Personally, I committed to myself early on that I would LEARN from my studies and not EVER play the "guess what someone wants" game. This started early for me. I can suggest very specific examples from as far back as 2nd grade where I challenged the established authority on what it was they were trying to do and whether their methods were appropriate. (Okay, I was rather a freak.) In ALL possible cases, I have challenged the unfair problems with multiple solutions - sometimes deliberately incorrect. In cases where I could have little influence, I sometimes just took my lumps. This can be difficult, realizing and accepting that one is not in control of one's own life and that the errors of others can mess with us. Again, for me, I choose to go with personal integrity rather than bowing to the system. Most often, those I challenged were delighted to have the challenge. I have found the same to be true in the other direction. Those that challenge me either teach me something new and I change my views or the challenge provides for me an opportunity to strengthen my original position.
Apptitude exams are tricky. One must question what aptitudes are being challenged. It is not always clear.
Placement exams are very tricky. Most want to do well on them. That's a bit odd as it is intended for placement. One should do as well as one can. One should not perform over one's actual current ability.
Note 1: The Society of Actuaries went through some growing pains not too long ago. They completely discarded a certain question type from their syllabus. They received enough complaints and the discussion was of sufficient strength that they decided simply never to write such a question again. This is excellent evidence that those in authority can be persuaded.
Note 2: I could not find documentation for it, but I recall a single high school student some years ago rather embarrassing one of the big college entrance exam folks. In a 3 Dimensional geometry problem, the student proved that the exam committee was simply wrong. The committee ate their error and gave a higher score. This is excellent evidence that those in authority are not necessarily tyrants.
Well, that's quite a bit of discussion over the five seemingly-harmless numbers where we started!
The significant thing here is that you are given a short list of possible "answers", and the only way to approach the problem is to consider each of the four proposed answers in turn, and see if there is some way of relating it to the previous terms in the series. The relation between the terms may not be mathematical, in a conventional sense, at all. For example, look at this thread that was recently posted in this forum, where the answer depends on reversing the digits of each of the numbers in the series.
That said, I have to say that the answer given to the present problem, namely that "all the numbers are divisors of 3471", seems a bit pathetic to me. The question in the other thread is a genuine test of lateral thinking. Anyone who spots that the numbers there are the square numbers with the digits reversed is likely to be fairly confident that they have had the insight to see the correct solution. The answer to the question in this thread, on the other hand, looks quite arbitrary and unconvincing. The question does not test either mathematical or lateral thinking in any worthwhile way. I would not want to work for any employer who used a question like that in an aptitude test for job candidates.