Exact solutions for the scattering of a fast projectile x on deuterium are compared with various versions of the fixed scatterers approximation. The content of the approximations for a nucleon and a different projectile is discussed. The calculations show the approximate agreement of angular distributions in forward direction and the amount of disagreement in the backward hemisphere. In the case of nucleon scattering the importance of nucleon exchange, neglected in the FSA, is explicitly demonstrated. As expected, the quality of the tested approximations rapidly improves with diminishing mass ratio Mx/MN.