Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 982 · 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 27 children, 17 like cricket, 16 like football and 10 like both. How many like neither? (a) 10 (b) 4 (c) 14 (d) 5
2. 2.In a class of 28 children, 11 like dance, 18 like music and 5 like both. How many like at least one of the two? (a) 19 (b) 24 (c) 28 (d) 29
3. 3.In a class of 26 children, 9 like tea, 20 like coffee and 5 like both. How many like at least one of the two? (a) 19 (b) 26 (c) 24 (d) 29
4. 4.In a class of 33 children, 20 like dance, 18 like music and 4 like neither. How many like both? (a) 4 (b) 5 (c) 29 (d) 9
5. 5.In a class of 32 children, 24 like maths, 13 like science and 2 like neither. How many like both? (a) 30 (b) 2 (c) 7 (d) 5
6. 6.In a class of 42 children, 20 like tea, 21 like coffee and 5 like neither. How many like both? (a) 3 (b) 5 (c) 37 (d) 4
7. 7.In a class of 31 children, 20 like cricket, 14 like football and 3 like neither. How many like both? (a) 7 (b) 28 (c) 6 (d) 3
8. 8.In a class of 17 children, 8 like cricket, 10 like football and 2 like both. How many like only cricket? (a) 2 (b) 7 (c) 8 (d) 6
9. 9.In a class of 21 children, 13 like tea, 7 like coffee and 4 like neither. How many like both? (a) 3 (b) 4 (c) 17 (d) 2
10. 10.In a class of 39 children, 17 like cricket, 14 like football and 2 like both. How many like at least one of the two? (a) 27 (b) 39 (c) 29 (d) 31
11. 11.In a class of 33 children, 22 like tea, 13 like coffee and 10 like both. How many like neither? (a) 18 (b) 10 (c) 9 (d) 8
12. 12.In a class of 37 children, 31 like dance, 15 like music and 2 like neither. How many like both? (a) 35 (b) 2 (c) 11 (d) 9
13. 13.In a class of 31 children, 8 like dance, 21 like music and 7 like neither. How many like both? (a) 24 (b) 7 (c) 6 (d) 5
14. 14.In a class of 24 children, 16 like maths, 8 like science and 5 like both. How many like only maths? (a) 16 (b) 11 (c) 5 (d) 3
15. 15.In a class of 35 children, 24 like tea, 19 like coffee and 11 like both. How many like neither? (a) 3 (b) 11 (c) 4 (d) 14
16. 16.In a class of 40 children, 12 like tea, 25 like coffee and 8 like neither. How many like both? (a) 8 (b) 5 (c) 6 (d) 32
17. 17.In a class of 40 children, 23 like mangoes, 24 like bananas and 3 like neither. How many like both? (a) 10 (b) 37 (c) 3 (d) 7
18. 18.In a class of 36 children, 10 like cricket, 23 like football and 7 like both. How many like at least one of the two? (a) 36 (b) 19 (c) 33 (d) 26
19. 19.In a class of 30 children, 24 like cricket, 7 like football and 4 like both. How many like only cricket? (a) 3 (b) 23 (c) 20 (d) 24
20. 20.In a class of 13 children, 6 like dance, 8 like music and 2 like both. How many like at least one of the two? (a) 13 (b) 12 (c) 14 (d) 10
21. 21.In a class of 28 children, 23 like cricket, 10 like football and 6 like both. How many like neither? (a) 2 (b) 7 (c) 6 (d) 1
22. 22.In a class of 25 children, 11 like dance, 8 like music and 2 like both. How many like at least one of the two? (a) 19 (b) 15 (c) 25 (d) 17
23. 23.In a class of 26 children, 8 like cricket, 11 like football and 3 like both. How many like at least one of the two? (a) 13 (b) 26 (c) 16 (d) 19
24. 24.In a class of 32 children, 16 like maths, 14 like science and 3 like both. How many like neither? (a) 5 (b) 8 (c) 3 (d) 2
25. 25.In a class of 24 children, 10 like maths, 8 like science and 2 like both. How many like at least one of the two? (a) 18 (b) 24 (c) 16 (d) 14
26. 26.In a class of 19 children, 10 like dance, 10 like music and 3 like neither. How many like both? (a) 4 (b) 16 (c) 1 (d) 3
27. 27.In a class of 30 children, 15 like mangoes, 11 like bananas and 8 like neither. How many like both? (a) 5 (b) 22 (c) 8 (d) 4
28. 28.In a class of 37 children, 10 like tea, 25 like coffee and 7 like neither. How many like both? (a) 30 (b) 7 (c) 5 (d) 6
29. 29.In a class of 39 children, 20 like maths, 20 like science and 9 like both. How many like neither? (a) 8 (b) 9 (c) 17 (d) 7
30. 30.In a class of 30 children, 21 like mangoes, 10 like bananas and 3 like both. How many like only mangoes? (a) 18 (b) 21 (c) 7 (d) 20
31. 31.In a class of 28 children, 6 like cricket, 18 like football and 3 like both. How many like at least one of the two? (a) 21 (b) 24 (c) 28 (d) 18
32. 32.In a class of 40 children, 19 like maths, 20 like science and 5 like neither. How many like both? (a) 3 (b) 4 (c) 35 (d) 5
33. 33.In a class of 42 children, 12 like cricket, 27 like football and 7 like both. How many like neither? (a) 3 (b) 17 (c) 7 (d) 10
34. 34.In a class of 42 children, 21 like cricket, 19 like football and 7 like both. How many like neither? (a) 9 (b) 2 (c) 16 (d) 7
35. 35.In a class of 33 children, 18 like mangoes, 18 like bananas and 4 like both. How many like only mangoes? (a) 14 (b) 18 (c) 15 (d) 4
36. 36.In a class of 36 children, 12 like tea, 16 like coffee and 2 like both. How many like at least one of the two? (a) 24 (b) 36 (c) 28 (d) 26
37. 37.In a class of 35 children, 28 like dance, 17 like music and 12 like both. How many like at least one of the two? (a) 45 (b) 33 (c) 35 (d) 21
38. 38.In a class of 46 children, 27 like cricket, 23 like football and 7 like neither. How many like both? (a) 4 (b) 39 (c) 7 (d) 11
39. 39.In a class of 24 children, 16 like mangoes, 9 like bananas and 5 like neither. How many like both? (a) 5 (b) 19 (c) 6 (d) 1
40. 40.In a class of 57 children, 28 like mangoes, 28 like bananas and 8 like both. How many like at least one of the two? (a) 56 (b) 57 (c) 40 (d) 48

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