Correct Answer – Choice E. 99 students attended neither of the events.
Total 180 students.
At least 45% attended the prom night.
So, the number should be a minimum of 45% of 180 = 81 students.
At least 40% took part in the debate.
So, the number should be a minimum of 40% of 180 = 72 students.
We have been asked to find out the maximum number of students who attended neither the prom night nor the debate.
If set A represents those who attended the prom night and set B represents those who attended the debate,
Set (A U B) will give us the set of students who attended at least one of the two events.
And Set (A U B)’ will give the set of students who attended neither of the two events.
If we have to maximize (A U B)’, we have to minimize (A U B).
n(A U B) = n(A) + n(B) – n(A n B)
In this question, n(A U B) = 81 + 72 – n(A n B) = 153 – n(A n B)
If n(A U B) has to be minimized, we should maximize n(A n B).
The maximum value that n(A n B) can take is the smaller of n(A) and n(B).
So, max n(A n B) = n(B) = 72.
Therefore, min n(A U B) = 153 – 72 = 81.
Hence, max n(A U B)” = 180 – 81 = 99