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Venn Totals

Practise reading and creating Venn diagrams containing two and three sets and the number of elements in those sets.
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This is level 4: Adding information to a Venn diagram containing three intersecting sets with some problem solving required. You can earn a trophy if you get at least 7 questions correct.

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Buzz

Rag

Gossip

Which newspapers do you read?

The island of Null has three daily newspapers. They are The Buzz, The Rag and The Gossip. 401 people on the island were asked which of these newspapers they read regularly. The Venn diagram above shows the number of people that read each newspaper. Enter the numbers in each section of the diagram by using the information provided:
  • 82 people did not read any of the newspapers;
  • 45 people read both The Buzz and The Rag;
  • 54 people read both The Buzz and The Gossip;
  • 60 people read both The Rag and The Gossip;
  • 66 people read The Buzz only;
  • 75 people read The Rag only;
  • 59 people read The Gossip only;

How many people read all three newspapers?		 Correct Wrong

How many people read at least two newspapers?		 Correct Wrong
Check

This is Venn Totals level 4. You can also try:
Level 1 Level 2 Level 3 Venn Diagram Venn Paint Venn Pairs

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
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Whose Idea Was This?

Did you enjoy doing this 'Venn Totals' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept.
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Description of Levels

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Level 1 - Reading information from a Venn diagram containing two intersecting sets.

Level 2 - Reading information from a Venn diagram containing three intersecting sets.

Level 3 - Adding information to a Venn diagram containing three intersecting sets.

Level 4 - Adding information to a Venn diagram containing three intersecting sets with some problem solving required.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Example

This video is Art of Problem Solving's Richard Rusczyk introducing 3-circle Venn diagrams as a counting technique.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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