Until the second century B.C.E., Roman classes were defined according to
c.male initiative and actions
d.a civic lottery
Until the second century AD, in Rome is was the male lineage that established social class and status.
You have a gaytard teacher if they are using the BCE nomenclature.
I believe it's
c. Male initiative and actions.
The problem with this answer is slaves - could sometimes buy their freedom from their master or the master could free them (for his own reasons).
This however was probably not the case for the vast majority of slaves, so if you consider 'Slaves' as a class, they were born into slavery and very rarely could they exit it, so the answer would be a)
If you're talking about the two general classes: Patricians and Plebeians, the answer could be c) but you should still check my answer in google or with others.
Patricians were basically like noblemen and were the rich of society - Plebeians were those who were middle-class to poor but they were free citizens.
Plebeians in the late years of the Republic could be found in the Senate and could be very rich.
The problem here is what your question really means. A Plebeian could never become a Patrician but they had the same opportunities and many Plebeians became Senators, wealthy land owners and rich families.
I'm not sure about the dates so I would suggest verifying what I've said so that I'm not wrong.
Just to clear this one up ...
a. Roman classes were defined by male lineage.
Patricians (noblemen) belonged to a particular 'gens', something between a family and a clan (Julius Caesar belonged to the 'gens Julia', which traced its ancestry to Trojan nobility, or thought it did).
Plebeians were born plebeians and remained that way.
For a fuller picture, feel free to check out: