"We are studying together."
What?! I was marked wrong and the correct solution is given as Εμείς διαβάζουμε μαζί. Isn't that just "We read/are reading together"? To me that is quite different from "we are studying together." I wrote Σπουδάζουμε μαζί. Is that not acceptable?
"to study" is "μελετώ" or "σπουδάζω" but graecophones often say "διαβάζω" and mean "μελετώ". "μελετώ" and "σπουδάζω" are not synonyms.
"σπουδάζω" is associated with institutional education, especially of the higher level like university. I'll give you a couple of examples to better understand it's usage. Let's assume that you study architecture at uni. Someone may ask you "Τι σπουδάζεις;" and then you would reply "Σπουδάζω αρχιτεκτονική." Another example: "Πού σπουδάζεις;" "Σπουδάζω στο Αριστοτέλειο Πανεπιστήμιο." In this case, "σπουδάζω" has "φοιτώ" as a synonym: "Φοιτώ στο πολυτεχνείο." Compare with "φοιτητής"="student", especially one in higher education. "σπουδάζω" is more common than "φοιτώ", but "φοιτητής" is more common than "σπουδαστής".
You would use "μελετώ" in all other contexts, institutional education not excluded, just different usage: "Μελετώ τα μαθήματά μου" = "I am studying my lessons". If you ask someone "Πού μελετάς;" this will be understood as asking about the space one uses to study, e.g. at home, in the library.
Taking all of the above into account, I don't think that "we are studying together" translates very well to "σπουδάζουμε μαζί", this would have been "we study together", as "σπουδάζω" is a continuous, long-term kind of activity. The most accurate translation is "μελετούμε μαζί". Please forgive my minimal formatting, I don't know how to do fancy stuff here!
Study can mean διαβάζω/μελετάω but can also mean σπουδάζω. It's added now!
The take away is that "διαβάζω" can have different meanings depending on the context. When a kid and his grandfather "διαβάζουν" the newspaper together, they are "reading" it. When two college students "διαβάζουν" their reading assignment together, they are "studying" it. I can appreciate the frustration when words have multiple meanings... it happens to me as I try to learn Spanish...