## Exam-Style Question on Sets## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 17. This question is similar to one that appeared on an IB Studies paper in 2012. The use of a calculator is allowed.

Sumville has three newspapers: The Chronicle, The Express and Moon, and The Scribe.

It has been found that

- 35% of the town’s population read The Chronicle,
- 42% read The Express and Moon,
- 51% read The Scribe,
- 4% read The Chronicle and The Express and Moon only,
- 10% read The Chronicle and The Scribe only,
- 15% read The Express and Moon and The Scribe only, and
- 7% of the population reads all three newspapers.

(a) Draw a Venn diagram to represent this information. Label A the set that represents The Chronicle readers, B the set that represents The Express and Moon readers, and C the set that represents The Scribe readers.

(b) What percentage of the population does not read any of the three newspapers?

(c) Find the percentage of the population that reads exactly one newspaper.

(d) Find the percentage of the population that reads The Chronicle or The Express and Moon but not The Scribe.

A local radio station states that 71% of the population reads either The Express and Moon or The Scribe.

(e) Use your Venn diagram to decide whether the statement is true and justify your answer.

The population of Sumville is 180 000. The local radio station claimed that 65 000 of the town’s citizens read at least two of the local newspapers.

(f) Find the percentage error in this claim.

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