B1. The sum of four fractions is less than 1. Three of these fractions are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{10}$. The fourth fraction is $\frac{1}{n}$, where $n$ is a positive integer. What values could $n$ take?
Solution
We are given that $\frac{1}{2}+\frac{1}{3}+\frac{1}{10}+\frac{1}{n}<1$. Therefore $\frac{15+10+3}{30}+\frac{1}{n}<1$. Hence $\frac{28}{30}+\frac{1}{n}<1$. So $\frac{1}{n}<\frac{1}{15}$. Therefore $n$ could be any positive integer greater than 15 .