Why would water, and not saltwater, undergo electrolysis?
What is the "correct" answer

You are asking why the answer key has water and not saltwater as an answer. Decomposition is defined as:


  A reaction where a single compound breaks down into simpler compounds.


For salt water, the salt reacts at one electrode, and the water at the other, and you are making NaOH. For pure water, you are splitting water into the elements. Neither process matches the definition of decomposition that I quote exactly, but pure water is the better fit.

In your question, you write:


  I was thinking that water in itself is not conductive and therefore will not facilitate electrolysis by itself.


The half reactions could be written as:

$$\ce{2H2O + 2e- -&gt; H2 + 2OH-}$$ and 

$$\ce{H2O -&gt; 1/2 O2 + 2H+ + 2e-}$$

So there are protons produced at one electrode and hydroxides at the other (You could also have protons be reduced at one electrode, and hydroxide oxidized at the other - the net effect is the same). The protons are very mobile in water and will quickly diffuse and neutralize the hydroxide. This takes care of the charge transport through the solution.

Is this a good question?

No, but most multiple choice questions aren't.