Also, please realize that, like I mentioned above, this only holds if they are assuming 3 segments of EQUAL length; if they aren't, though one could go through various mental and mathematical contortions so as to arrive at the answer, the easiest way I could see would be like so:
Assume that the length of the first segment was 4, the length of the second 12, and the length of the third 8 (after the first cut and before the second cut). Now, the sum total of these is 24, which is choice A. The reason why the second segment couldn't be 6 instead of 12 (using the lowest integer, 1, for the length of the final integral segments instead of 2 as I do here) is because this would add up to 18 (4+6+8), which is not among the choices given. Ditto for the other various permutations (8+6+8 = 22; 4+6+16 = 26; neither of which are given). Now, one knock on this method (and the question in general) is that it assumes that the secondary segments are cut into 4, 6, and 8 equal integral pieces, respectively, with no remainder.
However, this assumption is, in fact, implicit in the entire question; if we are to view it as such, my first answer is still the more plausible one, as if we have to "read meaning" into the question (re: equal-length segments), we must do so consistently (both prior to the first AND second round of cuts), and this would necessitate the answer I gave previously of E) 72.
In either instance, however, the question is poorly phrased now that I think about it. Though my first reaction was to solve it in the manner illustrated in my previous post, this would mean that the fact that the 3 segments were of equal length would have to be merely understood, rather than explicitly stated as a condition; this reflects poor question writing imo.
In the second condition (the alternative explanation seen above), we would still have to assume the same exact thing, as even if we are to assume that the original 3 segments are unequal in length, we are then assuming that the second cut results in equal-length segments (for instance, you can cut a strip of length 8 into either 4 pieces of length 2, or 4 pieces of lengths 1, 2, 4, and 1; as you can see, either way the notion of equality of lengths is implicit). Furthermore, the "alternative" method also exposes the piss-poor wording of the question even further, as "24" wouldn't be the "minimal length of the wire" (as they ask for), but rather would be "the minimal length of the wire among the choices given" (and there is a difference between these two). Because, clearly, we could assume that the length of each of the 3 resultant segments present after the first cut (assuming unequal lengths) was 4, 12, and 8; these would then be cut again into 4, 6, and 8 segments (now changing it up and assuming equal-length cuts), which would result in 12 segments of length 1 (4/1 + 8/1) and 6 of length 2 (12/2) for a total of 24, which would be choice A.
As you can see from either scenario, somewhere along the line, we must make the implicit decision that we are assuming equal cuts; the first scenario (previous post) is the "cleaner" one imo, and was more intuitive to me, so I stand by it. My sister, after looking at this problem, got me further into thinking about this notion of unequal cuts, because right away she stated that it didn't mention that they were 3 segments of equal length (it's funny how people's minds work differently 🙂; though I did grant this in my previous post-- see the parenthetical), and I quickly came up with the above rationale as to why, even if we assume such a thing, the first scenario is still more plausible.
In summary, the question is too ambiguous for its own good, but if I were a betting man, I'd still wager on the answer given in my previous post. I wanted to post this as sort of an exploration of alternative thought processes, since my sister got me started down that road, despite the fact that I was aware of the assumption I was making about equal length segments. I also realize that this might be hard to follow, as writing about math and logic is not my forte-- it's convoluted (and quite possibly insubstantial 😉), I know. For this, I apologize. 😛
And if this all boils down to the fact that you forgot to copy down the part question which stated that they were 3 (and eventually 4, 6, and 8) pieces of equal length, well, you've cost me 10 minutes of my life that I want back. 😀 Maybe I just think too much-- that's why I'm about to go play basketball, where I don't have to think at all. 😳
