Sorry, let me rephrase the question:

Can anyone explain, in detail, why the outer join solution is faster than the Subquery solution in this example?  Is the Exists method fastest of all?

I've examined all three on a limited number of rows and the performance and the plans are identical.  Why do you reckon one will be faster than the next with table growth?

Correct me if I'm wrong, but when you do a left outer join the left part of the join has a full table scan.  How is this faster than a subquery based on an index compared to another column based upon an index?  Also, I can't see the difference in using EXISTS over a standard subquery as it still is effectively comparing values inside the EXISTS subquery?

Also the LEFT JOIN thing looks nice, but how would you work it if (as it would seem a more reasonable requirement) you wanted the people who hadn't taken the SQL Server exam BUT HAD TAKEN another?