Hands up who would've assumed the battery had been stolen at the end of the study (as opposed to the beginning)!?
Thinking like a thief (!)... wouldn't you want a new battery, rather than one that's already been going for 150 days and might run out...? In truth, I don't think it's obvious when to assume the battery is stolen, but the only sensible possibilities are at the start or at the end. Since the calculations in each case are straightforward, in the exam you'd just try both until you got an answer that matched.
"Thinking like a thief (!)"... wouldn't it make most sense to steal the battery at the point you claimed it exploded? (And make that time 0 if you wish to nick it at the start)... Or wouldn't you feel less prone to being caught out during unexpected visits by the electronic's company staff? I feel like this question wouldn't wasted precious minutes in the exams!
You know the battery wasn't stolen at the point they claimed it exploded as you've already shown that that gives an inconsistent result. So, it really only leaves the start and the end of the experiment. (They obviously weren't a very clever thief as they failed to cover their tracks!)
