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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 135 · 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, 16 play chess, 11 play carrom and 3 play both. How many play exactly one of the two?
  2. 2.In a group of 36 children, 22 play chess, 23 play carrom and 12 play both. How many play only chess?
  3. 3.In a group of 41 children, 14 enjoy drawing, 23 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  4. 4.In a group of 27 children, 17 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing only Hindi songs?
  5. 5.In a group of 30 children, 17 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  6. 6.In a group of 34 children, 16 sing Hindi songs, 18 sing English songs and 9 sing both. How many sing at least one of the two?
  7. 7.In a group of 35 grown-ups, 14 drink tea, 22 drink coffee and 2 drink both. How many drink at least one of the two?
  8. 8.In a group of 20 children, 6 sing Hindi songs, 12 sing English songs and 3 sing both. How many sing neither of the two?
  9. 9.In a group of 31 children, 24 play cricket, 13 play football and 10 play both. How many play only cricket?
  10. 10.In a group of 34 children, 16 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  11. 11.In a group of 47 children, 18 play chess, 31 play carrom and 11 play both. How many play neither of the two?
  12. 12.In a group of 31 children, 14 like mangoes, 12 like bananas and 6 like both. How many like neither of the two?
  13. 13.In a group of 42 children, 14 play chess, 25 play carrom and 7 play both. How many play exactly one of the two?
  14. 14.In a group of 46 children, 12 like mangoes, 25 like bananas and 6 like both. How many like only bananas?
  15. 15.In a group of 41 grown-ups, 20 drink tea, 27 drink coffee and 9 drink both. How many drink only coffee?
  16. 16.In a group of 40 children, 19 play chess, 21 play carrom and 5 play both. How many play neither of the two?
  17. 17.In a group of 36 children, 20 play cricket, 18 play football and 10 play both. How many play neither of the two?
  18. 18.In a group of 53 grown-ups, 27 drink tea, 24 drink coffee and 11 drink both. How many drink neither of the two?
  19. 19.In a group of 29 grown-ups, 21 drink tea, 9 drink coffee and 4 drink both. How many drink only coffee?
  20. 20.In a group of 33 children, 11 sing Hindi songs, 16 sing English songs and 6 sing both. How many sing neither of the two?
  21. 21.In a group of 29 children, 13 like mangoes, 18 like bananas and 9 like both. How many like exactly one of the two?
  22. 22.In a group of 37 children, 17 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 37 children, 15 sing Hindi songs, 21 sing English songs and 11 sing both. How many sing exactly one of the two?
  24. 24.In a group of 27 children, 13 like mangoes, 14 like bananas and 9 like both. How many like exactly one of the two?
  25. 25.In a group of 42 children, 31 play cricket, 18 play football and 11 play both. How many play neither of the two?
  26. 26.In a group of 30 grown-ups, 18 drink tea, 19 drink coffee and 10 drink both. How many drink exactly one of the two?
  27. 27.In a group of 21 children, 8 sing Hindi songs, 8 sing English songs and 4 sing both. How many sing only Hindi songs?
  28. 28.In a group of 25 children, 5 play cricket, 21 play football and 2 play both. How many play neither of the two?
  29. 29.In a group of 40 children, 15 play cricket, 23 play football and 6 play both. How many play only cricket?
  30. 30.In a group of 29 children, 9 play cricket, 13 play football and 2 play both. How many play at least one of the two?
  31. 31.In a group of 45 children, 31 sing Hindi songs, 18 sing English songs and 12 sing both. How many sing only English songs?
  32. 32.In a group of 38 children, 12 play chess, 21 play carrom and 2 play both. How many play only carrom?
  33. 33.In a group of 43 children, 21 enjoy drawing, 30 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  34. 34.In a group of 48 children, 27 play chess, 28 play carrom and 10 play both. How many play at least one of the two?
  35. 35.In a group of 51 children, 17 play cricket, 30 play football and 11 play both. How many play at least one of the two?
  36. 36.In a group of 48 children, 31 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 27 grown-ups, 18 drink tea, 7 drink coffee and 2 drink both. How many drink at least one of the two?
  38. 38.In a group of 21 children, 10 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 32 grown-ups, 10 drink tea, 13 drink coffee and 4 drink both. How many drink exactly one of the two?
  40. 40.In a group of 44 children, 18 sing Hindi songs, 19 sing English songs and 6 sing both. How many sing neither of the two?

Answer key

  1. 21
  2. 10
  3. 9
  4. 14
  5. 3
  6. 25
  7. 34
  8. 5
  9. 14
  10. 2
  11. 9
  12. 11
  13. 25
  14. 19
  15. 18
  16. 5
  17. 8
  18. 13
  19. 5
  20. 12
  21. 13
  22. 32
  23. 14
  24. 9
  25. 4
  26. 17
  27. 4
  28. 1
  29. 9
  30. 20
  31. 6
  32. 19
  33. 40
  34. 45
  35. 36
  36. 25
  37. 23
  38. 5
  39. 15
  40. 13

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