Question

$65\%$ of students in a class like cartoon movies, $70\%$ like horror movies and $75\%$ like war movies. What is the smallest percentage of students liking all the three types of movies ?

• A. $30\%$
• B. $20\%$
• C. $10\%$
• D. $5\%$
• E. $Noneofthese$

Answer 1

The correct option is C $10\%$

$n\left(A\right)=65\to n\left(\overline{A}\right)=35$

$n\left(B\right)=70\to n\left(\overline{B}\right)=30$

$n\left(C\right)=75\to n\left(\overline{C}\right)=25$

$\therefore n{(\overline{A}\bigcap \overline{B}\bigcap \overline{C})}_{max}=35+30+25=90$

$\therefore n(A\bigcap B\bigcap C)=100-90=10$