Question

In a class of 100 students, 73 like apple, 80 like orange, and 52 like grapes. It may be possible that some students do not like any of these three fruits. Find the difference between the maximum and minimum possible number of students who like all three fruits.

• A. 47
• B. 48
• C. 53
• D. 52

Answer 1

The Correct Option is A

The maximum number of students who like all three fruits occurs when the students who like apple, orange, and grapes overlap as much as possible. In this case, the maximum number is the smallest of the three sets: \[ Maximum = \min(73, 80, 52) = 52 \] The minimum number of students who like all three fruits occurs when the students who like apple, orange, and grapes overlap as little as possible. The minimum number is calculated as follows: \[ Minimum = 73 + 80 + 52 - 100 = 105 \] The difference between the maximum and minimum is: \[ Difference = 105 - 52 = 47 \] To find the difference between the maximum and minimum number of students liking all fruits, calculate the overlap cases as maximum and minimum.