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The solvable Farb growth of a group quantifies how well-approximated thegroup is by its finite solvable quotients. In this note we present a newcharacterization of polycyclic groups which are virtually nilpotent. That is,we show that a group has solvable Farb growth which is at most polynomial in$\log(n)$ if and only if the group is polycyclic and virtually nilpotent. Wealso give new results concerning approximating oriented surface groups bynilpotent quotients. As a consequence of this, we prove that a natural number$C$ exists so that any nontrivial element of the $Ck$th term of the lowercentral series of a finitely generated oriented surface group must have wordlength at least $k$. Here $C$ depends only on the choice of generating set.Finally, we give some results giving new lower bounds for the solvable Farbgrowth of some metabelian groups (including the Lamplighter groups).

Approximating a group by its solvable quotients