The condition of validity of the direct-interaction approximation and the Reynolds-number reversed expansion truncated at the lowest nontrivial order is assessed numerically for a dynamical system composed of coupled equations of many variables with quadratic-nonlinear terms of weak or strong coupling as well as linear-viscous and randomly forcing terms. Although these two theories lead to an identical set of integro-differential equations for the correlation function of the dependent variables and the response function, their parameter regions of validity are different from each other. The procedure of the direct-interaction approximation is valid for larger number of degrees of freedom if the nonlinear couplings are as weak as the Navier-Stokes equation, but not when the nonlinear coupling is strong. The Reynolds-number reversed expansion, on the other hand, is justified whenever the nonlinear term is smaller in magnitude than the other terms irrespective of the strength of the nonlinear coupling.