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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 55 · 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 26 children, 10 play cricket, 8 play football and 3 play both. How many play neither of the two?
  2. 2.In a group of 26 children, 18 like mangoes, 11 like bananas and 5 like both. How many like at least one of the two?
  3. 3.In a group of 53 children, 18 sing Hindi songs, 28 sing English songs and 8 sing both. How many sing exactly one of the two?
  4. 4.In a group of 36 children, 24 play cricket, 19 play football and 12 play both. How many play only cricket?
  5. 5.In a group of 35 children, 17 play chess, 9 play carrom and 4 play both. How many play only carrom?
  6. 6.In a group of 45 children, 27 play cricket, 20 play football and 7 play both. How many play neither of the two?
  7. 7.In a group of 33 children, 21 like mangoes, 22 like bananas and 11 like both. How many like only mangoes?
  8. 8.In a group of 21 children, 12 enjoy drawing, 7 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  9. 9.In a group of 46 children, 19 like mangoes, 20 like bananas and 8 like both. How many like neither of the two?
  10. 10.In a group of 30 children, 8 sing Hindi songs, 14 sing English songs and 2 sing both. How many sing at least one of the two?
  11. 11.In a group of 34 grown-ups, 20 drink tea, 10 drink coffee and 6 drink both. How many drink only tea?
  12. 12.In a group of 41 children, 10 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 29 children, 13 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  14. 14.In a group of 29 children, 7 play chess, 20 play carrom and 4 play both. How many play at least one of the two?
  15. 15.In a group of 45 children, 15 play cricket, 21 play football and 6 play both. How many play at least one of the two?
  16. 16.In a group of 31 children, 17 enjoy drawing, 16 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 43 children, 18 play chess, 20 play carrom and 2 play both. How many play neither of the two?
  18. 18.In a group of 25 children, 6 play cricket, 15 play football and 3 play both. How many play neither of the two?
  19. 19.In a group of 29 children, 11 like mangoes, 11 like bananas and 2 like both. How many like only mangoes?
  20. 20.In a group of 46 grown-ups, 25 drink tea, 24 drink coffee and 12 drink both. How many drink at least one of the two?
  21. 21.In a group of 42 children, 22 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing exactly one of the two?
  22. 22.In a group of 39 children, 27 play chess, 21 play carrom and 11 play both. How many play at least one of the two?
  23. 23.In a group of 46 children, 19 enjoy drawing, 31 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 48 children, 20 sing Hindi songs, 19 sing English songs and 3 sing both. How many sing neither of the two?
  25. 25.In a group of 47 children, 23 play cricket, 26 play football and 9 play both. How many play exactly one of the two?
  26. 26.In a group of 25 children, 11 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 34 children, 21 enjoy drawing, 15 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  28. 28.In a group of 45 children, 26 play chess, 26 play carrom and 10 play both. How many play only chess?
  29. 29.In a group of 26 children, 16 play cricket, 14 play football and 11 play both. How many play at least one of the two?
  30. 30.In a group of 58 children, 27 enjoy drawing, 31 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  31. 31.In a group of 36 children, 13 like mangoes, 16 like bananas and 4 like both. How many like only bananas?
  32. 32.In a group of 44 children, 23 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing exactly one of the two?
  33. 33.In a group of 33 children, 14 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 21 children, 12 like mangoes, 9 like bananas and 6 like both. How many like only bananas?
  35. 35.In a group of 35 grown-ups, 15 drink tea, 16 drink coffee and 10 drink both. How many drink at least one of the two?
  36. 36.In a group of 32 grown-ups, 16 drink tea, 20 drink coffee and 11 drink both. How many drink at least one of the two?
  37. 37.In a group of 35 children, 13 enjoy drawing, 16 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  38. 38.In a group of 41 children, 22 enjoy drawing, 19 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 35 children, 16 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  40. 40.In a group of 23 children, 14 play chess, 11 play carrom and 4 play both. How many play only carrom?

Answer key

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

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