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 group of 110 students, 23 students did not participate in any of the two games: Badminton and Chess. 45 students participated in Badminton and 61 students participated in Chess. How many students participated in Badminton only?
In a class of 100 students, every student has passed in one or more of the three subjects, i.e History, Economics and English. Among all the student, 24 students have passed in English only, 14 students have passed in History only 11 students have passed in both English and Economics only, and 12 students have passed in both English and History only. A total of 50 students have passed in History. If only 5 students have passed in all three subjects, then how many students have passed in Economies only?
60 students participated in one or more of the three competitions, i. e. Quiz, Extempore and Debate. A total of 22 students participated either in Quiz only or in Extempore only. 4 students participated in all three competitions. A total of 14 students participated in any of the two competitions only. How many students participated in Debated only?
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
