Linda wrote down a natural number. When she divided the number by $$7$$, the remainder was $$5$$. What is the remainder when twice that number is divided by $$7$$? ． 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder 
The remainder of $$A$$ $$\div7$$ is $$5$$, and $$2A=A+A$$. Therefore the remainder of $$2A\div7$$ is $$5+5=10$$. $$10= 7+3$$, therefore the remainder is $$3$$. 