TrueNappa wrote:留学に ( ) ビザの申請が必要になる。
a. ともに b. したがって c. 伴って d. つれて
These four points can be kind of fuzzy, but here are the points as I understand them:
ともに = expresses concurrent change going on at the same time. Since you say とともに and not にともに, this obviously isn't the right one anyway.
したがって = has a ton of usages, but ultimately shows something going in accordance with something else. For example あなたの指図に従って彼を首にしました。
In accordance with your instructions, I fired him., ALC. 「郷に入れば郷に従え」is another example. You can certainly go in accordance with the law, someone's directions, or the customs of the land, but unless I'm mistaken it doesn't really seem to go with the single concept of 留学.
伴って = expresses a change coming along with something else. The example I learned was 地震に伴って津波が起こる. In this case the tsunami comes about because of the earthquake. In the case of that test question, it seems to make sense that one's studying overseas would bring about a need for a visa application.
つれて = is a common-sense, natural association. "As A happens, B does too." For example 時代の変化につれて、人々の考え方も変わっていく.
I also found this site having done a quick search on the matter. It doesn't address 伴う but you might find it helpful:
http://home.alc.co.jp/db/owa/jpn_npa?stage=2&sn=207
This is how I understand them anyway. Hope you can find it of some use. Good luck with the JLPT!