Question

95% of the students in a class have taken Marketing, 80% have chosen Finance, 84% have chosen operations (ops), and 90% have chosen Human Resources (HR). What is the maximum and minimum percentage of people who have chosen all of the four?
80% and 56%
95% and 53%
80% and 49%
80% and 51%

Answer 1

95% of the students in a class have taken Marketing, 80% have chosen Finance, 84% have chosen operations (ops), and 90% have chosen Human Resources (HR). What is the maximum and minimum percentage of people who have chosen all of the four?

80% and 56% is the answer

Answer 2

The maximum and minimum percentage of people who have chosen all of the four are $80\%$ and $49\%$

Step-by-step explanation:

Given:Students who have opted for marketing$=95\%$

Students who have opted for Finance$=80\%$

Students who have opted for Operations$=84\%$

Students who have opted for Human Resources$=90\%$

To Find:The maximum and minimum percentage of people who have chosen all of the four

Concept/Formula used:By using Venn Diagrams

Maximum percentage of people who have chosen all of the four$=80\%$

People opting finance is $80\%$ , it comprises the smallest percentage of the total available for the overlap of students studying other subjects.

Minimum percentage of people who have chosen all of the four

$=100\%-$Max number of students studying 3 subjects or less

$= 100\%-(100\%-95\%)-(100\%-80\%)-(100\%-84\%)-(100\%-90\%)$

$=100\%-5\%-20\%-16\%-10\%$

$=49\%$

The maximum and minimum percentage of people who have chosen all of the four are $80\%$ and $49\%$