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Algebra I.S.I. and C.M.I. Entrance Problem Solving Marathon

Sets and Venn diagrams |B.Math Entrance

Try this beautiful problem from B.Math Entrance Exam based on sets and venn diagrams. You may use sequential hints to solve the problem.

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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