Structure determination problems require application of knowledge. They can test some or all of the following:

1.  Your understanding of reactions - the functional group transformation plus any regiochemistry and stereochemistry issues and mechanisms.
2.  How reactions and functional group interconversions are interrelated.
3.  Use of spectropscopic data  (e.g. number of types of H or C, IR bands etc.)
4.  Use of stereochemical data (e.g. enantiomers etc.)
5.  Use of other chemical data (e.g. functional groups test results, numbers of isomers)

The most common reasons for students to struggle with these questions are:

Is there a good way to try to solve such a question ?   YES

1.   Convert the paragraph from the question into a flow chart of all the information : EVERY PICTURE TELLS A STORY !
2.   Interpret the data as you write out the flow chart. Remember each reaction tells you something about the starting material and the product of that reaction.
3.   Include all relevant data (e.g. spectroscopic data, chirality information etc.)
4.   Anytime there is a name of a compound, draw the structure.

Somewhere in the problem there will be a KEY .... this is where you know the MOST about a particular compound in the sequence. It might be the name of a compound, or it may be number of types of C or H present or even chirality information.   IF YOU GET THE KEY STRUCTURE, most of the rest can be readily worked out from there, but you will have to work backwards and forwards from that point.

DON'T  TRY TO GUESS "A" and feed it through the question until it "breaks". It will rarely work first time and is a very time inefficient method.

The problems are like good Suduko problems.... no guessing or trial and error is needed, there should always be something that allows you to logically deduce the next piece.