Where is the question from? (It always helps if you can tell us that.)
Type L questions, at least on GL Assessment papers, are never "every other one". You and your daughter have fought valiantly with it though, and possibly found the only logic there is to be had out of it. You are right to conclude that even if it was to be "every other one", you do not have enough information to get to the 6th pair.
There are definitely no mirror codes (which also occur very rarely, if ever on these questions), and therefore according to the "usual" rules" of a straightforward progression:
:: the first pairs are +9, +7, (+11/15), +5
:: the second pairs are 7, 11, 3, +11
I am afraid that I can see no logic whatsoever there!
Even if someone can find a solution, it is a ridiculously overcomplicated question. I suspect it is an error, though.
