1) Federico has a collection of toy soldiers; he knows he has a bit less than 100, but certainly at least 30. He arranges them in rows of 7 and has one soldier left over; then he arranges them in rows of 10 and this time has 2 soldiers left over. How many soldiers does he have in total $\begin{array}{lllll}\text { (A) } 32 & \text { (B) } 50 & \text { (C) } 62 & \text { (D) } 71 & \text { (E) } 92\end{array}$
## 1. The answer is $\mathbf{( E )}$.

The number $n$ of toy soldiers Alberto has is a two-digit number, between 30 and 99. Since arranging the soldiers in rows of 10 leaves two left over, the units digit of $n$ is 2. Since arranging them in rows of 7 leaves 1 left over, $n$ is of the form $7k + 1$, where $k$ is a natural number. The only number between 30 and 99 of this form that ends in 2 is 92.

[Problem proposed by S. Monica]