599÷231\approx 102.16$$
Now, multiply the integer quotient by 231 to find the correct number matching the prefix $235$:
$$\text{Number}=231\times 102=23562$$
Comparing $23562$ with $235xy$, we get:
$$x=6\text{and}y=2$$
Calculating the value of $(x-y)$:
$$x-y=6-2=4$$