Dividing a certain two$$-$$digit number by $$7$$ leaves a remainder of $$5$$; dividing it by $$11$$ leaves a remainder of $$9$$. What is the smallest possible value of this number? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders
The number when added by $$2$$ is divisible by $$7$$ and by $$11$$. Hence, the smallest value is $$7\times 11-2=75$$. 