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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 150 · 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, 19 enjoy drawing, 19 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 50 children, 26 enjoy drawing, 28 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  3. 3.In a group of 49 children, 27 play cricket, 22 play football and 7 play both. How many play only cricket?
  4. 4.In a group of 36 children, 11 enjoy drawing, 18 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  5. 5.In a group of 59 grown-ups, 30 drink tea, 30 drink coffee and 10 drink both. How many drink exactly one of the two?
  6. 6.In a group of 37 children, 19 enjoy drawing, 17 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  7. 7.In a group of 30 children, 21 play chess, 9 play carrom and 6 play both. How many play only chess?
  8. 8.In a group of 25 grown-ups, 18 drink tea, 16 drink coffee and 12 drink both. How many drink exactly one of the two?
  9. 9.In a group of 39 children, 15 sing Hindi songs, 23 sing English songs and 4 sing both. How many sing exactly one of the two?
  10. 10.In a group of 34 grown-ups, 16 drink tea, 10 drink coffee and 2 drink both. How many drink at least one of the two?
  11. 11.In a group of 27 children, 13 sing Hindi songs, 17 sing English songs and 10 sing both. How many sing at least one of the two?
  12. 12.In a group of 55 children, 29 enjoy drawing, 24 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 42 children, 17 play chess, 24 play carrom and 10 play both. How many play exactly one of the two?
  14. 14.In a group of 48 children, 18 play cricket, 22 play football and 7 play both. How many play only football?
  15. 15.In a group of 44 children, 27 play chess, 16 play carrom and 10 play both. How many play at least one of the two?
  16. 16.In a group of 34 children, 14 sing Hindi songs, 15 sing English songs and 9 sing both. How many sing exactly one of the two?
  17. 17.In a group of 23 children, 15 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 51 children, 19 like mangoes, 29 like bananas and 12 like both. How many like only mangoes?
  19. 19.In a group of 26 children, 11 play cricket, 15 play football and 2 play both. How many play exactly one of the two?
  20. 20.In a group of 25 children, 9 sing Hindi songs, 13 sing English songs and 4 sing both. How many sing only Hindi songs?
  21. 21.In a group of 41 children, 21 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing at least one of the two?
  22. 22.In a group of 51 children, 24 play cricket, 26 play football and 12 play both. How many play only cricket?
  23. 23.In a group of 35 children, 21 play cricket, 16 play football and 7 play both. How many play exactly one of the two?
  24. 24.In a group of 36 children, 23 play chess, 23 play carrom and 12 play both. How many play only chess?
  25. 25.In a group of 33 children, 26 sing Hindi songs, 14 sing English songs and 10 sing both. How many sing exactly one of the two?
  26. 26.In a group of 41 children, 25 sing Hindi songs, 14 sing English songs and 6 sing both. How many sing exactly one of the two?
  27. 27.In a group of 29 grown-ups, 20 drink tea, 16 drink coffee and 11 drink both. How many drink neither of the two?
  28. 28.In a group of 38 children, 12 like mangoes, 20 like bananas and 9 like both. How many like only mangoes?
  29. 29.In a group of 37 children, 9 like mangoes, 15 like bananas and 2 like both. How many like exactly one of the two?
  30. 30.In a group of 46 children, 16 enjoy drawing, 24 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  31. 31.In a group of 46 children, 25 sing Hindi songs, 14 sing English songs and 7 sing both. How many sing only Hindi songs?
  32. 32.In a group of 23 grown-ups, 7 drink tea, 15 drink coffee and 4 drink both. How many drink only tea?
  33. 33.In a group of 35 children, 28 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 27 children, 16 play chess, 10 play carrom and 4 play both. How many play only chess?
  35. 35.In a group of 24 grown-ups, 12 drink tea, 8 drink coffee and 5 drink both. How many drink exactly one of the two?
  36. 36.In a group of 47 children, 26 play cricket, 19 play football and 10 play both. How many play at least one of the two?
  37. 37.In a group of 43 children, 23 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  38. 38.In a group of 28 grown-ups, 15 drink tea, 18 drink coffee and 12 drink both. How many drink neither of the two?
  39. 39.In a group of 48 grown-ups, 24 drink tea, 20 drink coffee and 5 drink both. How many drink only tea?
  40. 40.In a group of 51 children, 19 like mangoes, 25 like bananas and 5 like both. How many like neither of the two?

Answer key

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

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