What does not work is a person who cannot recognize a good solution. Some managers can pull off relying on their team members to spot and solve problems with minimal intervention. But this is usually a receipt for disaster. There are always situations when a manager needs to dig deeper and challenge a particular solution brought up by a team member because the solution will have an impact on some other area that the report is not aware. So, again, even if managers are not good at out of the box thinking they need to evolve in order to develop an intuition that allows them to accept or challenge a solution coming from someone else. 

Be aware also that there are managers that in spite being good at solving problems have issues when executing; let's just say "they don't get the job done". This is a problem that most of the times has to do with lack of experience or too much "strategic thinking" but can be due to other factors, usually detectable through these tests.