In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of the people, the percentage of administrators shall be in the range of ___________.
To find the percentage range of administrators, we first need to calculate the total number of people and the number of administrators.
From the diagram, we identify the numbers in each category:
- Teachers only in the triangle: \(70\)
- Researchers only in the circle: \(40\)
- Administrators only in the rectangle: \(20\)
- Intersection of Teachers and Administrators (triangle and rectangle): \(10\)
- Intersection of Administrators and Researchers (rectangle and circle): \(20\)
Now, add these values to find the total number of people:
- Total = Teachers only + Researchers only + Administrators only + Intersection of Teachers and Administrators + Intersection of Administrators and Researchers
- Total = \(70 + 40 + 20 + 10 + 20 = 160\)
Next, calculate the total number of administrators:
- Administrators = Administrators only + Intersection of Teachers and Administrators + Intersection of Administrators and Researchers
- Administrators = \(20 + 10 + 20 = 50\)
Now, calculate the percentage of administrators:
- Percentage of Administrators = \(\left( \frac{50}{160} \right) \times 100 \approx 31.25\%\)
Therefore, the percentage range of administrators is 31 to 45.
Important Questions from Venn Diagrams
Each row of Column-I has three items and each item is represented by a circle in Column-II. The arrangement of circles in Column-II represents the relationship among the items in Column-I.
Identify the option that has the most appropriate match between Column-I and Column-II.
Note: The figure shown are representative.
Column-I Column-II (1) Animal, Zebra, Giraffe (P) 
(2) Director, Producer, Actor (Q) 
(3) Word, Sentence, Novel (R) 
(4) Pianist, Guitarist, Instrumentalist (S) 
- To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?
- Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?
- 500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?
Out of \(100\) textile companies, \(10\) companies are involved in spinning, weaving and chemical processing, \(25\) companies are involved in spinning and chemical processing, and \(30\) companies are involved in weaving and chemical processing. If \(65\) companies are involved in chemical processing, the number of companies involved {ONLY} in chemical processing is ________________________.
