11 plus - Venn diagrams A

Some people in a music class were asked whether they played the piano or the violin.

The Venn diagram shows the results.

How many people played the piano and the violin?

• 3

• 2

• 5

• 10

Answer explanation

There are two people that appear in the piano circle AND the violin circle - the yellow area. They play both.

Some people in a music class were asked whether they played the piano or the violin.

The Venn diagram shows the results.

How many people played the violin?

• 2

• 5

• 3

• 7

Answer explanation

The people that play the violin are shown in the yellow and green areas that make up the circle for violin.

2 + 3 = 5

Some people in a music class were asked whether they played the piano or the violin.

The Venn diagram shows the results.

How many people played just one instrument?

• 2

• 5

• 8

• 10

Answer explanation

The red area shows the people who played just the piano

The green area shows the people who played just the violin

5 + 3 = 8

Some people in a music class were asked whether they played the piano or the violin.

The Venn diagram shows the results.

How many people didn't play either the violin or the piano?

• 2

• 13

• 3

• 1

Answer explanation

The people who are outside the circles didn't play either the piano or the violin.

There are 3 of them.

Some people in a music class were asked whether they played the piano or the violin.

The Venn diagram shows the results.

How many people were included in the survey?

• 12

• 21

• 10

• 13

Answer explanation

Add up the people in the Venn diagram, including the ones who didn't play either instrument.

There are 13.

The Venn diagram shows which numbers belong in some groups of multiples.

8 is a multiple of 2 but it is not a multiple of 3 or 5 so it sits in the green area.

Where should number 4 sit?

• The white area

• The yellow area

• The green area

• The blue area

Answer explanation

4 is a multiple of 2 but not a multiple of 3 or 5.

The Venn diagram shows which numbers belong in some groups of multiples.

Which number could go in the yellow area?

• 2

• 3

• 6

• 30

Answer explanation

6 is a multiple of 2 and of 3 but not a multiple of 5

30 is a multiple of 2, 3 and 5 so would go in the white area in the middle

The Venn diagram shows which numbers belong in some groups of multiples.

Which number could go in the pink area?

• 30

• 15

• 10

• 20

Answer explanation

The pink area is for numbers that are multiples of 3 and 5 but not 2.

15 is a multiple of 3 and 5 but not a multiple of 2.

30 would go in the white area in the middle as it is also a multiple of 2.

The Venn diagram shows which numbers belong in some groups of multiples.

Where should number 120 go?

• In the pink area

• In the yellow area

• In the white area in the middle

• In the light blue area

Answer explanation

120 is a multiple of 2, 3 and 5 so it goes in the white middle area

30, 60 and 90 would also do in the white middle area.

The Venn diagram shows which numbers belong in some groups of multiples.

Which of these numbers would sit in the yellow area?

• 42

• 40

• 33

• 30

Answer explanation

The numbers in the yellow area are multiples of 2 and 3 but not 5

42 is a multiple of 2 and of 3 but not a multiple of 5