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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 216 · 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 39 children, 21 play cricket, 8 play football and 5 play both. How many play neither of the two?
  2. 2.In a group of 25 children, 9 like mangoes, 15 like bananas and 3 like both. How many like only mangoes?
  3. 3.In a group of 41 children, 22 like mangoes, 14 like bananas and 10 like both. How many like at least one of the two?
  4. 4.In a group of 40 children, 25 enjoy drawing, 13 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  5. 5.In a group of 20 children, 15 sing Hindi songs, 14 sing English songs and 11 sing both. How many sing exactly one of the two?
  6. 6.In a group of 38 children, 15 like mangoes, 14 like bananas and 2 like both. How many like exactly one of the two?
  7. 7.In a group of 39 children, 12 play cricket, 22 play football and 5 play both. How many play only cricket?
  8. 8.In a group of 46 children, 23 play cricket, 26 play football and 12 play both. How many play at least one of the two?
  9. 9.In a group of 27 children, 11 play cricket, 16 play football and 7 play both. How many play exactly one of the two?
  10. 10.In a group of 32 grown-ups, 16 drink tea, 19 drink coffee and 11 drink both. How many drink only coffee?
  11. 11.In a group of 38 children, 16 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  12. 12.In a group of 33 children, 5 play cricket, 18 play football and 2 play both. How many play neither of the two?
  13. 13.In a group of 28 children, 17 play cricket, 12 play football and 3 play both. How many play only cricket?
  14. 14.In a group of 50 children, 31 enjoy drawing, 23 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  15. 15.In a group of 47 children, 23 play chess, 20 play carrom and 5 play both. How many play neither of the two?
  16. 16.In a group of 49 children, 19 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 31 grown-ups, 21 drink tea, 16 drink coffee and 10 drink both. How many drink only tea?
  18. 18.In a group of 46 children, 20 like mangoes, 18 like bananas and 5 like both. How many like at least one of the two?
  19. 19.In a group of 46 children, 23 like mangoes, 23 like bananas and 5 like both. How many like only mangoes?
  20. 20.In a group of 20 children, 10 play chess, 5 play carrom and 2 play both. How many play only carrom?
  21. 21.In a group of 33 children, 20 enjoy drawing, 11 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  22. 22.In a group of 45 children, 25 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  23. 23.In a group of 48 children, 26 like mangoes, 32 like bananas and 12 like both. How many like only bananas?
  24. 24.In a group of 39 children, 21 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  25. 25.In a group of 44 children, 21 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  26. 26.In a group of 22 children, 14 like mangoes, 14 like bananas and 9 like both. How many like only bananas?
  27. 27.In a group of 43 children, 12 play chess, 23 play carrom and 7 play both. How many play only carrom?
  28. 28.In a group of 39 children, 23 play cricket, 18 play football and 12 play both. How many play neither of the two?
  29. 29.In a group of 48 grown-ups, 23 drink tea, 28 drink coffee and 8 drink both. How many drink only coffee?
  30. 30.In a group of 34 grown-ups, 21 drink tea, 20 drink coffee and 9 drink both. How many drink only coffee?
  31. 31.In a group of 28 children, 12 sing Hindi songs, 23 sing English songs and 8 sing both. How many sing at least one of the two?
  32. 32.In a group of 37 children, 23 sing Hindi songs, 16 sing English songs and 10 sing both. How many sing only Hindi songs?
  33. 33.In a group of 30 children, 19 enjoy drawing, 8 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 37 grown-ups, 20 drink tea, 25 drink coffee and 11 drink both. How many drink only tea?
  35. 35.In a group of 23 grown-ups, 6 drink tea, 11 drink coffee and 3 drink both. How many drink exactly one of the two?
  36. 36.In a group of 37 grown-ups, 20 drink tea, 9 drink coffee and 6 drink both. How many drink exactly one of the two?
  37. 37.In a group of 49 children, 21 play chess, 21 play carrom and 8 play both. How many play only chess?
  38. 38.In a group of 36 children, 19 enjoy drawing, 15 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  39. 39.In a group of 53 grown-ups, 32 drink tea, 27 drink coffee and 12 drink both. How many drink exactly one of the two?
  40. 40.In a group of 53 children, 21 enjoy drawing, 19 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?

Answer key

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

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