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You can look at the units that are given in the problem! If they give you mol/L (molarity) then you will use concentration to find K but if they give you torr, atmospheres (atm), or bar, then you will use partial pressure.
If the problems ask for Kc or Kp, that gives a pretty clear indication of what is desired. If they just ask for K, look at the units that they give. There is a good chance that you can figure out what they are asking for based on if the amounts given to you are in mol/L, atm, bar, etc. Also, the chemical equation itself could provide an extra suggestion (ex: all but one of the reactants and products in a reaction are gases, so converting the one non-gas's concentration to partial pressures would make sense, or the same situation but the reactants and products are mainly in aqueous solution).
It usually depends on the units that are given. If the reactants and products are all gases, then Kp can be used. However, it still may be easier to first calculate Kc because the question may provide numbers in terms of moles and liters.
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