  Inspired by the newly observed three resonances X(1835), X(2120) and X(2370),
in this work we systematically study the two-body strong decays and double pion
decays of $\eta(1295)/\eta(1475)$, $\eta(1760)/X(1835)$ and $X(2120)/X(2370)$
by categorizing $\eta(1295)/\eta(1475)$, $\eta(1760)/X(1835)$, X(2120) and
X(2370) as the radial excitations of $\eta(548)/\eta^\prime(958)$. Our
numerical results indicate the followings: (1) The obtained theoretical strong
decay widths of three pseudoscalar states $\eta(1295)$, $\eta(1475)$ and
$\eta(1760)$ are consistent with the experimental measurements; (2) X(1835)
could be the second radial excitation of $\eta^\prime(958)$; (3) X(2120) and
X(2370) can be explained as the third and fourth radial excitations of
$\eta(548)/\eta^\prime(958)$, respectively.
