Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 120 · 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 41 children, 24 like cricket, 14 like football and 6 like both. How many like neither? (a) 15 (b) 9 (c) 6 (d) 3
2. 2.In a class of 35 children, 14 like maths, 21 like science and 4 like both. How many like at least one of the two? (a) 27 (b) 32 (c) 31 (d) 35
3. 3.In a class of 21 children, 15 like mangoes, 13 like bananas and 10 like both. How many like at least one of the two? (a) 28 (b) 8 (c) 18 (d) 21
4. 4.In a class of 41 children, 22 like mangoes, 24 like bananas and 8 like both. How many like at least one of the two? (a) 30 (b) 41 (c) 38 (d) 46
5. 5.In a class of 52 children, 25 like maths, 26 like science and 7 like neither. How many like both? (a) 5 (b) 7 (c) 45 (d) 6
6. 6.In a class of 38 children, 16 like tea, 25 like coffee and 5 like neither. How many like both? (a) 5 (b) 3 (c) 33 (d) 8
7. 7.In a class of 31 children, 15 like mangoes, 19 like bananas and 6 like both. How many like at least one of the two? (a) 31 (b) 28 (c) 34 (d) 22
8. 8.In a class of 37 children, 15 like maths, 22 like science and 2 like both. How many like neither? (a) 3 (b) 4 (c) 2 (d) 0
9. 9.In a class of 31 children, 22 like maths, 11 like science and 3 like both. How many like neither? (a) 3 (b) 2 (c) 4 (d) 1
10. 10.In a class of 33 children, 22 like dance, 8 like music and 4 like both. How many like neither? (a) 7 (b) 4 (c) 3 (d) 11
11. 11.In a class of 37 children, 29 like dance, 18 like music and 12 like both. How many like only dance? (a) 19 (b) 6 (c) 17 (d) 29
12. 12.In a class of 24 children, 8 like maths, 15 like science and 4 like both. How many like only maths? (a) 9 (b) 8 (c) 11 (d) 4
13. 13.In a class of 50 children, 27 like dance, 28 like music and 9 like both. How many like only dance? (a) 27 (b) 22 (c) 18 (d) 19
14. 14.In a class of 32 children, 19 like mangoes, 16 like bananas and 12 like both. How many like neither? (a) 9 (b) 10 (c) 12 (d) 21
15. 15.In a class of 48 children, 23 like maths, 25 like science and 9 like both. How many like at least one of the two? (a) 40 (b) 39 (c) 30 (d) 48
16. 16.In a class of 53 children, 30 like mangoes, 27 like bananas and 11 like both. How many like neither? (a) 11 (b) 18 (c) 7 (d) 8
17. 17.In a class of 34 children, 16 like dance, 26 like music and 4 like neither. How many like both? (a) 4 (b) 12 (c) 8 (d) 30
18. 18.In a class of 33 children, 19 like dance, 16 like music and 7 like both. How many like at least one of the two? (a) 21 (b) 35 (c) 28 (d) 33
19. 19.In a class of 34 children, 25 like dance, 14 like music and 8 like both. How many like neither? (a) 4 (b) 11 (c) 8 (d) 3
20. 20.In a class of 38 children, 25 like dance, 15 like music and 5 like neither. How many like both? (a) 5 (b) 7 (c) 33 (d) 2
21. 21.In a class of 36 children, 23 like dance, 13 like music and 4 like both. How many like at least one of the two? (a) 32 (b) 33 (c) 28 (d) 36
22. 22.In a class of 28 children, 10 like cricket, 15 like football and 7 like neither. How many like both? (a) 7 (b) 4 (c) 5 (d) 21
23. 23.In a class of 37 children, 19 like maths, 19 like science and 3 like both. How many like only maths? (a) 19 (b) 18 (c) 3 (d) 16
24. 24.In a class of 24 children, 16 like mangoes, 16 like bananas and 11 like both. How many like only mangoes? (a) 8 (b) 16 (c) 11 (d) 5
25. 25.In a class of 43 children, 24 like maths, 19 like science and 4 like both. How many like only maths? (a) 24 (b) 15 (c) 4 (d) 20
26. 26.In a class of 29 children, 6 like cricket, 21 like football and 3 like both. How many like only cricket? (a) 8 (b) 3 (c) 18 (d) 6
27. 27.In a class of 36 children, 19 like cricket, 11 like football and 9 like neither. How many like both? (a) 27 (b) 4 (c) 9 (d) 3
28. 28.In a class of 41 children, 17 like maths, 24 like science and 5 like both. How many like neither? (a) 5 (b) 6 (c) 0 (d) 10
29. 29.In a class of 33 children, 18 like dance, 20 like music and 5 like neither. How many like both? (a) 28 (b) 10 (c) 11 (d) 5
30. 30.In a class of 32 children, 10 like cricket, 24 like football and 4 like both. How many like only cricket? (a) 20 (b) 6 (c) 10 (d) 8
31. 31.In a class of 33 children, 23 like cricket, 8 like football and 3 like both. How many like neither? (a) 2 (b) 8 (c) 3 (d) 5
32. 32.In a class of 24 children, 9 like maths, 11 like science and 10 like neither. How many like both? (a) 6 (b) 10 (c) 7 (d) 14
33. 33.In a class of 29 children, 16 like cricket, 14 like football and 11 like both. How many like neither? (a) 10 (b) 11 (c) 9 (d) 21
34. 34.In a class of 35 children, 12 like cricket, 19 like football and 3 like both. How many like at least one of the two? (a) 35 (b) 28 (c) 25 (d) 31
35. 35.In a class of 32 children, 18 like mangoes, 12 like bananas and 8 like both. How many like at least one of the two? (a) 14 (b) 22 (c) 32 (d) 30
36. 36.In a class of 35 children, 9 like cricket, 19 like football and 3 like both. How many like only cricket? (a) 6 (b) 9 (c) 16 (d) 3
37. 37.In a class of 35 children, 17 like maths, 12 like science and 3 like both. How many like only maths? (a) 17 (b) 9 (c) 14 (d) 23
38. 38.In a class of 33 children, 22 like maths, 18 like science and 3 like neither. How many like both? (a) 30 (b) 10 (c) 7 (d) 3
39. 39.In a class of 54 children, 25 like cricket, 25 like football and 5 like both. How many like only cricket? (a) 29 (b) 25 (c) 20 (d) 5
40. 40.In a class of 46 children, 25 like maths, 25 like science and 8 like both. How many like at least one of the two? (a) 34 (b) 46 (c) 42 (d) 50

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