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How would you solve this problem? Try to solve it.

 

 A group of 30 students went on a camping trip.  Of these, 12 return with both sunburns and insect bites, and 20 report sunburn.  How many suffered only insect bites if it is known that only three students suffered neither?

 

        Some people enjoy problems of this type as fun puzzles; whereas, others find them to be a real headache.  People who recognize and are able to solve problems of this type often obtain more information from data given in business meetings or when reading news reports than other people. This may lead to better business and personal decisions. Further, it is one type of problem often found on gateway exams such as MCAT (medical school), LSAT (law school), ASVAB (military), GRE (graduate school), and the Civil Service Exam (federal employment).  The intention of these types of questions is to determine if a person is able to think logically.  In this lesson, we will be learning a method for visualizing and solving such problems.  But first, we need to learn a few more terms involving sets that can aid us in solving problems.

        We will come back to the above problem later and solve it with an approach that uses set concepts.