Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 352 · 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 34 children, 16 like maths, 28 like science and 1 like neither. How many like both? (a) 33 (b) 11 (c) 10 (d) 1
2. 2.In a class of 54 children, 26 like dance, 25 like music and 10 like neither. How many like both? (a) 10 (b) 7 (c) 44 (d) 8
3. 3.In a class of 47 children, 22 like tea, 22 like coffee and 5 like neither. How many like both? (a) 42 (b) 2 (c) 3 (d) 5
4. 4.In a class of 22 children, 12 like cricket, 12 like football and 3 like neither. How many like both? (a) 3 (b) 5 (c) 2 (d) 19
5. 5.In a class of 35 children, 24 like tea, 15 like coffee and 7 like both. How many like only tea? (a) 17 (b) 8 (c) 20 (d) 24
6. 6.In a class of 37 children, 21 like dance, 14 like music and 5 like both. How many like only dance? (a) 16 (b) 23 (c) 9 (d) 21
7. 7.In a class of 29 children, 12 like maths, 15 like science and 4 like both. How many like only maths? (a) 11 (b) 14 (c) 12 (d) 8
8. 8.In a class of 41 children, 22 like maths, 30 like science and 1 like neither. How many like both? (a) 40 (b) 12 (c) 1 (d) 11
9. 9.In a class of 41 children, 30 like dance, 21 like music and 11 like both. How many like neither? (a) 2 (b) 12 (c) 11 (d) 1
10. 10.In a class of 48 children, 26 like cricket, 24 like football and 8 like both. How many like neither? (a) 14 (b) 6 (c) 7 (d) 8
11. 11.In a class of 31 children, 20 like cricket, 13 like football and 6 like both. How many like only cricket? (a) 7 (b) 14 (c) 18 (d) 20
12. 12.In a class of 34 children, 15 like cricket, 20 like football and 10 like neither. How many like both? (a) 10 (b) 11 (c) 24 (d) 1
13. 13.In a class of 25 children, 12 like tea, 21 like coffee and 1 like neither. How many like both? (a) 24 (b) 9 (c) 8 (d) 1
14. 14.In a class of 36 children, 11 like dance, 22 like music and 7 like both. How many like at least one of the two? (a) 36 (b) 33 (c) 19 (d) 26
15. 15.In a class of 24 children, 13 like maths, 8 like science and 4 like both. How many like only maths? (a) 13 (b) 9 (c) 4 (d) 16
16. 16.In a class of 35 children, 28 like dance, 15 like music and 9 like both. How many like at least one of the two? (a) 25 (b) 35 (c) 34 (d) 43
17. 17.In a class of 35 children, 17 like maths, 10 like science and 2 like both. How many like only maths? (a) 17 (b) 15 (c) 25 (d) 8
18. 18.In a class of 34 children, 11 like maths, 16 like science and 3 like both. How many like only maths? (a) 13 (b) 18 (c) 8 (d) 11
19. 19.In a class of 27 children, 17 like tea, 14 like coffee and 7 like both. How many like only tea? (a) 7 (b) 13 (c) 10 (d) 17
20. 20.In a class of 14 children, 8 like cricket, 7 like football and 3 like both. How many like only cricket? (a) 5 (b) 4 (c) 8 (d) 7
21. 21.In a class of 30 children, 19 like mangoes, 8 like bananas and 5 like neither. How many like both? (a) 2 (b) 3 (c) 5 (d) 25
22. 22.In a class of 20 children, 10 like mangoes, 13 like bananas and 7 like both. How many like only mangoes? (a) 7 (b) 10 (c) 6 (d) 3
23. 23.In a class of 39 children, 29 like maths, 19 like science and 1 like neither. How many like both? (a) 38 (b) 1 (c) 9 (d) 10
24. 24.In a class of 37 children, 18 like maths, 21 like science and 8 like neither. How many like both? (a) 8 (b) 2 (c) 29 (d) 10
25. 25.In a class of 21 children, 9 like dance, 13 like music and 6 like both. How many like neither? (a) 11 (b) 4 (c) 5 (d) 6
26. 26.In a class of 27 children, 11 like maths, 16 like science and 6 like neither. How many like both? (a) 6 (b) 5 (c) 21 (d) 7
27. 27.In a class of 47 children, 28 like mangoes, 21 like bananas and 10 like neither. How many like both? (a) 2 (b) 10 (c) 37 (d) 12
28. 28.In a class of 47 children, 21 like maths, 24 like science and 8 like both. How many like neither? (a) 8 (b) 2 (c) 10 (d) 18
29. 29.In a class of 26 children, 12 like tea, 18 like coffee and 5 like both. How many like at least one of the two? (a) 26 (b) 25 (c) 20 (d) 30
30. 30.In a class of 22 children, 8 like dance, 15 like music and 4 like neither. How many like both? (a) 1 (b) 18 (c) 5 (d) 4
31. 31.In a class of 21 children, 8 like tea, 15 like coffee and 4 like both. How many like neither? (a) 6 (b) 4 (c) 3 (d) 2
32. 32.In a class of 29 children, 21 like tea, 13 like coffee and 10 like both. How many like neither? (a) 5 (b) 15 (c) 6 (d) 10
33. 33.In a class of 40 children, 23 like mangoes, 23 like bananas and 8 like both. How many like neither? (a) 8 (b) 10 (c) 2 (d) 3
34. 34.In a class of 27 children, 12 like cricket, 15 like football and 8 like both. How many like at least one of the two? (a) 11 (b) 20 (c) 19 (d) 27
35. 35.In a class of 21 children, 12 like maths, 10 like science and 3 like both. How many like neither? (a) 5 (b) 3 (c) 1 (d) 2
36. 36.In a class of 53 children, 23 like mangoes, 25 like bananas and 5 like both. How many like only mangoes? (a) 18 (b) 28 (c) 20 (d) 23
37. 37.In a class of 33 children, 10 like dance, 23 like music and 6 like both. How many like neither? (a) 12 (b) 0 (c) 6 (d) 7
38. 38.In a class of 51 children, 26 like mangoes, 24 like bananas and 7 like both. How many like at least one of the two? (a) 50 (b) 51 (c) 36 (d) 43
39. 39.In a class of 31 children, 17 like tea, 23 like coffee and 1 like neither. How many like both? (a) 30 (b) 9 (c) 1 (d) 10
40. 40.In a class of 32 children, 18 like cricket, 19 like football and 2 like neither. How many like both? (a) 5 (b) 30 (c) 7 (d) 2

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad