1. In one lyceum, $76 \%$ of the students have at least once not done their homework, and $\frac{5}{37}$ sometimes forget their second pair of shoes. Find the number of students in the lyceum, if it is more than 1000 but less than 2000.
Solution. Since $76 \%=\frac{76}{100}=\frac{19}{25}$, and the numbers 25 and 37 are coprime, the number of students is a multiple of $25 \cdot 37$, i.e., $925 \mathrm{k}$, where k is a natural number. Since $1000<925 k<2000$, then $\mathrm{k}=2$, and the number of students $925 \cdot 2$ $=1850$.

Answer. 1850

Recommendations for checking. Only the correct answer - 0 points. Answer with verification - 1 point. If there is no reference to the coprimality of the numbers 25 and 37, deduct 1 point. Computational errors - deduct no less than 2 points (depending on the impact on the solution).