Estudié mucho, de modo que pude aprobar el examen.

[morbrorper]

English Sentence

I studied hard so that I could pass the examination.

I think it ought to be pudiera, as the English could be rewritten as "…, in order to pass…”.

[Adrianxu]

I think the best translation for the spanish phrase is:
“I studied a lot, so(that’s why) I managed to pass the examination.”

@morbrorper

I think it ought to be pudiera

You are right.
For the translation CM gives :
“I studied hard so that I could pass the examination.”
Estudié mucho, de modo que pudiera aprobar el examen.
Estudié mucho para aprobar el examen.