QUESTION

Twenty-five freshmen saw Star Gazers Part I, 36 saw Star Gazers Part II, and 17 saw both movies. How many freshmen saw one movie, but did not see both?

SOLUTION

As you can see above the attached picture of a Venn diagram uses circles (or any simple closed curves) inside a rectangle to represent relationships among groups of people or objects.

• The rectangle represents all freshmen. Circle A represents those who saw Star Gazers Part I. Circle B represents those who saw Star Gazers Part II. The overlap represents those who saw both movies. Therefore there are 36 - 17 = 19 freshmen who did not see Star Gazers Part I and 25 - 17 = 8 freshmen who did not see Star Gazers Part II. A total of 19 + 8 = 27 freshmen saw one movie but did not see both.