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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 65 · 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 38 children, 18 enjoy drawing, 24 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 19 grown-ups, 12 drink tea, 10 drink coffee and 6 drink both. How many drink exactly one of the two?
  3. 3.In a group of 33 grown-ups, 19 drink tea, 19 drink coffee and 10 drink both. How many drink only tea?
  4. 4.In a group of 52 children, 21 enjoy drawing, 24 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  5. 5.In a group of 30 children, 17 like mangoes, 23 like bananas and 11 like both. How many like neither of the two?
  6. 6.In a group of 37 children, 14 play cricket, 19 play football and 6 play both. How many play at least one of the two?
  7. 7.In a group of 22 children, 17 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 34 grown-ups, 20 drink tea, 9 drink coffee and 6 drink both. How many drink only coffee?
  9. 9.In a group of 33 children, 25 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing only English songs?
  10. 10.In a group of 19 children, 7 sing Hindi songs, 12 sing English songs and 3 sing both. How many sing neither of the two?
  11. 11.In a group of 14 children, 6 like mangoes, 9 like bananas and 2 like both. How many like neither of the two?
  12. 12.In a group of 21 grown-ups, 7 drink tea, 10 drink coffee and 3 drink both. How many drink only tea?
  13. 13.In a group of 36 children, 14 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  14. 14.In a group of 43 children, 28 play cricket, 23 play football and 12 play both. How many play at least one of the two?
  15. 15.In a group of 31 children, 21 play chess, 14 play carrom and 11 play both. How many play at least one of the two?
  16. 16.In a group of 48 children, 22 play chess, 30 play carrom and 11 play both. How many play neither of the two?
  17. 17.In a group of 33 children, 16 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  18. 18.In a group of 36 grown-ups, 17 drink tea, 17 drink coffee and 2 drink both. How many drink neither of the two?
  19. 19.In a group of 37 children, 22 sing Hindi songs, 14 sing English songs and 2 sing both. How many sing exactly one of the two?
  20. 20.In a group of 38 children, 21 sing Hindi songs, 11 sing English songs and 2 sing both. How many sing exactly one of the two?
  21. 21.In a group of 47 children, 29 like mangoes, 12 like bananas and 9 like both. How many like neither of the two?
  22. 22.In a group of 31 children, 13 play cricket, 18 play football and 4 play both. How many play only cricket?
  23. 23.In a group of 37 children, 14 enjoy drawing, 30 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 44 children, 20 sing Hindi songs, 27 sing English songs and 12 sing both. How many sing only English songs?
  25. 25.In a group of 36 children, 13 enjoy drawing, 16 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 45 children, 25 play cricket, 15 play football and 8 play both. How many play at least one of the two?
  27. 27.In a group of 47 children, 17 play cricket, 27 play football and 8 play both. How many play only football?
  28. 28.In a group of 39 children, 20 enjoy drawing, 7 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  29. 29.In a group of 42 children, 17 play cricket, 29 play football and 11 play both. How many play neither of the two?
  30. 30.In a group of 18 children, 9 like mangoes, 7 like bananas and 4 like both. How many like neither of the two?
  31. 31.In a group of 45 children, 22 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 44 children, 27 like mangoes, 22 like bananas and 8 like both. How many like neither of the two?
  33. 33.In a group of 33 children, 14 play chess, 19 play carrom and 9 play both. How many play only carrom?
  34. 34.In a group of 25 children, 10 enjoy drawing, 13 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  35. 35.In a group of 29 children, 21 like mangoes, 10 like bananas and 5 like both. How many like exactly one of the two?
  36. 36.In a group of 45 children, 21 play chess, 20 play carrom and 2 play both. How many play neither of the two?
  37. 37.In a group of 22 children, 6 sing Hindi songs, 16 sing English songs and 3 sing both. How many sing exactly one of the two?
  38. 38.In a group of 38 children, 21 like mangoes, 11 like bananas and 5 like both. How many like neither of the two?
  39. 39.In a group of 49 children, 25 like mangoes, 23 like bananas and 5 like both. How many like neither of the two?
  40. 40.In a group of 27 grown-ups, 18 drink tea, 15 drink coffee and 10 drink both. How many drink neither of the two?

Answer key

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

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