Venn diagram question

Question

 

A survey of 84 students on campus showed that 30 read the Campus Observer student newspaper that morning, 25 read the news via the Internet that morning, and 19 read the local city paper that morning. Nine read the Campus Observer and the Internet news that morning, while four read the Internet news and the local paper, eight read the Campus Observer and the local city paper, and one person read the Campus Observer, the Internet news, and the local paper.How many read the Internet news or local paper but not both?

There are students who read the Internet news or local paper but not both.

Answer 1

Hi Jessica,

 

Below is the link to our Venn diagram for this problem:

 

https://dl.dropbox.com/s/msux48ejpkc7fjv/Venn_Disgram_Students.png?raw=1

 

The three overlapping circles represent the three groups of students (by morning reading habit) identified in the problem.  The blue numbers are the given total (single + combination) numbers for each circle, the green numbers are the given combination numbers involving two or more circles, and the red numbers are our calculated single ( non-combination) numbers for each circle.  The calculations for each red number are shown in parentheses under each red number.

 

Our answer concerning the total number for students ONLY reading the Internet News or the Local Paper, BUT NOT BOTH, is the sum of the red numbers for these two student groups:  

    Single Local Paper # + Single Internet News # = 6 + 11 = 17

 

Venn diagrams are very useful for visually representing the numerical relationships between sets of data.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.