The main results of this paper are: (1) There exist quasi-isometric groups \(G\) and \(H\) such that \(G\) is solvable but \(H\) is not virtually solvable. (2) There exist quasi-isometric groups \(G\) and \(H\) such that \(G\) has no torsion but no subgroup of finite index in \(H\) is torsion-free. This shows that virtual solvability and the property of being virtually torsion-free are not geometric properties.