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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 401 · 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 41 children, 9 play cricket, 20 play football and 3 play both. How many play exactly one of the two?
  2. 2.In a group of 46 grown-ups, 21 drink tea, 19 drink coffee and 5 drink both. How many drink at least one of the two?
  3. 3.In a group of 60 children, 32 play cricket, 29 play football and 12 play both. How many play neither of the two?
  4. 4.In a group of 38 children, 10 enjoy drawing, 16 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  5. 5.In a group of 29 children, 10 play cricket, 12 play football and 5 play both. How many play at least one of the two?
  6. 6.In a group of 22 grown-ups, 10 drink tea, 12 drink coffee and 3 drink both. How many drink exactly one of the two?
  7. 7.In a group of 38 children, 17 sing Hindi songs, 8 sing English songs and 2 sing both. How many sing neither of the two?
  8. 8.In a group of 40 children, 19 play cricket, 20 play football and 2 play both. How many play exactly one of the two?
  9. 9.In a group of 28 children, 15 sing Hindi songs, 15 sing English songs and 10 sing both. How many sing exactly one of the two?
  10. 10.In a group of 37 grown-ups, 20 drink tea, 16 drink coffee and 5 drink both. How many drink only tea?
  11. 11.In a group of 39 children, 23 play chess, 9 play carrom and 6 play both. How many play exactly one of the two?
  12. 12.In a group of 43 children, 22 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  13. 13.In a group of 49 children, 25 like mangoes, 26 like bananas and 9 like both. How many like at least one of the two?
  14. 14.In a group of 36 children, 25 play cricket, 17 play football and 9 play both. How many play only cricket?
  15. 15.In a group of 46 grown-ups, 20 drink tea, 26 drink coffee and 6 drink both. How many drink only coffee?
  16. 16.In a group of 35 children, 21 enjoy drawing, 18 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 30 grown-ups, 19 drink tea, 11 drink coffee and 4 drink both. How many drink exactly one of the two?
  18. 18.In a group of 40 children, 6 sing Hindi songs, 22 sing English songs and 2 sing both. How many sing only Hindi songs?
  19. 19.In a group of 49 children, 26 play cricket, 23 play football and 8 play both. How many play only cricket?
  20. 20.In a group of 27 children, 17 play cricket, 12 play football and 4 play both. How many play exactly one of the two?
  21. 21.In a group of 39 children, 10 enjoy drawing, 24 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  22. 22.In a group of 24 children, 6 play chess, 11 play carrom and 2 play both. How many play neither of the two?
  23. 23.In a group of 38 children, 9 play chess, 19 play carrom and 3 play both. How many play exactly one of the two?
  24. 24.In a group of 28 children, 10 like mangoes, 15 like bananas and 4 like both. How many like neither of the two?
  25. 25.In a group of 41 children, 10 sing Hindi songs, 22 sing English songs and 4 sing both. How many sing only English songs?
  26. 26.In a group of 45 children, 24 play chess, 14 play carrom and 4 play both. How many play neither of the two?
  27. 27.In a group of 44 children, 25 play chess, 19 play carrom and 8 play both. How many play only carrom?
  28. 28.In a group of 61 children, 27 play chess, 31 play carrom and 11 play both. How many play neither of the two?
  29. 29.In a group of 45 children, 21 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing neither of the two?
  30. 30.In a group of 38 children, 6 enjoy drawing, 23 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  31. 31.In a group of 25 children, 11 play cricket, 14 play football and 5 play both. How many play only football?
  32. 32.In a group of 44 children, 28 play cricket, 24 play football and 10 play both. How many play only football?
  33. 33.In a group of 53 children, 26 like mangoes, 25 like bananas and 9 like both. How many like only bananas?
  34. 34.In a group of 45 children, 21 like mangoes, 17 like bananas and 8 like both. How many like only mangoes?
  35. 35.In a group of 35 grown-ups, 15 drink tea, 26 drink coffee and 8 drink both. How many drink neither of the two?
  36. 36.In a group of 30 children, 14 sing Hindi songs, 19 sing English songs and 10 sing both. How many sing exactly one of the two?
  37. 37.In a group of 48 children, 26 play chess, 19 play carrom and 10 play both. How many play neither of the two?
  38. 38.In a group of 29 children, 19 enjoy drawing, 9 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  39. 39.In a group of 50 children, 25 play chess, 21 play carrom and 8 play both. How many play only carrom?
  40. 40.In a group of 39 children, 17 play chess, 21 play carrom and 2 play both. How many play exactly one of the two?

Answer key

  1. 23
  2. 35
  3. 11
  4. 22
  5. 17
  6. 16
  7. 15
  8. 35
  9. 10
  10. 15
  11. 20
  12. 19
  13. 42
  14. 16
  15. 20
  16. 9
  17. 22
  18. 4
  19. 18
  20. 21
  21. 10
  22. 9
  23. 22
  24. 7
  25. 18
  26. 11
  27. 11
  28. 14
  29. 5
  30. 26
  31. 9
  32. 14
  33. 16
  34. 13
  35. 2
  36. 13
  37. 13
  38. 16
  39. 13
  40. 34

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