GCSE · Venn diagrams & set notation

Venn diagramsExam-style questions

Building a Venn diagram from worded information — why you fill the overlap first and work outwards, what the number in a region actually counts, the universal set and the "neither" region outside the circles, and how the grand total pins down whichever region is missing.

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13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
$100$ $100$ people were asked which of apples, bananas and cherries they had eaten in the last week.
- $52$ had eaten apples,
- $41$ had eaten bananas,
- $39$ had eaten cherries,
- $20$ had eaten apples and bananas,
- $17$ had eaten apples and cherries,
- $15$ had eaten bananas and cherries,
- $9$ had eaten none of the three fruits.
(a) Work out how many of the $100$ $100$ people had eaten all three fruits.

(b) Work out how many of the $100$ $100$ people had eaten exactly one of the three fruits.
Level 5 · 6 marksTry it
2
A youth club has $64$ members. Every member does at least one of drama and dance.

$28$ members do drama but not dance.

The number of members who do both drama and dance is $3$ times the number who do dance but not drama.

(a) Work out how many members do dance.

(b) Work out how many members do drama.
Level 5 · 5 marksTry it