Two-Way Tables and Venn Diagram Reasoning - Worksheets, Questions and Revision

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11+ · Two-way tables and Venn diagrams

EP.M128 Two-Way Tables and Venn Diagram Reasoning

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 55 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A survey of 28 pupils asked which of two games they liked. The results were recorded in this table.

Football Cricket
Boys 11 4
Girls 9 4

How many pupils like cricket?
  • A) 4
  • B) 9
  • C) 8
  • D) 15
  • E) 20
(Total for Question 1 is 1 mark)
2
In a survey of 40 pupils the table shows whether they own a bike.

Owns bike Yes Owns bike No
Cats 12 5
Dogs 6 17

How many pupils own a bike?
  • A) 28
  • B) 18
  • C) 17
  • D) 25
  • E) 19
(Total for Question 2 is 1 mark)
3
In a class of 26 pupils, 15 play football, 11 play chess and 6 play both football and chess. How many pupils play neither football nor chess?
  • A) 4
  • B) 6
  • C) 7
  • D) 8
  • E) 10
(Total for Question 3 is 1 mark)
4
A shop recorded purchases by 52 customers. 16 bought bananas. What is the probability that a randomly chosen customer bought bananas?
  • A) 16/52
  • B) 4/13
  • C) 16/50
  • D) 1/4
  • E) 8/26
(Total for Question 4 is 1 mark)
5
A factory has morning and evening shifts. The table shows how many workers of each sex work each shift.

Morning Evening
Male 13 11
Female 17 19

How many females work the morning shift?
  • A) 13
  • B) 11
  • C) 17
  • D) 30
  • E) 6
(Total for Question 5 is 1 mark)
6
The table below shows a small cinema's customers.

Child Adult
Matinee 9 13
Evening 7 15

How many adults attended the cinema in total?
  • A) 13
  • B) 15
  • C) 28
  • D) 22
  • E) 16
(Total for Question 6 is 1 mark)
7
A questionnaire of 36 pupils recorded whether they like science and whether they like art. The table shows:

Like science only: 15
Like art only: 3
Like both: x
Total who like at least one subject: 30

How many like both science and art?
  • A) 3
  • B) 6
  • C) 7
  • D) 9
  • E) 12
(Total for Question 7 is 1 mark)
8
The two-way table shows students' choices of after-school clubs.

Drama Music Total
Chosen Club Yes Yes
Boys 7 5 12
Girls 9 7 16
Total 16 12 28

What fraction of the students chose Music?
  • A) 12/28
  • B) 3/7
  • C) 6/14
  • D) 12/26
  • E) 7/16
(Total for Question 8 is 1 mark)
9
Fill in the missing cell in the table. The table shows pets owned by 30 pupils.

Cats Dogs Total
Yes 10 8 18
No 5 7 12
Total 15 15 30

Is the table consistent? If not, give the correct value for the missing cell or explain.
(Total for Question 9 is 1 mark)
10
A class completes a survey about owning a tablet and owning a smartphone. The table shows some counts.

Smartphone Yes Smartphone No Total
Tablet Yes 8 4 12
Tablet No 6 6 12
Total 14 10 24

How many pupils own both a tablet and a smartphone?
  • A) 8
  • B) 6
  • C) 4
  • D) 12
  • E) 14
(Total for Question 10 is 1 mark)
11
From this table we see pupils who bring packed lunch and those who bring lunch money.

Packed lunch Yes Packed lunch No
Lunch money Yes 10 4
Lunch money No 6 10

How many pupils bring neither packed lunch nor lunch money?
  • A) 6
  • B) 10
  • C) 4
  • D) 16
  • E) 30
(Total for Question 11 is 1 mark)
12
A small snack stall recorded purchases by 40 customers. 18 bought cakes, 9 bought sandwiches and 6 bought both. How many bought only a cake?
  • A) 12
  • B) 9
  • C) 6
  • D) 18
  • E) 24
(Total for Question 12 is 1 mark)
13
The table shows pupils taking French and German.

German Not German Total
Takes French 7 5 12
Does not take 6 12 18
Total 13 17 30

(a) How many pupils take German? (b) How many pupils take neither French nor German?
(a)How many pupils take German?(1)
(b)How many pupils take neither French nor German?(1)
(Total for Question 13 is 2 marks)
14
In a survey of 50 pupils, 28 like maths, 22 like history and 10 like both. Work out how many pupils like neither maths nor history.
(Total for Question 14 is 2 marks)
15
A class of 24 pupils were asked if they take piano lessons and if they take violin lessons. The results are:

Takes piano only: 7
Takes violin only: 4
Takes both: ?
Takes neither: 5

(a) How many pupils take both piano and violin? (b) How many pupils take at least one of the two instruments?
(a)How many pupils take both piano and violin?(1)
(b)How many pupils take at least one of the two instruments?(2)
(Total for Question 15 is 3 marks)
16
A table shows students who cycle to school and who use public transport.

Public Yes Public No Total
Cycle Yes 9 7 16
Cycle No 5 13 18
Total 14 20 34

How many students do not cycle and do not use public transport?
(Total for Question 16 is 2 marks)
17
In a school of 60 pupils, 30 study French, 28 study Spanish and 12 study both. A pupil is chosen at random. Work out the probability that the pupil studies exactly one of the two languages. Give your answer as a fraction in simplest form.
(Total for Question 17 is 3 marks)
18
A Venn diagram shows pupils who like swimming (S) and pupils who like cycling (C). 20 pupils like swimming, 16 like cycling and 9 like both. How many pupils like either swimming or cycling or both?
(Total for Question 18 is 3 marks)
19
A school asked 100 pupils whether they prefer early lunch, late lunch, or no preference. The results were recorded as: early 42, late 38, no preference 20. The headteacher realises the counts must add to 100. Is the table complete and consistent? If not, suggest a possible reason why and correct the numbers so they sum to 100.
(Total for Question 19 is 3 marks)
Mark scheme · EP.M128 Two-Way Tables and Venn Diagram Reasoning

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19