Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 188 · 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 37 children, 8 like maths, 21 like science and 10 like neither. How many like both? (a) 3 (b) 10 (c) 2 (d) 27
2. 2.In a class of 34 children, 7 like mangoes, 21 like bananas and 4 like both. How many like neither? (a) 4 (b) 6 (c) 10 (d) 14
3. 3.In a class of 21 children, 13 like dance, 13 like music and 3 like neither. How many like both? (a) 5 (b) 3 (c) 8 (d) 18
4. 4.In a class of 39 children, 24 like mangoes, 16 like bananas and 5 like both. How many like only mangoes? (a) 24 (b) 19 (c) 11 (d) 23
5. 5.In a class of 40 children, 21 like dance, 22 like music and 5 like neither. How many like both? (a) 3 (b) 5 (c) 35 (d) 8
6. 6.In a class of 21 children, 16 like maths, 6 like science and 1 like neither. How many like both? (a) 20 (b) 1 (c) 2 (d) 3
7. 7.In a class of 43 children, 14 like cricket, 29 like football and 9 like both. How many like only cricket? (a) 9 (b) 14 (c) 20 (d) 5
8. 8.In a class of 39 children, 20 like cricket, 25 like football and 9 like both. How many like only cricket? (a) 16 (b) 11 (c) 20 (d) 14
9. 9.In a class of 26 children, 15 like mangoes, 17 like bananas and 9 like both. How many like only mangoes? (a) 15 (b) 9 (c) 8 (d) 6
10. 10.In a class of 45 children, 27 like tea, 20 like coffee and 6 like neither. How many like both? (a) 2 (b) 39 (c) 8 (d) 6
11. 11.In a class of 15 children, 10 like maths, 11 like science and 7 like both. How many like at least one of the two? (a) 7 (b) 21 (c) 14 (d) 15
12. 12.In a class of 27 children, 18 like tea, 5 like coffee and 2 like both. How many like only tea? (a) 16 (b) 22 (c) 18 (d) 3
13. 13.In a class of 41 children, 25 like cricket, 17 like football and 7 like both. How many like only cricket? (a) 10 (b) 18 (c) 25 (d) 24
14. 14.In a class of 38 children, 29 like tea, 15 like coffee and 3 like neither. How many like both? (a) 6 (b) 3 (c) 35 (d) 9
15. 15.In a class of 34 children, 11 like maths, 19 like science and 8 like neither. How many like both? (a) 8 (b) 5 (c) 26 (d) 4
16. 16.In a class of 48 children, 26 like tea, 21 like coffee and 9 like both. How many like at least one of the two? (a) 48 (b) 38 (c) 47 (d) 29
17. 17.In a class of 41 children, 17 like maths, 19 like science and 5 like both. How many like neither? (a) 10 (b) 15 (c) 5 (d) 11
18. 18.In a class of 43 children, 16 like mangoes, 30 like bananas and 12 like both. How many like only mangoes? (a) 13 (b) 16 (c) 18 (d) 4
19. 19.In a class of 33 children, 13 like mangoes, 24 like bananas and 5 like neither. How many like both? (a) 5 (b) 9 (c) 28 (d) 4
20. 20.In a class of 41 children, 26 like mangoes, 14 like bananas and 6 like both. How many like at least one of the two? (a) 34 (b) 28 (c) 41 (d) 40
21. 21.In a class of 38 children, 27 like cricket, 18 like football and 11 like both. How many like neither? (a) 15 (b) 4 (c) 5 (d) 11
22. 22.In a class of 38 children, 21 like dance, 16 like music and 7 like both. How many like at least one of the two? (a) 30 (b) 37 (c) 23 (d) 38
23. 23.In a class of 46 children, 23 like maths, 28 like science and 3 like neither. How many like both? (a) 5 (b) 3 (c) 8 (d) 43
24. 24.In a class of 36 children, 10 like tea, 20 like coffee and 3 like both. How many like neither? (a) 9 (b) 12 (c) 6 (d) 3
25. 25.In a class of 17 children, 9 like cricket, 6 like football and 4 like neither. How many like both? (a) 13 (b) 3 (c) 4 (d) 2
26. 26.In a class of 37 children, 18 like maths, 25 like science and 6 like neither. How many like both? (a) 12 (b) 31 (c) 6 (d) 13
27. 27.In a class of 45 children, 25 like maths, 18 like science and 10 like neither. How many like both? (a) 35 (b) 10 (c) 9 (d) 8
28. 28.In a class of 48 children, 24 like mangoes, 24 like bananas and 4 like both. How many like at least one of the two? (a) 48 (b) 45 (c) 44 (d) 40
29. 29.In a class of 25 children, 19 like tea, 15 like coffee and 12 like both. How many like neither? (a) 3 (b) 12 (c) 15 (d) 4
30. 30.In a class of 32 children, 7 like maths, 19 like science and 10 like neither. How many like both? (a) 10 (b) 5 (c) 4 (d) 22
31. 31.In a class of 25 children, 12 like dance, 14 like music and 9 like both. How many like at least one of the two? (a) 8 (b) 26 (c) 17 (d) 25
32. 32.In a class of 18 children, 8 like mangoes, 12 like bananas and 5 like both. How many like neither? (a) 3 (b) 5 (c) 8 (d) 4
33. 33.In a class of 25 children, 9 like maths, 17 like science and 3 like neither. How many like both? (a) 4 (b) 3 (c) 1 (d) 22
34. 34.In a class of 35 children, 24 like mangoes, 8 like bananas and 4 like both. How many like neither? (a) 7 (b) 4 (c) 11 (d) 3
35. 35.In a class of 34 children, 14 like maths, 20 like science and 4 like both. How many like at least one of the two? (a) 26 (b) 30 (c) 34 (d) 31
36. 36.In a class of 37 children, 22 like maths, 9 like science and 3 like both. How many like at least one of the two? (a) 25 (b) 37 (c) 31 (d) 28
37. 37.In a class of 35 children, 12 like maths, 22 like science and 9 like both. How many like only maths? (a) 13 (b) 12 (c) 3 (d) 9
38. 38.In a class of 44 children, 24 like cricket, 18 like football and 8 like neither. How many like both? (a) 36 (b) 6 (c) 7 (d) 8
39. 39.In a class of 18 children, 9 like tea, 7 like coffee and 3 like both. How many like neither? (a) 8 (b) 3 (c) 5 (d) 2
40. 40.In a class of 44 children, 19 like mangoes, 27 like bananas and 8 like both. How many like neither? (a) 7 (b) 14 (c) 8 (d) 6

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