Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 176 · 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 30 children, 11 like tea, 21 like coffee and 7 like both. How many like at least one of the two? (a) 18 (b) 30 (c) 32 (d) 25
2. 2.In a class of 29 children, 13 like cricket, 14 like football and 3 like both. How many like only cricket? (a) 13 (b) 10 (c) 11 (d) 15
3. 3.In a class of 33 children, 18 like dance, 11 like music and 2 like both. How many like neither? (a) 8 (b) 6 (c) 2 (d) 4
4. 4.In a class of 37 children, 10 like maths, 19 like science and 10 like neither. How many like both? (a) 10 (b) 3 (c) 2 (d) 27
5. 5.In a class of 43 children, 19 like mangoes, 26 like bananas and 7 like both. How many like neither? (a) 6 (b) 5 (c) 7 (d) 12
6. 6.In a class of 17 children, 9 like cricket, 10 like football and 3 like neither. How many like both? (a) 5 (b) 3 (c) 2 (d) 14
7. 7.In a class of 37 children, 27 like tea, 13 like coffee and 7 like both. How many like only tea? (a) 6 (b) 20 (c) 27 (d) 24
8. 8.In a class of 27 children, 18 like maths, 9 like science and 4 like both. How many like neither? (a) 4 (b) 0 (c) 5 (d) 8
9. 9.In a class of 41 children, 22 like tea, 17 like coffee and 4 like neither. How many like both? (a) 3 (b) 4 (c) 37 (d) 2
10. 10.In a class of 50 children, 24 like dance, 24 like music and 7 like both. How many like only dance? (a) 26 (b) 7 (c) 24 (d) 17
11. 11.In a class of 42 children, 15 like dance, 31 like music and 12 like both. How many like only dance? (a) 15 (b) 3 (c) 11 (d) 19
12. 12.In a class of 22 children, 13 like dance, 12 like music and 4 like both. How many like at least one of the two? (a) 17 (b) 22 (c) 25 (d) 21
13. 13.In a class of 35 children, 20 like mangoes, 15 like bananas and 2 like both. How many like only mangoes? (a) 18 (b) 13 (c) 2 (d) 20
14. 14.In a class of 20 children, 7 like mangoes, 10 like bananas and 7 like neither. How many like both? (a) 7 (b) 5 (c) 13 (d) 4
15. 15.In a class of 36 children, 19 like dance, 15 like music and 7 like both. How many like neither? (a) 2 (b) 7 (c) 16 (d) 9
16. 16.In a class of 34 children, 16 like cricket, 22 like football and 8 like both. How many like at least one of the two? (a) 22 (b) 30 (c) 38 (d) 34
17. 17.In a class of 24 children, 11 like cricket, 10 like football and 7 like neither. How many like both? (a) 5 (b) 17 (c) 7 (d) 4
18. 18.In a class of 27 children, 17 like tea, 6 like coffee and 2 like both. How many like at least one of the two? (a) 19 (b) 23 (c) 21 (d) 27
19. 19.In a class of 27 children, 20 like maths, 13 like science and 8 like both. How many like neither? (a) 10 (b) 8 (c) 2 (d) 3
20. 20.In a class of 28 children, 10 like cricket, 15 like football and 6 like both. How many like only cricket? (a) 10 (b) 13 (c) 4 (d) 9
21. 21.In a class of 17 children, 8 like cricket, 10 like football and 3 like neither. How many like both? (a) 1 (b) 4 (c) 14 (d) 3
22. 22.In a class of 45 children, 27 like dance, 22 like music and 6 like neither. How many like both? (a) 10 (b) 39 (c) 6 (d) 4
23. 23.In a class of 48 children, 27 like dance, 25 like music and 7 like both. How many like at least one of the two? (a) 48 (b) 38 (c) 45 (d) 52
24. 24.In a class of 26 children, 18 like dance, 13 like music and 6 like both. How many like neither? (a) 2 (b) 1 (c) 6 (d) 7
25. 25.In a class of 30 children, 12 like cricket, 24 like football and 9 like both. How many like at least one of the two? (a) 18 (b) 30 (c) 27 (d) 36
26. 26.In a class of 36 children, 19 like cricket, 21 like football and 10 like both. How many like only cricket? (a) 19 (b) 15 (c) 11 (d) 9
27. 27.In a class of 39 children, 20 like mangoes, 28 like bananas and 3 like neither. How many like both? (a) 9 (b) 3 (c) 36 (d) 12
28. 28.In a class of 43 children, 31 like mangoes, 18 like bananas and 12 like both. How many like only mangoes? (a) 6 (b) 25 (c) 19 (d) 31
29. 29.In a class of 31 children, 9 like maths, 22 like science and 3 like neither. How many like both? (a) 3 (b) 28 (c) 4 (d) 2
30. 30.In a class of 31 children, 17 like dance, 18 like music and 7 like both. How many like only dance? (a) 10 (b) 13 (c) 17 (d) 11
31. 31.In a class of 28 children, 15 like mangoes, 17 like bananas and 11 like both. How many like neither? (a) 11 (b) 7 (c) 8 (d) 18
32. 32.In a class of 48 children, 28 like dance, 30 like music and 1 like neither. How many like both? (a) 47 (b) 10 (c) 1 (d) 11
33. 33.In a class of 34 children, 11 like cricket, 21 like football and 3 like both. How many like at least one of the two? (a) 32 (b) 34 (c) 29 (d) 26
34. 34.In a class of 33 children, 25 like tea, 12 like coffee and 1 like neither. How many like both? (a) 32 (b) 5 (c) 4 (d) 1
35. 35.In a class of 36 children, 25 like dance, 22 like music and 12 like both. How many like neither? (a) 13 (b) 1 (c) 12 (d) 2
36. 36.In a class of 30 children, 12 like dance, 20 like music and 9 like both. How many like at least one of the two? (a) 32 (b) 23 (c) 14 (d) 30
37. 37.In a class of 37 children, 24 like dance, 17 like music and 6 like both. How many like only dance? (a) 18 (b) 24 (c) 20 (d) 11
38. 38.In a class of 37 children, 18 like mangoes, 20 like bananas and 4 like neither. How many like both? (a) 33 (b) 5 (c) 4 (d) 1
39. 39.In a class of 41 children, 24 like maths, 17 like science and 9 like neither. How many like both? (a) 8 (b) 10 (c) 9 (d) 32
40. 40.In a class of 33 children, 19 like tea, 24 like coffee and 12 like both. How many like only tea? (a) 7 (b) 19 (c) 9 (d) 12

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