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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 62 · 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 33 children, 13 play cricket, 26 play football and 7 play both. How many play neither of the two?
  2. 2.In a group of 44 children, 19 enjoy drawing, 26 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  3. 3.In a group of 34 children, 11 play cricket, 16 play football and 2 play both. How many play only football?
  4. 4.In a group of 29 children, 17 play cricket, 21 play football and 10 play both. How many play only football?
  5. 5.In a group of 35 children, 22 play cricket, 7 play football and 2 play both. How many play neither of the two?
  6. 6.In a group of 29 children, 10 play chess, 22 play carrom and 6 play both. How many play only chess?
  7. 7.In a group of 31 children, 6 play chess, 13 play carrom and 3 play both. How many play at least one of the two?
  8. 8.In a group of 45 children, 26 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  9. 9.In a group of 40 children, 11 enjoy drawing, 23 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  10. 10.In a group of 42 children, 16 sing Hindi songs, 23 sing English songs and 12 sing both. How many sing only Hindi songs?
  11. 11.In a group of 36 children, 21 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  12. 12.In a group of 40 grown-ups, 20 drink tea, 16 drink coffee and 8 drink both. How many drink exactly one of the two?
  13. 13.In a group of 51 children, 19 sing Hindi songs, 27 sing English songs and 7 sing both. How many sing only English songs?
  14. 14.In a group of 41 grown-ups, 24 drink tea, 21 drink coffee and 10 drink both. How many drink at least one of the two?
  15. 15.In a group of 31 grown-ups, 10 drink tea, 25 drink coffee and 5 drink both. How many drink at least one of the two?
  16. 16.In a group of 33 children, 7 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing only English songs?
  17. 17.In a group of 44 children, 24 like mangoes, 22 like bananas and 11 like both. How many like only mangoes?
  18. 18.In a group of 27 children, 9 play cricket, 9 play football and 6 play both. How many play exactly one of the two?
  19. 19.In a group of 27 children, 10 like mangoes, 11 like bananas and 5 like both. How many like neither of the two?
  20. 20.In a group of 28 children, 16 enjoy drawing, 21 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 25 children, 11 play chess, 18 play carrom and 7 play both. How many play only chess?
  22. 22.In a group of 25 children, 12 like mangoes, 10 like bananas and 5 like both. How many like only mangoes?
  23. 23.In a group of 46 children, 24 play cricket, 13 play football and 6 play both. How many play only cricket?
  24. 24.In a group of 26 children, 9 like mangoes, 20 like bananas and 6 like both. How many like only mangoes?
  25. 25.In a group of 27 children, 17 enjoy drawing, 17 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 36 children, 25 play cricket, 17 play football and 12 play both. How many play only football?
  27. 27.In a group of 33 children, 12 like mangoes, 26 like bananas and 7 like both. How many like at least one of the two?
  28. 28.In a group of 34 children, 13 like mangoes, 29 like bananas and 10 like both. How many like at least one of the two?
  29. 29.In a group of 37 children, 7 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing exactly one of the two?
  30. 30.In a group of 24 children, 15 like mangoes, 17 like bananas and 10 like both. How many like only mangoes?
  31. 31.In a group of 48 children, 19 like mangoes, 22 like bananas and 6 like both. How many like exactly one of the two?
  32. 32.In a group of 24 children, 7 like mangoes, 8 like bananas and 2 like both. How many like only bananas?
  33. 33.In a group of 29 children, 13 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing neither of the two?
  34. 34.In a group of 51 children, 24 play cricket, 24 play football and 7 play both. How many play neither of the two?
  35. 35.In a group of 26 children, 15 enjoy drawing, 11 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 39 children, 14 play chess, 19 play carrom and 7 play both. How many play at least one of the two?
  37. 37.In a group of 41 grown-ups, 21 drink tea, 21 drink coffee and 6 drink both. How many drink neither of the two?
  38. 38.In a group of 33 children, 18 play chess, 19 play carrom and 7 play both. How many play only chess?
  39. 39.In a group of 35 children, 9 play cricket, 20 play football and 2 play both. How many play only football?
  40. 40.In a group of 23 children, 5 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?

Answer key

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

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