  Let $G$ be a finite group and $\psi(G) = \sum_{g \in G} o(g)$, where $o(g)$
denotes the order of $g \in G$. In [M. Herzog, et. al., Two new criteria for
solvability of finite groups, J. Algebra, 2018], the authors put forward the
following conjecture: \textbf{Conjecture.} \textit{If $G$ is a group of order
$n$ and $\psi(G)>211\psi(C_n)/1617 $, where $C_n$ is the cyclic group of order
$n$, then $G$ is solvable.} In this paper we prove the validity of this
conjecture.
