In a survey of 260 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice, and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.
85
To determine how many students were taking neither apple juice nor orange juice, we can use the principle of inclusion-exclusion in set theory. Let's define:
- Total number of students surveyed: \( N = 260 \)
- Students taking apple juice: \( A = 100 \)
- Students taking orange juice: \( O = 150 \)
- Students taking both apple and orange juice: \( A \cap O = 75 \)
The formula for finding the number of students taking either apple juice or orange juice (or both) is:
\[ |A \cup O| = |A| + |O| - |A \cap O| \]
Substituting the values, we get:
\[ |A \cup O| = 100 + 150 - 75 = 175 \]
This means 175 students were taking either apple juice or orange juice or both. To find the number of students taking neither, we subtract this from the total number of students:
\[ N - |A \cup O| = 260 - 175 = 85 \]
Therefore, 85 students were taking neither apple juice nor orange juice.
The correct answer is 85.
Important Questions from Venn Diagram Problems
In a class of 75 students, 40 students participate in Cricket, 28 students participate in Hockey, and 12 students participate in both Cricket and Hockey, whereas 19 students do not participate in any of the two sports. How many students participate only in Hockey?
How many students like french?
A. 30
B. 35
C. 40
D. 45
What is the ratio of students who like Spanish to those who like German?
A. 2/3
B. 1/2
C. 3/2
D. 4/9
How many students like only one language?
A. 65
B. 70
C. 75
D. 85
L and A are classmates as well as good friends. In a class of 30 students, L has 10 unique friends and 5 friends who are common to A. A has a total of 17 friends in the class. How many students are friends with neither L nor A?
