My humble 2016 JLPT N3 thread

I agree with ariariari: If you enjoy doing your kanken drills, it's a good idea to continue! Learning is just so much easier when you are having fun
And Kanken 7 already covers 640 kanji (at least that's what a quick lookup on wikipedia said). I wouldn't call that "such a low level" anymore ^^ Actually the first estimate I found for the kanji you need to know at n3 is also ~650 (on the German wikipedia, but I think it's just an estimate from the old "non-N" tests). Yes not all of them will be the same, but there will be a huge overlap. And it will probably also help with your reading speed a bit as well

Of course if you are only doing your kanken drills, you might run into problems on the grammar and listening parts of n3, but you said you were having a tutor and working on that as well. I think that's fine Even if you are going slow, you are bound to progress in those areas as well!