There is nothing wrong with the question, but you need to recognize where the gray area is. If you were an umpire, some pitches a clearly balls or strikes, but some could be either. This is how it is with some reactions.
In some recent posts, there has been confusion about this type of question. This is what I suggest you should expect. If reagents are listed, they should be interpreted as initiating a reaction or playing a kinetically important role. If a nucleophile or base is indicated, it should cause a reaction to occur.
For learning, I prefer to learn clear examples. Then you can compare the factors in a prospective reaction with ones that you know how they occur. A tertiary halide will not undergo an SN2 reaction. If an anion is listed, it will catalyze an E2 elimination. If only solvents are listed, it is meant to be an SN1 reaction. Because SN1 and E1 reactions have the same intermediate, both products will be found.
If you have a primary halide, then an SN2 reaction will occur. However, allylic and benzylic halides can also undergo SN1 reactions.
If you have secondary halide, this will be the gray area. If the anion is an alkoxide or more basic, then E2-elimination occurs, less basic anions result in SN2 reactions.
If your professor adheres to these guidelines, then it should be easier to make the predictions. However, concentration is also a factor in the mechanisms. If you have a secondary or tertiary halide, if it is diluted sufficiently, the solvent may result in bond cleavage independent of the nucleophile/base. In those cases, the mechanism can switch from SN2 or E2 to SN1/E1. I don't know any rules or guides that can help in those instances. It is better for your professor to be aware of possible ambiguity and properly indicate what is expected in the question.