Holidays

Of the 35 students in the class, seven were on holiday in Germany and just as many in Italy. Five students visited Austria. There were 21 students in none of these countries. One student visited all three. There were two students in Italy and Austria and one student in Austria and Germany. How many students visited Germany or Italy (a), Austria or Italy (b), or Germany or Austria (c)?

Correct answer:

a =  11
b =  9
c =  10

Step-by-step explanation:

$$\begin{gathered} I=7 \\ N=7 \\ R=5 \\ IR=2 \\ RN=1 \\ INR=1 \\ I+N+R-INR-x-1-1-0=35-21 \\ 7+7+5-1-x-1-1-0=35-21 \\ x=2 \\ x=\frac{2}{1}=2 \\ x=2 \\ a=N+I-x-INR=7+7-2-1=11 \end{gathered}$$

$b=I+R-2-1=7+5-2-1=9$

$$\begin{gathered} c=N+R-1-1=7+5-1-1=10 \\ \text{ Verifying Solution: } \\ t=3+2+1+1+0+4+3+21=35 \end{gathered}$$

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