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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 68 · 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 21 children, 13 play cricket, 15 play football and 8 play both. How many play only football?
  2. 2.In a group of 34 children, 14 play cricket, 8 play football and 2 play both. How many play exactly one of the two?
  3. 3.In a group of 22 children, 14 play cricket, 8 play football and 3 play both. How many play at least one of the two?
  4. 4.In a group of 53 grown-ups, 23 drink tea, 29 drink coffee and 10 drink both. How many drink only coffee?
  5. 5.In a group of 17 children, 8 play chess, 10 play carrom and 4 play both. How many play neither of the two?
  6. 6.In a group of 29 children, 16 like mangoes, 20 like bananas and 9 like both. How many like neither of the two?
  7. 7.In a group of 45 children, 28 play cricket, 23 play football and 10 play both. How many play only cricket?
  8. 8.In a group of 30 children, 10 play cricket, 10 play football and 3 play both. How many play neither of the two?
  9. 9.In a group of 46 children, 27 sing Hindi songs, 25 sing English songs and 8 sing both. How many sing only English songs?
  10. 10.In a group of 41 children, 19 play cricket, 20 play football and 8 play both. How many play only cricket?
  11. 11.In a group of 38 grown-ups, 24 drink tea, 14 drink coffee and 10 drink both. How many drink at least one of the two?
  12. 12.In a group of 35 children, 19 enjoy drawing, 11 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  13. 13.In a group of 33 children, 7 play chess, 20 play carrom and 2 play both. How many play neither of the two?
  14. 14.In a group of 49 children, 28 sing Hindi songs, 25 sing English songs and 8 sing both. How many sing only Hindi songs?
  15. 15.In a group of 41 children, 14 play cricket, 18 play football and 2 play both. How many play only football?
  16. 16.In a group of 38 children, 9 sing Hindi songs, 25 sing English songs and 5 sing both. How many sing exactly one of the two?
  17. 17.In a group of 36 children, 15 play chess, 8 play carrom and 2 play both. How many play at least one of the two?
  18. 18.In a group of 35 grown-ups, 12 drink tea, 16 drink coffee and 3 drink both. How many drink only tea?
  19. 19.In a group of 35 children, 12 like mangoes, 15 like bananas and 5 like both. How many like at least one of the two?
  20. 20.In a group of 50 children, 29 play cricket, 24 play football and 10 play both. How many play neither of the two?
  21. 21.In a group of 56 children, 27 play cricket, 25 play football and 8 play both. How many play only cricket?
  22. 22.In a group of 28 children, 20 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  23. 23.In a group of 46 children, 19 sing Hindi songs, 27 sing English songs and 11 sing both. How many sing neither of the two?
  24. 24.In a group of 34 children, 16 enjoy drawing, 10 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  25. 25.In a group of 35 children, 15 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  26. 26.In a group of 40 children, 31 sing Hindi songs, 16 sing English songs and 11 sing both. How many sing neither of the two?
  27. 27.In a group of 30 children, 24 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing only Hindi songs?
  28. 28.In a group of 46 children, 24 play chess, 25 play carrom and 10 play both. How many play only chess?
  29. 29.In a group of 35 children, 22 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing only Hindi songs?
  30. 30.In a group of 24 children, 7 play chess, 8 play carrom and 3 play both. How many play only carrom?
  31. 31.In a group of 36 children, 14 play chess, 27 play carrom and 9 play both. How many play exactly one of the two?
  32. 32.In a group of 28 children, 16 sing Hindi songs, 19 sing English songs and 9 sing both. How many sing at least one of the two?
  33. 33.In a group of 34 children, 18 sing Hindi songs, 19 sing English songs and 5 sing both. How many sing only Hindi songs?
  34. 34.In a group of 53 children, 29 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  35. 35.In a group of 36 children, 25 sing Hindi songs, 11 sing English songs and 6 sing both. How many sing at least one of the two?
  36. 36.In a group of 33 children, 11 sing Hindi songs, 19 sing English songs and 3 sing both. How many sing neither of the two?
  37. 37.In a group of 30 children, 16 play cricket, 14 play football and 5 play both. How many play only cricket?
  38. 38.In a group of 12 children, 7 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  39. 39.In a group of 30 children, 14 like mangoes, 23 like bananas and 8 like both. How many like only bananas?
  40. 40.In a group of 31 children, 18 play chess, 8 play carrom and 5 play both. How many play at least one of the two?

Answer key

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

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