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4MA1/2H Jan 2021, Question 16: Three-Set Venn Diagrams

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

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The question, in short

Use the given Venn diagram data for subjects R, F and G, with x students studying French only, to complete the diagram and then find how many study Russian given 80 students in total.

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, using x where needed for the French-only region.

  1. 1Put 4 in the centre, where all three circles overlap
  2. 2R and F only: 10 − 4 = 6; F and G only: 13 − 4 = 9; R and G only: 6 − 4 = 2
  3. 3G only: 24 − 4 − 9 − 2 = 9
  4. 4F only = x, R only = 2x, and 11 outside the circles

AnswerVenn diagram with regions filled as follows: Russian only = 2x, French only = x, German only = 9, R∩F only = 6, F∩G only = 9, R∩G only = 2, R∩F∩G = 4, none = 11

Part (b) · 3 marks

Using the total of 80 students, determine the number who study Russian.

  1. 1Add all regions: 2x + x + 6 + 2 + 4 + 9 + 9 + 11 = 80
  2. 23x + 41 = 80, so x = 13
  3. 3Russian = 2x + 6 + 2 + 4 = 26 + 12 = 38

Answer38

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