Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 324 · 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 26 children, 19 like maths, 7 like science and 4 like both. How many like only maths? (a) 19 (b) 4 (c) 3 (d) 15
2. 2.In a class of 32 children, 22 like mangoes, 11 like bananas and 2 like both. How many like only mangoes? (a) 22 (b) 21 (c) 9 (d) 20
3. 3.In a class of 34 children, 13 like dance, 24 like music and 5 like both. How many like only dance? (a) 13 (b) 8 (c) 19 (d) 10
4. 4.In a class of 44 children, 27 like maths, 22 like science and 9 like both. How many like at least one of the two? (a) 49 (b) 31 (c) 44 (d) 40
5. 5.In a class of 41 children, 19 like dance, 25 like music and 6 like neither. How many like both? (a) 3 (b) 6 (c) 35 (d) 9
6. 6.In a class of 37 children, 11 like maths, 22 like science and 3 like both. How many like neither? (a) 10 (b) 7 (c) 3 (d) 4
7. 7.In a class of 32 children, 22 like cricket, 11 like football and 4 like both. How many like neither? (a) 2 (b) 7 (c) 4 (d) 3
8. 8.In a class of 39 children, 21 like mangoes, 20 like bananas and 4 like both. How many like neither? (a) 6 (b) 3 (c) 2 (d) 4
9. 9.In a class of 26 children, 11 like mangoes, 12 like bananas and 6 like both. How many like neither? (a) 9 (b) 3 (c) 15 (d) 6
10. 10.In a class of 22 children, 10 like dance, 12 like music and 4 like both. How many like neither? (a) 5 (b) 4 (c) 8 (d) 0
11. 11.In a class of 40 children, 10 like maths, 22 like science and 10 like neither. How many like both? (a) 2 (b) 10 (c) 30 (d) 3
12. 12.In a class of 48 children, 28 like cricket, 28 like football and 2 like neither. How many like both? (a) 10 (b) 46 (c) 2 (d) 8
13. 13.In a class of 32 children, 9 like cricket, 23 like football and 3 like both. How many like only cricket? (a) 9 (b) 20 (c) 6 (d) 3
14. 14.In a class of 36 children, 17 like mangoes, 16 like bananas and 4 like both. How many like at least one of the two? (a) 29 (b) 36 (c) 33 (d) 25
15. 15.In a class of 38 children, 22 like mangoes, 14 like bananas and 7 like neither. How many like both? (a) 6 (b) 31 (c) 5 (d) 7
16. 16.In a class of 27 children, 14 like maths, 17 like science and 6 like both. How many like at least one of the two? (a) 25 (b) 19 (c) 27 (d) 31
17. 17.In a class of 29 children, 8 like cricket, 22 like football and 2 like neither. How many like both? (a) 1 (b) 2 (c) 3 (d) 27
18. 18.In a class of 25 children, 19 like mangoes, 15 like bananas and 3 like neither. How many like both? (a) 9 (b) 3 (c) 22 (d) 12
19. 19.In a class of 23 children, 12 like mangoes, 11 like bananas and 3 like neither. How many like both? (a) 20 (b) 3 (c) 2 (d) 4
20. 20.In a class of 48 children, 20 like maths, 21 like science and 9 like neither. How many like both? (a) 2 (b) 9 (c) 3 (d) 39
21. 21.In a class of 45 children, 28 like mangoes, 17 like bananas and 10 like both. How many like neither? (a) 11 (b) 0 (c) 20 (d) 10
22. 22.In a class of 33 children, 23 like maths, 9 like science and 6 like both. How many like only maths? (a) 23 (b) 17 (c) 24 (d) 3
23. 23.In a class of 30 children, 12 like cricket, 22 like football and 6 like both. How many like neither? (a) 2 (b) 3 (c) 6 (d) 8
24. 24.In a class of 27 children, 14 like cricket, 18 like football and 6 like both. How many like at least one of the two? (a) 27 (b) 32 (c) 20 (d) 26
25. 25.In a class of 19 children, 8 like cricket, 11 like football and 4 like both. How many like at least one of the two? (a) 16 (b) 19 (c) 11 (d) 15
26. 26.In a class of 38 children, 10 like tea, 27 like coffee and 7 like both. How many like neither? (a) 1 (b) 7 (c) 8 (d) 15
27. 27.In a class of 37 children, 21 like cricket, 13 like football and 5 like both. How many like at least one of the two? (a) 34 (b) 37 (c) 24 (d) 29
28. 28.In a class of 43 children, 18 like tea, 22 like coffee and 2 like both. How many like at least one of the two? (a) 40 (b) 43 (c) 36 (d) 38
29. 29.In a class of 39 children, 21 like dance, 22 like music and 11 like both. How many like only dance? (a) 10 (b) 11 (c) 17 (d) 21
30. 30.In a class of 19 children, 11 like mangoes, 10 like bananas and 4 like both. How many like at least one of the two? (a) 13 (b) 19 (c) 17 (d) 21
31. 31.In a class of 28 children, 13 like cricket, 13 like football and 5 like both. How many like only cricket? (a) 13 (b) 8 (c) 15 (d) 5
32. 32.In a class of 45 children, 19 like maths, 27 like science and 9 like both. How many like only maths? (a) 10 (b) 18 (c) 9 (d) 19
33. 33.In a class of 28 children, 9 like tea, 18 like coffee and 5 like both. How many like neither? (a) 6 (b) 1 (c) 5 (d) 11
34. 34.In a class of 49 children, 25 like cricket, 25 like football and 10 like both. How many like neither? (a) 8 (b) 19 (c) 9 (d) 10
35. 35.In a class of 36 children, 22 like cricket, 13 like football and 7 like both. How many like only cricket? (a) 23 (b) 22 (c) 15 (d) 6
36. 36.In a class of 20 children, 9 like tea, 7 like coffee and 2 like both. How many like at least one of the two? (a) 14 (b) 20 (c) 12 (d) 16
37. 37.In a class of 34 children, 7 like cricket, 23 like football and 4 like both. How many like only cricket? (a) 7 (b) 3 (c) 11 (d) 19
38. 38.In a class of 34 children, 14 like tea, 28 like coffee and 2 like neither. How many like both? (a) 2 (b) 10 (c) 32 (d) 8
39. 39.In a class of 21 children, 11 like maths, 9 like science and 6 like both. How many like at least one of the two? (a) 21 (b) 8 (c) 14 (d) 20
40. 40.In a class of 44 children, 22 like tea, 22 like coffee and 9 like neither. How many like both? (a) 9 (b) 35 (c) 8 (d) 10

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