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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 20 · 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 42 children, 24 play chess, 23 play carrom and 9 play both. How many play only chess?
  2. 2.In a group of 36 children, 20 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 27 children, 13 like mangoes, 8 like bananas and 5 like both. How many like only bananas?
  4. 4.In a group of 37 children, 18 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  5. 5.In a group of 47 children, 23 play chess, 23 play carrom and 7 play both. How many play neither of the two?
  6. 6.In a group of 43 grown-ups, 23 drink tea, 18 drink coffee and 5 drink both. How many drink only tea?
  7. 7.In a group of 36 grown-ups, 7 drink tea, 19 drink coffee and 4 drink both. How many drink exactly one of the two?
  8. 8.In a group of 45 children, 27 sing Hindi songs, 22 sing English songs and 9 sing both. How many sing only Hindi songs?
  9. 9.In a group of 28 grown-ups, 7 drink tea, 15 drink coffee and 3 drink both. How many drink only tea?
  10. 10.In a group of 42 grown-ups, 14 drink tea, 19 drink coffee and 2 drink both. How many drink only tea?
  11. 11.In a group of 27 children, 21 play cricket, 9 play football and 6 play both. How many play only cricket?
  12. 12.In a group of 41 children, 22 like mangoes, 11 like bananas and 4 like both. How many like at least one of the two?
  13. 13.In a group of 40 children, 12 sing Hindi songs, 17 sing English songs and 4 sing both. How many sing exactly one of the two?
  14. 14.In a group of 23 children, 16 play chess, 11 play carrom and 5 play both. How many play only chess?
  15. 15.In a group of 35 children, 18 play cricket, 14 play football and 10 play both. How many play exactly one of the two?
  16. 16.In a group of 20 children, 6 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 28 children, 11 play chess, 15 play carrom and 6 play both. How many play only carrom?
  18. 18.In a group of 40 children, 23 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing only English songs?
  19. 19.In a group of 52 children, 32 enjoy drawing, 24 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  20. 20.In a group of 45 children, 20 sing Hindi songs, 21 sing English songs and 9 sing both. How many sing only English songs?
  21. 21.In a group of 39 children, 18 enjoy drawing, 31 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  22. 22.In a group of 30 children, 17 play chess, 15 play carrom and 3 play both. How many play only carrom?
  23. 23.In a group of 39 children, 7 sing Hindi songs, 21 sing English songs and 3 sing both. How many sing exactly one of the two?
  24. 24.In a group of 34 children, 17 play cricket, 18 play football and 11 play both. How many play at least one of the two?
  25. 25.In a group of 42 grown-ups, 15 drink tea, 17 drink coffee and 3 drink both. How many drink only coffee?
  26. 26.In a group of 30 children, 18 play chess, 14 play carrom and 7 play both. How many play at least one of the two?
  27. 27.In a group of 42 children, 15 sing Hindi songs, 20 sing English songs and 7 sing both. How many sing neither of the two?
  28. 28.In a group of 44 children, 21 play cricket, 14 play football and 3 play both. How many play at least one of the two?
  29. 29.In a group of 44 children, 24 sing Hindi songs, 22 sing English songs and 5 sing both. How many sing exactly one of the two?
  30. 30.In a group of 32 children, 13 enjoy drawing, 27 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  31. 31.In a group of 32 children, 9 enjoy drawing, 10 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 46 children, 29 play cricket, 17 play football and 12 play both. How many play at least one of the two?
  33. 33.In a group of 40 children, 24 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing at least one of the two?
  34. 34.In a group of 41 children, 10 sing Hindi songs, 20 sing English songs and 2 sing both. How many sing at least one of the two?
  35. 35.In a group of 32 children, 20 play cricket, 12 play football and 6 play both. How many play only cricket?
  36. 36.In a group of 22 children, 12 like mangoes, 11 like bananas and 5 like both. How many like only bananas?
  37. 37.In a group of 36 grown-ups, 29 drink tea, 16 drink coffee and 11 drink both. How many drink neither of the two?
  38. 38.In a group of 36 children, 20 play cricket, 14 play football and 10 play both. How many play only cricket?
  39. 39.In a group of 48 children, 22 sing Hindi songs, 28 sing English songs and 11 sing both. How many sing only English songs?
  40. 40.In a group of 41 children, 26 play chess, 16 play carrom and 11 play both. How many play neither of the two?

Answer key

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

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