2025 HSC Chemistry, Question 29.
This is another badly drafted question. The examiners left out one key fact - was the argon added under isothermal conditions or adiabatic conditions? That is why you are all speculating about Avogadro' Law of gases and Gay Lussac's Law and all that other stuff. It's good that you are asking these questions because it shows you have extensive knowledge of Chemistry.
The addition of argon to the reaction vessel of fixed volume causes no change to the K value and no change to position of equilibrium. The concentrations of the NO2 and N2O4 are not changed by the addition of argon. We should use their partial pressures as a measure of their concentrations, and the partial pressures remain the same so the concentrations are the same. Therefore provided the argon is added under isothermal conditions (not adiabatic conditions) there will be no change of temperature.