Discussion
Set M has 42 students and set N has 60 students. At least 12 of the students in set M are not in set N. Which of the following cannot be the possible number of students in set N that are not in set M ?
Answer: C
The number that is not possible is 28.
At least 12 of set M's 42 students are outside N, so at most 42 - 12 = 30 students are in both sets. Set N has 60 students, so the number in N but not in M is
\[ \begin{aligned} 60 - (\text{common}) &\ge 60 - 30 \\ &= 30 \end{aligned} \]
Any value from 30 to 60 is possible, depending on how many students the two sets share. 32, 42 and 45 all lie in that range, but 28 is below the minimum of 30, so it cannot occur.
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