1. When one of two integers was increased 1996 times, and the other was reduced 96 times, their sum did not change. What can their quotient be
Solution. Let the first number be x, and the second y. Then the equation $1996 x+\frac{y}{96}=x+y$ must hold, from which we find that 2016x=y. Therefore, their quotient is 2016 or $\frac{1}{2016}$.

Answer: 2016 or $\frac{1}{2016}$.

Criteria: Full solution - 7 points; correct answer without solution 1 point.