In their seminal paper of 1923, Debye and Hückel provided the first appropriate description of the effect of ionic strength on the thermodynamic properties of dilute electrolyte solutions. This landmark work paved the way for what was later called the primitive model of electrolytes. At this level, an ionic solution is modeled as a collection of charged hard spheres in a dielectric continuum that manifests itself only through its dielectric constant. Numerical simulations have been reported in the literature for salts in a continuous solvent. In the present work, results obtained using various analytical theories are compared with Monte-Carlo (MC) simulation data (expected to be 'exact') taken from the literature, in the case of binary electrolytes in a continuous solvent mimicking water. The theories include the Debye-Hückel theory, the mean-spherical approximation (MSA), and the Pitzer approach. The MC data are about mean salt activity and osmotic coefficients, and also individual ion activity coefficients. Moreover, some remarks are made about the assumptions underlying the Debye-Hückel framework, and new formulas are derived for individual ion activity coefficients by following the method of Pitzer.