Try this beautiful problem from B.Math Entrance Exam based on** Sets and Venn diagrams**.

## Sets and Venn diagrams – B.Math Entrance

In a village of 1000 inhabitants, there are three newspapers P, Q,and R in circulation. Each of these papers is read by 500 persons. Papers P and Q are read by 250 persons, papers Q and R are read by 250 persons, papers R and P are read by 250 persons.All the three papers are read by 250 persons. Then the number of persons who read no newspaper at all

- is 500
- is 250
- is 0
- cannot be determined from the given information

**Key Concepts**

**Sets**

Venn diagrams

Algebra

## Check the Answer

But try the problem first…

Answer: is 0.

B. Math Entrance, India

Test of Mathematics at 10+2 Level by East West Press

## Try with Hints

First hint

Here n(P)=500, n(Q)=500, n(R)=500, n(PQ)=250, n(QR)=250, n(RP)=250, n(PQR)=250

Second Hint

n(P+Q+R)=n(P)+n(Q)+n(R)-n(PQ)-n(QR)-n(RP)+n(PQR)

Final Step

n(P+Q+R)=1000 Then P,Q and R read by 1000 inhabitantsand the number of persons who read no newspaper at all is 0.

## Other useful links

- https://www.cheenta.com/cubes-and-rectangles-math-olympiad-hanoi-2018/
- https://www.youtube.com/watch?v=Hgw5ls06aP8&t=25s