Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 159 · 40 questions

How to solve it (Do not count twice): n(A or B) = n(A) + n(B) − n(both) — otherwise the “both” group is counted twice. Only A = n(A) − n(both). Neither = total − n(A or B). Both = n(A) + n(B) − n(A or B).

1. 1.In a class of 22 children, 9 like mangoes, 13 like bananas and 3 like both. How many like only mangoes? (a) 9 (b) 6 (c) 3 (d) 10
2. 2.In a class of 24 children, 13 like tea, 14 like coffee and 2 like neither. How many like both? (a) 5 (b) 22 (c) 3 (d) 2
3. 3.In a class of 28 children, 9 like maths, 12 like science and 2 like both. How many like only maths? (a) 9 (b) 16 (c) 10 (d) 7
4. 4.In a class of 25 children, 16 like maths, 19 like science and 12 like both. How many like only maths? (a) 4 (b) 6 (c) 16 (d) 7
5. 5.In a class of 41 children, 21 like tea, 15 like coffee and 10 like neither. How many like both? (a) 31 (b) 6 (c) 10 (d) 5
6. 6.In a class of 38 children, 15 like maths, 31 like science and 11 like both. How many like only maths? (a) 4 (b) 15 (c) 20 (d) 7
7. 7.In a class of 36 children, 23 like cricket, 12 like football and 7 like both. How many like at least one of the two? (a) 35 (b) 28 (c) 21 (d) 36
8. 8.In a class of 33 children, 14 like maths, 21 like science and 3 like both. How many like only maths? (a) 11 (b) 18 (c) 14 (d) 12
9. 9.In a class of 33 children, 16 like dance, 18 like music and 2 like neither. How many like both? (a) 2 (b) 3 (c) 1 (d) 31
10. 10.In a class of 27 children, 11 like tea, 14 like coffee and 7 like both. How many like only tea? (a) 7 (b) 11 (c) 13 (d) 4
11. 11.In a class of 35 children, 9 like dance, 22 like music and 4 like both. How many like only dance? (a) 9 (b) 18 (c) 5 (d) 13
12. 12.In a class of 36 children, 23 like dance, 7 like music and 4 like both. How many like neither? (a) 14 (b) 6 (c) 4 (d) 10
13. 13.In a class of 38 children, 16 like cricket, 28 like football and 11 like both. How many like neither? (a) 6 (b) 16 (c) 11 (d) 5
14. 14.In a class of 23 children, 15 like dance, 13 like music and 8 like both. How many like neither? (a) 8 (b) 4 (c) 3 (d) 11
15. 15.In a class of 35 children, 18 like cricket, 19 like football and 5 like neither. How many like both? (a) 5 (b) 30 (c) 2 (d) 7
16. 16.In a class of 34 children, 24 like tea, 16 like coffee and 8 like both. How many like only tea? (a) 18 (b) 16 (c) 8 (d) 24
17. 17.In a class of 40 children, 22 like mangoes, 17 like bananas and 2 like both. How many like only mangoes? (a) 22 (b) 23 (c) 15 (d) 20
18. 18.In a class of 47 children, 26 like mangoes, 22 like bananas and 8 like both. How many like neither? (a) 7 (b) 15 (c) 6 (d) 8
19. 19.In a class of 36 children, 16 like tea, 12 like coffee and 2 like both. How many like only tea? (a) 24 (b) 16 (c) 14 (d) 10
20. 20.In a class of 31 children, 17 like cricket, 24 like football and 11 like both. How many like only cricket? (a) 13 (b) 6 (c) 7 (d) 17
21. 21.In a class of 34 children, 25 like maths, 10 like science and 6 like both. How many like neither? (a) 6 (b) 11 (c) 5 (d) 4
22. 22.In a class of 17 children, 13 like tea, 8 like coffee and 5 like both. How many like only tea? (a) 3 (b) 9 (c) 8 (d) 13
23. 23.In a class of 36 children, 21 like tea, 11 like coffee and 9 like neither. How many like both? (a) 6 (b) 27 (c) 9 (d) 5
24. 24.In a class of 34 children, 18 like mangoes, 16 like bananas and 8 like both. How many like neither? (a) 0 (b) 8 (c) 16 (d) 9
25. 25.In a class of 24 children, 17 like dance, 14 like music and 9 like both. How many like only dance? (a) 5 (b) 17 (c) 10 (d) 8
26. 26.In a class of 23 children, 8 like tea, 16 like coffee and 5 like both. How many like at least one of the two? (a) 24 (b) 14 (c) 23 (d) 19
27. 27.In a class of 21 children, 11 like maths, 14 like science and 1 like neither. How many like both? (a) 4 (b) 5 (c) 20 (d) 1
28. 28.In a class of 48 children, 21 like mangoes, 25 like bananas and 6 like both. How many like at least one of the two? (a) 34 (b) 40 (c) 48 (d) 46
29. 29.In a class of 44 children, 31 like dance, 21 like music and 4 like neither. How many like both? (a) 40 (b) 12 (c) 8 (d) 4
30. 30.In a class of 38 children, 18 like dance, 22 like music and 3 like neither. How many like both? (a) 5 (b) 3 (c) 35 (d) 2
31. 31.In a class of 34 children, 23 like tea, 14 like coffee and 11 like both. How many like only tea? (a) 12 (b) 3 (c) 20 (d) 23
32. 32.In a class of 18 children, 9 like maths, 11 like science and 6 like both. How many like at least one of the two? (a) 8 (b) 20 (c) 14 (d) 18
33. 33.In a class of 27 children, 12 like maths, 19 like science and 5 like both. How many like neither? (a) 1 (b) 6 (c) 5 (d) 2
34. 34.In a class of 40 children, 22 like dance, 16 like music and 7 like both. How many like only dance? (a) 24 (b) 9 (c) 22 (d) 15
35. 35.In a class of 30 children, 22 like maths, 8 like science and 4 like both. How many like at least one of the two? (a) 30 (b) 27 (c) 26 (d) 22
36. 36.In a class of 25 children, 15 like dance, 6 like music and 2 like both. How many like neither? (a) 4 (b) 8 (c) 2 (d) 6
37. 37.In a class of 35 children, 25 like maths, 12 like science and 5 like neither. How many like both? (a) 30 (b) 5 (c) 2 (d) 7
38. 38.In a class of 27 children, 12 like cricket, 19 like football and 1 like neither. How many like both? (a) 4 (b) 26 (c) 1 (d) 5
39. 39.In a class of 24 children, 9 like cricket, 13 like football and 6 like neither. How many like both? (a) 6 (b) 18 (c) 5 (d) 4
40. 40.In a class of 34 children, 20 like maths, 18 like science and 8 like both. How many like at least one of the two? (a) 30 (b) 38 (c) 34 (d) 22

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