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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 559 · 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 46 children, 25 play cricket, 17 play football and 5 play both. How many play only cricket?
  2. 2.In a group of 50 children, 18 play chess, 29 play carrom and 11 play both. How many play neither of the two?
  3. 3.In a group of 14 children, 8 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 51 grown-ups, 25 drink tea, 30 drink coffee and 11 drink both. How many drink exactly one of the two?
  5. 5.In a group of 40 children, 21 like mangoes, 21 like bananas and 3 like both. How many like exactly one of the two?
  6. 6.In a group of 35 grown-ups, 23 drink tea, 19 drink coffee and 11 drink both. How many drink at least one of the two?
  7. 7.In a group of 31 grown-ups, 11 drink tea, 18 drink coffee and 8 drink both. How many drink exactly one of the two?
  8. 8.In a group of 41 children, 29 play cricket, 21 play football and 12 play both. How many play neither of the two?
  9. 9.In a group of 36 children, 16 play chess, 27 play carrom and 11 play both. How many play exactly one of the two?
  10. 10.In a group of 35 grown-ups, 18 drink tea, 12 drink coffee and 8 drink both. How many drink only tea?
  11. 11.In a group of 49 children, 24 enjoy drawing, 26 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 36 children, 13 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  13. 13.In a group of 29 children, 6 play cricket, 16 play football and 2 play both. How many play at least one of the two?
  14. 14.In a group of 39 children, 15 like mangoes, 17 like bananas and 2 like both. How many like neither of the two?
  15. 15.In a group of 42 children, 24 play cricket, 18 play football and 8 play both. How many play only cricket?
  16. 16.In a group of 40 children, 25 play cricket, 17 play football and 12 play both. How many play neither of the two?
  17. 17.In a group of 24 children, 13 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  18. 18.In a group of 49 children, 18 enjoy drawing, 20 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  19. 19.In a group of 30 children, 18 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 58 children, 30 play chess, 28 play carrom and 11 play both. How many play neither of the two?
  21. 21.In a group of 32 children, 22 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  22. 22.In a group of 27 children, 14 like mangoes, 10 like bananas and 6 like both. How many like only mangoes?
  23. 23.In a group of 32 children, 11 play cricket, 25 play football and 5 play both. How many play only football?
  24. 24.In a group of 46 children, 25 enjoy drawing, 20 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  25. 25.In a group of 33 children, 22 play chess, 19 play carrom and 10 play both. How many play only chess?
  26. 26.In a group of 44 children, 22 play cricket, 15 play football and 3 play both. How many play only cricket?
  27. 27.In a group of 51 children, 27 like mangoes, 19 like bananas and 8 like both. How many like only bananas?
  28. 28.In a group of 51 children, 25 enjoy drawing, 29 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  29. 29.In a group of 32 grown-ups, 17 drink tea, 20 drink coffee and 8 drink both. How many drink neither of the two?
  30. 30.In a group of 39 children, 17 sing Hindi songs, 19 sing English songs and 4 sing both. How many sing only Hindi songs?
  31. 31.In a group of 40 children, 20 play cricket, 27 play football and 8 play both. How many play only cricket?
  32. 32.In a group of 30 grown-ups, 20 drink tea, 11 drink coffee and 8 drink both. How many drink neither of the two?
  33. 33.In a group of 29 grown-ups, 8 drink tea, 11 drink coffee and 4 drink both. How many drink neither of the two?
  34. 34.In a group of 29 children, 9 sing Hindi songs, 18 sing English songs and 4 sing both. How many sing at least one of the two?
  35. 35.In a group of 30 grown-ups, 16 drink tea, 18 drink coffee and 9 drink both. How many drink only coffee?
  36. 36.In a group of 44 grown-ups, 13 drink tea, 20 drink coffee and 3 drink both. How many drink at least one of the two?
  37. 37.In a group of 35 children, 23 sing Hindi songs, 15 sing English songs and 7 sing both. How many sing at least one of the two?
  38. 38.In a group of 40 children, 23 play chess, 9 play carrom and 5 play both. How many play only carrom?
  39. 39.In a group of 25 children, 12 play cricket, 17 play football and 5 play both. How many play exactly one of the two?
  40. 40.In a group of 36 children, 16 enjoy drawing, 27 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?

Answer key

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

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