JBMO-SL 2006 Problem 3

Let $n\ge 3$ be a natural number. A set of real numbers $\{x_1,x_2,\ldots,x_n\}$ is called summable if $\sum_{i=1}^n \frac{1}{x_i}=1$ . Prove that for every $n\ge 3$ there always exists a summable set which consists of $n$ elements such that the biggest element is: a) bigger than $2^{2n-2}$ b) smaller than $n^2$