Was there a limit to the number of senators in the Roman Republic?

by BenAzlay

I have seen everywhere that the republican senate in ancient Rome was 300 men strong. But people entered the Senate by being elected quaestor. Considering that there was 20 quaestors elected each year, it means it took only fifteen years to fill 300 seats. As senators were elected quaestor in their thirties, it's not like older senators died out as fast as new senators came to replace them. So if there was a limit of 300, what did all the quaestors who could not make it do?

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