Why do we have to find Q to see if its soluble or not if we have a solubility list?

In the very beginning of chemistry, you learned that some things are soluble and other things are insoluble. For example, in the old days, AgCl was insoluble and NaCl was soluble. BaSO4 was insoluble and Na2SO4 was soluble. Now you are learning that AgCl and BaSO4 are very slightly soluble. In particular, if [Ag+] x [Cl-] exceeds the solubility product constant (Ksp), then you get a precipitate. If not, not.