This is completely subjective, but Peter Brouwer sent in the problem that I thought satisfied both halves of the working definition of pseudocontext in the most spectacular fashion. This is it. This is as bad as it gets.
From the June 2001 Math B New York Regents examination [PDF]:
Jo Boaler gets the last word:
Students do however become trained and skillful at engaging in the make-believe of school mathematics questions at exactly the “right” level. They believe what they are told within the confines of the task and do not question its distance from reality. This probably contributes to students’ dichotomous view of situations as requiring either school mathematics or their own methods. Contexts such as the above [pseudocontext], merely perpetuate the mysterious image of school mathematics.
That’s it. Thanks for pitching in.