A teacher separated his students into three groups: successful, borderline successful, and unsuccessful. Sixty percent of the teacher’s students were placed in the first category, fifteen percent were placed in the second category, and twenty-five percent were placed in the third category; the teacher concluded that most of his students were successful.

In order for the teacher’s conclusion to be logically correct, it is necessary to assume that


a student who is not in the top sixty percent of the class is not successful

students in this teacher’s class are more likely to be successful than are most other students

students in classes in which only the top thirty percent are categorized as successful are more likely to succeed in a non-academic setting than are students in this teacher’s class

students are more likely to be successful than unsuccessful

it is possible to categorize students accurately as being successful, borderline successful, or unsuccessful