Question

There are 35 students in the University travel club. The following information in Venn diagram show how many students travel to Germany, France, and Spain. How many students have not been to Germany, Spain, or France?

Answer 1

Given:

There are 35 students in the university

The number of students that have not been to Germany, Spain, or France is:

$=\text{ 35 - number of students that have b}een\text{ to Germany, Spain or France}$

Let's find the number of students that have visited each country

The number of students that have visited only Germany:

$\begin{gathered} =14\text{ - }(7-3-2) \\ =\text{ 2} \end{gathered}$

The number of students that have visited only Spain:

$\begin{gathered} =\text{ 18- (5-3-2)} \\ =\text{ }8 \end{gathered}$

The number of students that have visited only France:

$\begin{gathered} =21\text{ - }7-3-5 \\ =\text{ 6} \end{gathered}$

The number of students that have been to Germany, Spain or France is:

$\begin{gathered} =\text{ 2+8+6 + 7+2+5}+3 \\ =\text{ 33} \end{gathered}$

The number that has not been to Germany, Spain, or France:

$\begin{gathered} =\text{ 35 - 33} \\ =\text{ 2} \end{gathered}$

Answer: 2