Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 713 · 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 33 children, 28 like cricket, 13 like football and 1 like neither. How many like both? (a) 9 (b) 8 (c) 1 (d) 32
2. 2.In a class of 36 children, 20 like maths, 14 like science and 8 like both. How many like neither? (a) 8 (b) 10 (c) 18 (d) 2
3. 3.In a class of 37 children, 19 like tea, 12 like coffee and 10 like neither. How many like both? (a) 27 (b) 10 (c) 4 (d) 5
4. 4.In a class of 39 children, 21 like tea, 18 like coffee and 7 like both. How many like neither? (a) 0 (b) 14 (c) 7 (d) 8
5. 5.In a class of 39 children, 16 like cricket, 24 like football and 8 like both. How many like only cricket? (a) 8 (b) 9 (c) 16 (d) 15
6. 6.In a class of 43 children, 19 like dance, 24 like music and 7 like both. How many like only dance? (a) 17 (b) 7 (c) 19 (d) 12
7. 7.In a class of 48 children, 32 like maths, 26 like science and 12 like both. How many like only maths? (a) 14 (b) 20 (c) 22 (d) 32
8. 8.In a class of 33 children, 17 like dance, 26 like music and 1 like neither. How many like both? (a) 10 (b) 1 (c) 32 (d) 11
9. 9.In a class of 16 children, 6 like mangoes, 6 like bananas and 2 like both. How many like only mangoes? (a) 4 (b) 2 (c) 10 (d) 6
10. 10.In a class of 29 children, 15 like dance, 17 like music and 4 like both. How many like at least one of the two? (a) 28 (b) 32 (c) 29 (d) 24
11. 11.In a class of 30 children, 15 like mangoes, 14 like bananas and 7 like both. How many like at least one of the two? (a) 15 (b) 22 (c) 30 (d) 29
12. 12.In a class of 37 children, 12 like cricket, 24 like football and 8 like neither. How many like both? (a) 6 (b) 7 (c) 8 (d) 29
13. 13.In a class of 25 children, 14 like cricket, 16 like football and 2 like neither. How many like both? (a) 23 (b) 2 (c) 7 (d) 5
14. 14.In a class of 35 children, 24 like dance, 11 like music and 5 like neither. How many like both? (a) 30 (b) 6 (c) 4 (d) 5
15. 15.In a class of 21 children, 11 like mangoes, 7 like bananas and 7 like neither. How many like both? (a) 14 (b) 5 (c) 4 (d) 7
16. 16.In a class of 24 children, 18 like maths, 16 like science and 12 like both. How many like neither? (a) 2 (b) 12 (c) 14 (d) 3
17. 17.In a class of 32 children, 23 like tea, 10 like coffee and 3 like both. How many like neither? (a) 1 (b) 5 (c) 3 (d) 2
18. 18.In a class of 25 children, 20 like tea, 12 like coffee and 8 like both. How many like at least one of the two? (a) 16 (b) 32 (c) 25 (d) 24
19. 19.In a class of 27 children, 19 like dance, 18 like music and 1 like neither. How many like both? (a) 26 (b) 1 (c) 11 (d) 10
20. 20.In a class of 48 children, 26 like maths, 22 like science and 8 like neither. How many like both? (a) 9 (b) 7 (c) 40 (d) 8
21. 21.In a class of 26 children, 16 like mangoes, 7 like bananas and 2 like both. How many like neither? (a) 3 (b) 2 (c) 7 (d) 5
22. 22.In a class of 34 children, 16 like tea, 18 like coffee and 8 like neither. How many like both? (a) 8 (b) 7 (c) 9 (d) 26
23. 23.In a class of 40 children, 26 like cricket, 16 like football and 7 like both. How many like at least one of the two? (a) 28 (b) 35 (c) 42 (d) 40
24. 24.In a class of 32 children, 17 like tea, 17 like coffee and 7 like both. How many like only tea? (a) 17 (b) 10 (c) 15 (d) 7
25. 25.In a class of 36 children, 17 like dance, 23 like music and 7 like both. How many like neither? (a) 3 (b) 10 (c) 7 (d) 4
26. 26.In a class of 43 children, 19 like cricket, 22 like football and 8 like neither. How many like both? (a) 35 (b) 6 (c) 7 (d) 8
27. 27.In a class of 23 children, 11 like maths, 18 like science and 8 like both. How many like only maths? (a) 3 (b) 10 (c) 11 (d) 5
28. 28.In a class of 43 children, 24 like cricket, 20 like football and 3 like neither. How many like both? (a) 4 (b) 40 (c) 1 (d) 3
29. 29.In a class of 43 children, 17 like cricket, 25 like football and 6 like both. How many like only cricket? (a) 11 (b) 19 (c) 18 (d) 17
30. 30.In a class of 15 children, 9 like mangoes, 9 like bananas and 2 like neither. How many like both? (a) 2 (b) 3 (c) 13 (d) 5
31. 31.In a class of 37 children, 12 like cricket, 18 like football and 2 like both. How many like only cricket? (a) 19 (b) 10 (c) 12 (d) 16
32. 32.In a class of 33 children, 16 like cricket, 12 like football and 4 like both. How many like neither? (a) 9 (b) 4 (c) 5 (d) 13
33. 33.In a class of 49 children, 26 like mangoes, 26 like bananas and 12 like both. How many like only mangoes? (a) 26 (b) 23 (c) 14 (d) 12
34. 34.In a class of 34 children, 25 like tea, 13 like coffee and 7 like both. How many like neither? (a) 10 (b) 7 (c) 4 (d) 3
35. 35.In a class of 46 children, 29 like mangoes, 19 like bananas and 11 like both. How many like neither? (a) 10 (b) 20 (c) 9 (d) 11
36. 36.In a class of 42 children, 20 like tea, 19 like coffee and 2 like both. How many like only tea? (a) 23 (b) 20 (c) 18 (d) 17
37. 37.In a class of 44 children, 26 like tea, 26 like coffee and 9 like both. How many like only tea? (a) 9 (b) 18 (c) 17 (d) 26
38. 38.In a class of 41 children, 20 like maths, 28 like science and 10 like both. How many like only maths? (a) 18 (b) 13 (c) 20 (d) 10
39. 39.In a class of 34 children, 8 like mangoes, 22 like bananas and 7 like neither. How many like both? (a) 4 (b) 27 (c) 3 (d) 7
40. 40.In a class of 21 children, 14 like cricket, 14 like football and 10 like both. How many like neither? (a) 4 (b) 10 (c) 3 (d) 13

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