In 2004 Google Labs published so called GLAT - Google Labs Aptitude Test.
Readers were asked to mail in their answers and promised that they would be contacted by Google if they scored well.
The declared reason was to attract high quality people into their ranks. Actually, it was a clever PR move which generated a lot of interest from it.
First, the public gets the idea that the company (= Google Labs, in this case) is hiring only very clever folks.
Second, the public gets the reminder that the company is on the map.
Third, you get much buzz, interest and involvement about this point. Public involvement is necessary for good PR. You may call it even 'viral marketing'.
The PR move for brains, intellectuals and know-it-all guys is to publish a test as if you were hiring folks.