## 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.

The worked solutions to these exam-style questions are only available to those who have a Transum Subscription. Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves. This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures. A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience. |

Drag this panel down to reveal the solution

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

©1997 - 2020 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/