Approximability of soluble groups of finite rank by certain classes of finite groups

For soluble groups of finite rank we obtain the necessary and sufficient condition to be a virtually residually finite $p$-group. We also prove that a soluble group $G$ of finite rank is residually $\pi$-finite for some finite set $\pi$ of primes if and only if it has no subgroups of type $Q$ and the torsion radical of $G$ is a finite group.