Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 429 · 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 39 children, 16 like tea, 17 like coffee and 3 like both. How many like only tea? (a) 16 (b) 22 (c) 14 (d) 13
2. 2.In a class of 24 children, 10 like mangoes, 11 like bananas and 10 like neither. How many like both? (a) 7 (b) 14 (c) 8 (d) 10
3. 3.In a class of 46 children, 18 like cricket, 23 like football and 9 like neither. How many like both? (a) 4 (b) 37 (c) 9 (d) 5
4. 4.In a class of 30 children, 13 like mangoes, 17 like bananas and 7 like both. How many like neither? (a) 8 (b) 14 (c) 0 (d) 7
5. 5.In a class of 27 children, 17 like dance, 17 like music and 9 like both. How many like neither? (a) 3 (b) 2 (c) 11 (d) 9
6. 6.In a class of 28 children, 13 like cricket, 17 like football and 6 like both. How many like only cricket? (a) 6 (b) 7 (c) 11 (d) 13
7. 7.In a class of 47 children, 20 like mangoes, 22 like bananas and 2 like both. How many like at least one of the two? (a) 42 (b) 47 (c) 38 (d) 40
8. 8.In a class of 44 children, 24 like maths, 18 like science and 4 like both. How many like neither? (a) 10 (b) 2 (c) 4 (d) 6
9. 9.In a class of 39 children, 21 like dance, 16 like music and 5 like both. How many like neither? (a) 12 (b) 5 (c) 2 (d) 7
10. 10.In a class of 25 children, 16 like dance, 15 like music and 4 like neither. How many like both? (a) 21 (b) 10 (c) 4 (d) 6
11. 11.In a class of 40 children, 14 like mangoes, 26 like bananas and 6 like neither. How many like both? (a) 34 (b) 7 (c) 5 (d) 6
12. 12.In a class of 35 children, 10 like cricket, 24 like football and 6 like both. How many like only cricket? (a) 10 (b) 4 (c) 18 (d) 11
13. 13.In a class of 48 children, 24 like dance, 27 like music and 6 like neither. How many like both? (a) 3 (b) 9 (c) 42 (d) 6
14. 14.In a class of 50 children, 28 like cricket, 21 like football and 9 like both. How many like neither? (a) 9 (b) 10 (c) 1 (d) 19
15. 15.In a class of 37 children, 10 like tea, 25 like coffee and 5 like both. How many like only tea? (a) 5 (b) 12 (c) 20 (d) 10
16. 16.In a class of 16 children, 7 like maths, 9 like science and 2 like both. How many like only maths? (a) 6 (b) 2 (c) 5 (d) 7
17. 17.In a class of 33 children, 16 like tea, 13 like coffee and 6 like both. How many like at least one of the two? (a) 29 (b) 17 (c) 33 (d) 23
18. 18.In a class of 18 children, 9 like cricket, 11 like football and 4 like both. How many like neither? (a) 6 (b) 3 (c) 2 (d) 4
19. 19.In a class of 50 children, 25 like cricket, 25 like football and 9 like neither. How many like both? (a) 41 (b) 9 (c) 8 (d) 10
20. 20.In a class of 34 children, 20 like cricket, 13 like football and 2 like both. How many like at least one of the two? (a) 29 (b) 34 (c) 33 (d) 31
21. 21.In a class of 38 children, 25 like dance, 10 like music and 7 like both. How many like neither? (a) 7 (b) 10 (c) 3 (d) 17
22. 22.In a class of 43 children, 28 like maths, 21 like science and 8 like both. How many like neither? (a) 2 (b) 8 (c) 10 (d) 3
23. 23.In a class of 36 children, 13 like cricket, 21 like football and 8 like both. How many like neither? (a) 2 (b) 8 (c) 18 (d) 10
24. 24.In a class of 42 children, 25 like maths, 27 like science and 11 like both. How many like neither? (a) 1 (b) 12 (c) 2 (d) 11
25. 25.In a class of 33 children, 9 like mangoes, 20 like bananas and 5 like both. How many like neither? (a) 4 (b) 5 (c) 14 (d) 9
26. 26.In a class of 27 children, 13 like maths, 12 like science and 6 like both. How many like only maths? (a) 7 (b) 13 (c) 15 (d) 6
27. 27.In a class of 24 children, 9 like mangoes, 8 like bananas and 3 like both. How many like neither? (a) 10 (b) 3 (c) 7 (d) 13
28. 28.In a class of 32 children, 27 like cricket, 10 like football and 2 like neither. How many like both? (a) 30 (b) 7 (c) 5 (d) 2
29. 29.In a class of 24 children, 7 like mangoes, 19 like bananas and 4 like both. How many like at least one of the two? (a) 26 (b) 24 (c) 18 (d) 22
30. 30.In a class of 34 children, 19 like dance, 15 like music and 4 like neither. How many like both? (a) 30 (b) 5 (c) 3 (d) 4
31. 31.In a class of 39 children, 29 like maths, 12 like science and 7 like neither. How many like both? (a) 2 (b) 7 (c) 9 (d) 32
32. 32.In a class of 20 children, 7 like dance, 14 like music and 2 like neither. How many like both? (a) 3 (b) 18 (c) 1 (d) 2
33. 33.In a class of 20 children, 14 like maths, 5 like science and 2 like both. How many like only maths? (a) 3 (b) 15 (c) 12 (d) 14
34. 34.In a class of 28 children, 11 like dance, 15 like music and 8 like both. How many like neither? (a) 18 (b) 8 (c) 10 (d) 2
35. 35.In a class of 41 children, 21 like mangoes, 20 like bananas and 3 like both. How many like only mangoes? (a) 21 (b) 3 (c) 17 (d) 18
36. 36.In a class of 24 children, 19 like tea, 6 like coffee and 2 like both. How many like only tea? (a) 18 (b) 4 (c) 19 (d) 17
37. 37.In a class of 31 children, 7 like dance, 18 like music and 3 like both. How many like at least one of the two? (a) 19 (b) 25 (c) 22 (d) 31
38. 38.In a class of 28 children, 14 like cricket, 10 like football and 7 like neither. How many like both? (a) 7 (b) 21 (c) 4 (d) 3
39. 39.In a class of 34 children, 16 like tea, 21 like coffee and 4 like both. How many like neither? (a) 5 (b) 4 (c) 1 (d) 2
40. 40.In a class of 30 children, 16 like cricket, 23 like football and 2 like neither. How many like both? (a) 2 (b) 9 (c) 11 (d) 28

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