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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 58 · 40 questions
TalentJR

How to think it through (Middle first): Put “both” in the overlap. Only A = A − both; only B = B − both; at least one = A + B − both. Neither = total − at least one; exactly one = only A + only B.

NameDateTime takenScore ___ / 40
  1. 1.In a group of 31 children, 16 play cricket, 5 play football and 2 play both. How many play exactly one of the two?
  2. 2.In a group of 34 children, 14 play cricket, 21 play football and 6 play both. How many play only football?
  3. 3.In a group of 32 children, 20 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  4. 4.In a group of 35 children, 18 enjoy drawing, 15 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 30 children, 18 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  6. 6.In a group of 26 children, 16 play cricket, 16 play football and 9 play both. How many play neither of the two?
  7. 7.In a group of 38 grown-ups, 16 drink tea, 16 drink coffee and 8 drink both. How many drink exactly one of the two?
  8. 8.In a group of 44 grown-ups, 22 drink tea, 14 drink coffee and 5 drink both. How many drink exactly one of the two?
  9. 9.In a group of 24 children, 15 play cricket, 17 play football and 12 play both. How many play only cricket?
  10. 10.In a group of 29 children, 13 play cricket, 20 play football and 9 play both. How many play neither of the two?
  11. 11.In a group of 50 children, 27 play cricket, 23 play football and 9 play both. How many play only cricket?
  12. 12.In a group of 29 children, 19 enjoy drawing, 19 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 25 children, 12 like mangoes, 14 like bananas and 2 like both. How many like at least one of the two?
  14. 14.In a group of 20 grown-ups, 10 drink tea, 7 drink coffee and 4 drink both. How many drink neither of the two?
  15. 15.In a group of 33 children, 22 enjoy drawing, 15 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 18 children, 11 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  17. 17.In a group of 37 children, 22 play cricket, 10 play football and 6 play both. How many play only cricket?
  18. 18.In a group of 45 children, 30 play cricket, 21 play football and 11 play both. How many play exactly one of the two?
  19. 19.In a group of 48 children, 29 play chess, 27 play carrom and 11 play both. How many play at least one of the two?
  20. 20.In a group of 50 children, 19 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 30 children, 14 play chess, 8 play carrom and 2 play both. How many play only chess?
  22. 22.In a group of 31 children, 17 like mangoes, 20 like bananas and 9 like both. How many like exactly one of the two?
  23. 23.In a group of 34 grown-ups, 18 drink tea, 16 drink coffee and 2 drink both. How many drink only tea?
  24. 24.In a group of 57 children, 31 play cricket, 30 play football and 11 play both. How many play at least one of the two?
  25. 25.In a group of 25 children, 12 sing Hindi songs, 18 sing English songs and 8 sing both. How many sing only English songs?
  26. 26.In a group of 21 children, 12 play cricket, 15 play football and 8 play both. How many play only football?
  27. 27.In a group of 36 children, 22 enjoy drawing, 21 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  28. 28.In a group of 45 children, 18 play cricket, 22 play football and 3 play both. How many play exactly one of the two?
  29. 29.In a group of 33 children, 12 play cricket, 21 play football and 8 play both. How many play at least one of the two?
  30. 30.In a group of 42 children, 21 enjoy drawing, 26 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 40 children, 25 play cricket, 23 play football and 11 play both. How many play only cricket?
  32. 32.In a group of 40 grown-ups, 26 drink tea, 16 drink coffee and 9 drink both. How many drink neither of the two?
  33. 33.In a group of 25 children, 12 play cricket, 17 play football and 5 play both. How many play exactly one of the two?
  34. 34.In a group of 28 children, 10 play cricket, 23 play football and 7 play both. How many play exactly one of the two?
  35. 35.In a group of 32 children, 22 play cricket, 7 play football and 3 play both. How many play only cricket?
  36. 36.In a group of 42 children, 19 play cricket, 25 play football and 5 play both. How many play neither of the two?
  37. 37.In a group of 32 children, 21 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  38. 38.In a group of 50 grown-ups, 22 drink tea, 23 drink coffee and 3 drink both. How many drink only tea?
  39. 39.In a group of 37 children, 12 like mangoes, 22 like bananas and 9 like both. How many like neither of the two?
  40. 40.In a group of 35 children, 12 sing Hindi songs, 16 sing English songs and 2 sing both. How many sing neither of the two?

Answer key

  1. 17
  2. 15
  3. 6
  4. 27
  5. 10
  6. 3
  7. 16
  8. 26
  9. 3
  10. 5
  11. 18
  12. 16
  13. 24
  14. 7
  15. 3
  16. 13
  17. 16
  18. 29
  19. 45
  20. 35
  21. 12
  22. 19
  23. 16
  24. 50
  25. 10
  26. 7
  27. 9
  28. 34
  29. 25
  30. 9
  31. 14
  32. 7
  33. 19
  34. 19
  35. 19
  36. 3
  37. 5
  38. 19
  39. 12
  40. 9

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