Lemmara logoLemmaraWorked solution

4MA1/2HR Jan 2020, Question 17: Three-Set Venn Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Complete a three-set Venn diagram for dog, cat and rabbit ownership using the given counts, then use the total of 50 students to find x and a set complement intersection.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

Fill each region of the Venn diagram with the number of students, writing expressions involving x where needed.

  1. 1All three = 6; D and R only = 9 − 6 = 3; C and R only = 8 − 6 = 2
  2. 2D and C only = x − 6
  3. 3R only = 20 − 3 − 2 − 6 = 9; outside = 5
  4. 4D only = 28 − (x − 6) − 9 = 25 − x; C only = 18 − (x − 6) − 8 = 16 − x
  5. 5D only 25 − x, D and C only x − 6, C only 16 − x, D and R only 3, all three 6, C and R only 2, R only 9, outside all three 5

AnswerD only 25 − x, D and C only x − 6, C only 16 − x, D and R only 3, all three 6, C and R only 2, R only 9, outside all three 5

Part (b) · 2 marks

Using the total of 50 students, determine the value of x.

  1. 1(25 − x) + (x − 6) + (16 − x) + 3 + 6 + 2 + 9 + 5 = 50
  2. 225 − x + x − 6 + 16 − x + 3 + 6 + 2 + 9 + 5 = 50
  3. 360 − x = 50
  4. 4x = 10

Answer10

Part (c) · 1 mark

Find the number of students in C′ ∩ D′.

  1. 1C′ ∩ D′ means no cat and no dog
  2. 2That is R only plus those outside all circles
  3. 3R only = 9, outside = 5
  4. 49 + 5 = 14

Answer14

Stuck on a step? Read the free lesson: Three-Set Venn Diagrams

Practise more three-set venn diagrams questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on three-set venn diagrams

Also searched as: 4MA1 2HR January 2020 · 4MA1/2HR · 4ma1 jan20 2hr · question 17.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.