Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 178 · 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 36 children, 17 like cricket, 12 like football and 2 like both. How many like at least one of the two? (a) 25 (b) 36 (c) 29 (d) 27
2. 2.In a class of 23 children, 14 like maths, 10 like science and 1 like neither. How many like both? (a) 1 (b) 22 (c) 3 (d) 2
3. 3.In a class of 36 children, 21 like cricket, 11 like football and 2 like both. How many like at least one of the two? (a) 36 (b) 30 (c) 32 (d) 28
4. 4.In a class of 29 children, 21 like tea, 6 like coffee and 3 like both. How many like neither? (a) 5 (b) 2 (c) 8 (d) 3
5. 5.In a class of 33 children, 19 like tea, 13 like coffee and 2 like both. How many like only tea? (a) 20 (b) 19 (c) 17 (d) 11
6. 6.In a class of 45 children, 18 like cricket, 32 like football and 7 like neither. How many like both? (a) 5 (b) 12 (c) 7 (d) 38
7. 7.In a class of 28 children, 18 like dance, 13 like music and 8 like both. How many like at least one of the two? (a) 23 (b) 31 (c) 28 (d) 15
8. 8.In a class of 38 children, 17 like tea, 17 like coffee and 3 like both. How many like neither? (a) 4 (b) 10 (c) 3 (d) 7
9. 9.In a class of 26 children, 21 like dance, 7 like music and 4 like both. How many like at least one of the two? (a) 26 (b) 28 (c) 20 (d) 24
10. 10.In a class of 32 children, 13 like cricket, 20 like football and 10 like both. How many like neither? (a) 9 (b) 10 (c) 19 (d) 8
11. 11.In a class of 36 children, 17 like mangoes, 26 like bananas and 3 like neither. How many like both? (a) 3 (b) 7 (c) 33 (d) 10
12. 12.In a class of 38 children, 13 like maths, 24 like science and 8 like neither. How many like both? (a) 6 (b) 7 (c) 30 (d) 8
13. 13.In a class of 24 children, 13 like maths, 14 like science and 6 like both. How many like neither? (a) 9 (b) 6 (c) 4 (d) 3
14. 14.In a class of 17 children, 7 like mangoes, 5 like bananas and 2 like both. How many like at least one of the two? (a) 12 (b) 8 (c) 10 (d) 17
15. 15.In a class of 35 children, 14 like mangoes, 23 like bananas and 11 like both. How many like neither? (a) 9 (b) 20 (c) 10 (d) 11
16. 16.In a class of 23 children, 7 like maths, 17 like science and 3 like both. How many like at least one of the two? (a) 18 (b) 21 (c) 24 (d) 23
17. 17.In a class of 50 children, 27 like mangoes, 26 like bananas and 8 like neither. How many like both? (a) 3 (b) 42 (c) 11 (d) 8
18. 18.In a class of 37 children, 21 like maths, 16 like science and 8 like both. How many like at least one of the two? (a) 30 (b) 29 (c) 37 (d) 21
19. 19.In a class of 39 children, 19 like cricket, 24 like football and 5 like neither. How many like both? (a) 34 (b) 4 (c) 9 (d) 5
20. 20.In a class of 25 children, 18 like maths, 12 like science and 7 like both. How many like neither? (a) 7 (b) 9 (c) 2 (d) 3
21. 21.In a class of 25 children, 14 like maths, 12 like science and 5 like neither. How many like both? (a) 20 (b) 5 (c) 1 (d) 6
22. 22.In a class of 33 children, 21 like mangoes, 7 like bananas and 7 like neither. How many like both? (a) 7 (b) 3 (c) 2 (d) 26
23. 23.In a class of 28 children, 5 like cricket, 20 like football and 2 like both. How many like only cricket? (a) 18 (b) 5 (c) 3 (d) 8
24. 24.In a class of 33 children, 24 like mangoes, 9 like bananas and 5 like both. How many like at least one of the two? (a) 29 (b) 28 (c) 33 (d) 23
25. 25.In a class of 35 children, 21 like tea, 16 like coffee and 8 like both. How many like neither? (a) 7 (b) 14 (c) 6 (d) 8
26. 26.In a class of 32 children, 21 like dance, 12 like music and 7 like both. How many like neither? (a) 13 (b) 6 (c) 5 (d) 7
27. 27.In a class of 26 children, 11 like cricket, 17 like football and 4 like both. How many like at least one of the two? (a) 20 (b) 28 (c) 24 (d) 26
28. 28.In a class of 48 children, 27 like dance, 28 like music and 9 like both. How many like at least one of the two? (a) 46 (b) 37 (c) 55 (d) 48
29. 29.In a class of 30 children, 12 like cricket, 22 like football and 6 like both. How many like neither? (a) 2 (b) 6 (c) 8 (d) 3
30. 30.In a class of 20 children, 11 like tea, 14 like coffee and 8 like both. How many like only tea? (a) 3 (b) 8 (c) 11 (d) 6
31. 31.In a class of 35 children, 26 like cricket, 12 like football and 6 like both. How many like only cricket? (a) 6 (b) 23 (c) 20 (d) 26
32. 32.In a class of 33 children, 21 like maths, 20 like science and 12 like both. How many like only maths? (a) 8 (b) 21 (c) 13 (d) 9
33. 33.In a class of 33 children, 19 like mangoes, 17 like bananas and 12 like both. How many like only mangoes? (a) 5 (b) 7 (c) 16 (d) 19
34. 34.In a class of 28 children, 22 like tea, 11 like coffee and 7 like both. How many like neither? (a) 2 (b) 7 (c) 3 (d) 9
35. 35.In a class of 20 children, 10 like cricket, 7 like football and 5 like neither. How many like both? (a) 2 (b) 15 (c) 5 (d) 3
36. 36.In a class of 40 children, 13 like cricket, 22 like football and 4 like both. How many like neither? (a) 13 (b) 5 (c) 4 (d) 9
37. 37.In a class of 21 children, 9 like tea, 6 like coffee and 2 like both. How many like only tea? (a) 9 (b) 15 (c) 4 (d) 7
38. 38.In a class of 45 children, 23 like maths, 25 like science and 6 like both. How many like at least one of the two? (a) 42 (b) 48 (c) 36 (d) 45
39. 39.In a class of 32 children, 15 like mangoes, 19 like bananas and 10 like both. How many like only mangoes? (a) 13 (b) 5 (c) 15 (d) 9
40. 40.In a class of 39 children, 28 like maths, 13 like science and 9 like both. How many like at least one of the two? (a) 23 (b) 39 (c) 41 (d) 32

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