What do job-application aptitude tests really measure?

It is common practice for companies (including financial companies) to use aptitude tests (mostly numerical and verbal reasoning) in order to assess candidates. I myself have done such tests and though I do not begrudge companies that use them, I have started to question their validity. Do they actually measure something useful? I explore this theme in a blog post on my life-related blog Meditations of Lambchop. Here is an extract from the post

This excellent essay, A Mathematician’s Lament, by Paul Lockhart has convinced me of something I suspected since learning actual mathematics at university (and not even, at first, within official lectures): our schooling ruins mathematics for children. The same kind of thinking that has created the education system appears to have infected human resource departments in most major companies. I refer, of course, to the ubiquitous use of aptitude tests (a subset of psychometric assessments).  It seems to me that our schools are satisfied with teaching arithmetic rather than mathematics and HR is satisfied with testing “skills” that no candidate will ever need. As with schooling it seems hardly anyone questions the current system. Read more here.