What's the meaning of "I'll drop by there on my way to class today"?
Well, I know there's an apartment complex around the corner that seems to have a few vacancies. I'll drop by there on my way to class today

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Before I go to my class I will stop at the apartment complex, then I will go to class. 
It implies that the apartment complex is along the route to school.

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It just means, "i will come by"

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It means I will go there first before I go to class today.