Find a whole number between $100$ and $200$ that has the following properties.  When the number is divided by $3$, the remainder is $1$.  When the number is divided by $4$, the remainder is $1$.  When the number is divided by $5$, the remainder is $1$.  When the number is divided by $7$, the remainder is $2$. 
Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules