Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 667 · 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 14 children, 8 like maths, 8 like science and 3 like both. How many like neither? (a) 4 (b) 1 (c) 2 (d) 3
2. 2.In a class of 26 children, 16 like tea, 10 like coffee and 2 like both. How many like neither? (a) 4 (b) 2 (c) 0 (d) 3
3. 3.In a class of 34 children, 16 like cricket, 23 like football and 7 like both. How many like neither? (a) 3 (b) 7 (c) 2 (d) 9
4. 4.In a class of 30 children, 12 like tea, 19 like coffee and 8 like neither. How many like both? (a) 9 (b) 1 (c) 22 (d) 8
5. 5.In a class of 33 children, 20 like maths, 13 like science and 8 like neither. How many like both? (a) 8 (b) 9 (c) 7 (d) 25
6. 6.In a class of 50 children, 29 like mangoes, 29 like bananas and 9 like both. How many like at least one of the two? (a) 49 (b) 40 (c) 58 (d) 50
7. 7.In a class of 40 children, 24 like dance, 12 like music and 6 like both. How many like neither? (a) 6 (b) 10 (c) 16 (d) 4
8. 8.In a class of 20 children, 12 like tea, 5 like coffee and 2 like both. How many like at least one of the two? (a) 15 (b) 13 (c) 20 (d) 17
9. 9.In a class of 40 children, 22 like dance, 13 like music and 3 like both. How many like neither? (a) 5 (b) 3 (c) 8 (d) 11
10. 10.In a class of 26 children, 14 like dance, 18 like music and 4 like neither. How many like both? (a) 6 (b) 10 (c) 22 (d) 4
11. 11.In a class of 24 children, 8 like mangoes, 16 like bananas and 2 like both. How many like neither? (a) 3 (b) 4 (c) 0 (d) 2
12. 12.In a class of 30 children, 22 like dance, 13 like music and 6 like both. How many like at least one of the two? (a) 30 (b) 29 (c) 35 (d) 23
13. 13.In a class of 28 children, 17 like maths, 9 like science and 4 like both. How many like neither? (a) 4 (b) 6 (c) 2 (d) 10
14. 14.In a class of 34 children, 10 like maths, 24 like science and 4 like both. How many like only maths? (a) 20 (b) 6 (c) 10 (d) 4
15. 15.In a class of 26 children, 14 like tea, 18 like coffee and 5 like neither. How many like both? (a) 21 (b) 11 (c) 5 (d) 6
16. 16.In a class of 26 children, 7 like mangoes, 13 like bananas and 4 like both. How many like neither? (a) 6 (b) 10 (c) 4 (d) 14
17. 17.In a class of 37 children, 22 like mangoes, 11 like bananas and 3 like both. How many like at least one of the two? (a) 37 (b) 33 (c) 27 (d) 30
18. 18.In a class of 27 children, 20 like tea, 6 like coffee and 2 like both. How many like at least one of the two? (a) 22 (b) 24 (c) 26 (d) 27
19. 19.In a class of 30 children, 19 like tea, 11 like coffee and 6 like both. How many like neither? (a) 0 (b) 12 (c) 7 (d) 6
20. 20.In a class of 32 children, 14 like maths, 17 like science and 8 like neither. How many like both? (a) 6 (b) 24 (c) 7 (d) 8
21. 21.In a class of 45 children, 28 like maths, 15 like science and 8 like both. How many like neither? (a) 2 (b) 8 (c) 10 (d) 18
22. 22.In a class of 37 children, 18 like cricket, 21 like football and 5 like both. How many like at least one of the two? (a) 29 (b) 34 (c) 39 (d) 37
23. 23.In a class of 29 children, 10 like maths, 25 like science and 7 like both. How many like neither? (a) 2 (b) 1 (c) 7 (d) 8
24. 24.In a class of 15 children, 10 like dance, 10 like music and 7 like both. How many like at least one of the two? (a) 13 (b) 15 (c) 20 (d) 6
25. 25.In a class of 26 children, 14 like mangoes, 11 like bananas and 2 like both. How many like neither? (a) 2 (b) 5 (c) 3 (d) 1
26. 26.In a class of 37 children, 26 like dance, 15 like music and 7 like neither. How many like both? (a) 30 (b) 4 (c) 11 (d) 7
27. 27.In a class of 26 children, 10 like dance, 17 like music and 4 like both. How many like at least one of the two? (a) 23 (b) 27 (c) 26 (d) 19
28. 28.In a class of 21 children, 13 like cricket, 15 like football and 9 like both. How many like neither? (a) 11 (b) 3 (c) 9 (d) 2
29. 29.In a class of 40 children, 15 like dance, 27 like music and 9 like both. How many like neither? (a) 16 (b) 7 (c) 8 (d) 9
30. 30.In a class of 31 children, 11 like tea, 18 like coffee and 7 like both. How many like neither? (a) 2 (b) 16 (c) 9 (d) 7
31. 31.In a class of 44 children, 32 like maths, 15 like science and 12 like both. How many like neither? (a) 21 (b) 9 (c) 10 (d) 12
32. 32.In a class of 45 children, 25 like mangoes, 16 like bananas and 6 like both. How many like only mangoes? (a) 25 (b) 19 (c) 10 (d) 29
33. 33.In a class of 37 children, 25 like maths, 18 like science and 7 like both. How many like at least one of the two? (a) 43 (b) 29 (c) 36 (d) 37
34. 34.In a class of 27 children, 22 like cricket, 8 like football and 4 like both. How many like only cricket? (a) 4 (b) 18 (c) 22 (d) 19
35. 35.In a class of 34 children, 16 like maths, 24 like science and 9 like both. How many like only maths? (a) 7 (b) 15 (c) 10 (d) 16
36. 36.In a class of 45 children, 21 like mangoes, 25 like bananas and 10 like both. How many like neither? (a) 19 (b) 9 (c) 8 (d) 10
37. 37.In a class of 34 children, 21 like dance, 10 like music and 3 like both. How many like at least one of the two? (a) 31 (b) 34 (c) 25 (d) 28
38. 38.In a class of 38 children, 16 like maths, 18 like science and 5 like both. How many like at least one of the two? (a) 34 (b) 29 (c) 24 (d) 38
39. 39.In a class of 32 children, 8 like cricket, 24 like football and 4 like both. How many like neither? (a) 8 (b) 4 (c) 5 (d) 0
40. 40.In a class of 54 children, 28 like maths, 28 like science and 12 like both. How many like only maths? (a) 28 (b) 12 (c) 16 (d) 26

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