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In Harry Potter and the Philosopher's Stone, Hagrid says,
'Oh, well - I was at Hogwarts meself but I - er - got expelled, ter tell yeh the truth. In me third year. They snapped me wand in half an' everything. But Dumbledore let me stay on as gamekeeper. Great man, Dumbledore.'
Philosopher's Stone, Chapter 4
This presumably means that Hagrid continued as gamekeeper right after his expulsion. This is also supported by the fact that Hagrid, an orphan, had nowhere else to go. At another point, Harry, fearing expulsion, thinks
He thought of Hagrid, expelled but allowed to stay on as gamekeeper. Perhaps he could be Hagrid's assistant. His stomach twisted as he imagined it, watching Ron and Hermione becoming wizards while he stumped around the grounds carrying Hagrid's bag.
Philosopher's Stone, Chapter 9
This indicates indirectly that Harry assumed that Hagrid became gamekeeper right after his expulsion.
However, in HP4, we see Molly reminiscing about the previous gamekeeper, Ogg.
...And reminisced at length about the gamekeeper before Hagrid, a man called Ogg.
Goblet of Fire, Chapter 31
Since Hagrid was expelled fifty-two years before this incident, I wondered how old Mrs Weasley had to be, and calculated it to be more than sixty-five ( since Molly didn't know Voldemort's real name, either, she couldn't gave been his contemporary).
But surely this is absurd, as I've always pictured the Weasleys to be in their forties. Could someone please resolve this conundrum?