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0580/31 May/Jun 2025, Question 26: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 4 marks

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The question, in short

Li surveys 28 students about speaking English (E) and Spanish (S): 15 speak English, 12 speak Spanish, 6 speak neither. Use a Venn diagram to complete regions and find counts.

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

Part (a) · 2 marks

Fill in all four regions of the Venn diagram for E and S using 28 students, 15 English, 12 Spanish, 6 neither.

  1. 1n(E ∪ S) = 28 − 6 = 22
  2. 2Both = 15 + 12 − 22 = 5
  3. 3E only = 15 − 5 = 10, S only = 12 − 5 = 7
  4. 4Write 6 outside the circles

AnswerE only 10, E ∩ S 5, S only 7, outside 6

Part (b) · 1 mark

State the number of students who speak English but not Spanish.

  1. 1English only = 15 − 5 = 10

Answer10

Part (c) · 1 mark

Given 28 students, 15 English, 12 Spanish, 6 neither, find n(E ∪ S).

  1. 1n(E ∪ S) = 10 + 5 + 7 = 22

Answer22

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Also searched as: 0580/31/M/J/25 · 0580_s25_qp_31 · 0580 s25 31 · question 26.
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