Let k be a positive integer with the following property: For every subset A of \{1,2, \ldots, 25\} with |A|=k, we can find distinct elements x and y of A such that \frac{2}{3} \leq \frac{x}{y} \leq \frac{3}{2}. Find the smallest possible value of k.
Let k be a positive integer with the following property: For every subset A of \{1,2, \ldots, 25\} with |A|=k, we can find distinct elements x and y of A such that \frac{2}{3} \leq \frac{x}{y} \leq \frac{3}{2}. Find the smallest possible value of k.