Question

In a certain group of 75 students, 16 students are taking physics, geography and English; 24 students are taking physics and geography, 30 students are taking physics and English; and 22 students are taking geography and English. However, 7 students are taking only physics, 10 students are taking only geography and 5 students are taking only English. How many of these students are taking physics?

• A. n(P) = 45
• B. n(P) = 35
• C. n(P) = 65
• D. n(P) = 55

Answer 1

The correct option is A n(P) = 45

7 students are taking Physics only.

So

$7=n\left(P\right)-n(P\cap G)-n(P\cap E)+n(P\cap G\cap E)$

$\Rightarrow n\left(P\right)=7$ $+n(P\cap G)+n(P\cap E)-n(P\cap G\cap E)$

So $n\left(P\right)=7+24+30-16=45$