What are they assessing?

The TSA claims that they are testing an individual for 'problem-solving skills, including numerical and spatial reasoning. critical thinking skills, including understanding argument and reasoning using everyday language.', but they are essentially testing how you will respond to the Oxford's of socratic method teaching. The tutorial system asks that students are critical and creative. Solving these problems will show that you have a base that can be built on. Scoring high is of course positive, but as long as you have a solid personal statement and display a reasonable ability this is pretty much all you will need.