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.

Source
Suggested Reading

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.

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