Mr. Pascal built a computer for multiplying numbers and named it "Ramanujan". But Ramanujan multiplies $(3, 5), (2, 4), (3, 4)$ and $(4, 7)$and results are $17, 10, 14$ and $34$. If Ramanujan multiplies $(5, 6)$, what will be the result?
Source: Bangladesh Math Olympiad 2015 Junior Category
I can not get the pattern. Can anyone give me a hint?
Hint (as requested): Think about other bases!
Though I'll remark that I dislike these types of problems, especially in competition mathematics, since you can describe any suitable formulation and use it to justify practically any answer - as evidenced by Matti P's comment.