That's a very interesting question - you're right to assume that "sluggish" and "slug" have a common origin. However you're wrong to assume that the latter comes from the former. It's actually the other way round: both "sluggish" and "slug" come from the Middle English word, "slugge", which meant "lazy person". What is this strange English exam you're taking that requires you to know word origins?!

Interesting question. According to the Shorter Oxford English Dictionary, it does come from the word 'slug', which, as I'm sure you know, is a slimy, slow-moving mollusc. That, in turn, is derived from old Norwegian 'slugg (a large, heavy body) and 'sluggje' (a heavy, slow person). I suppose the most important concept here is 'slow'!