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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 666 · 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 42 children, 19 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing neither of the two?
  2. 2.In a group of 38 children, 27 play cricket, 20 play football and 12 play both. How many play at least one of the two?
  3. 3.In a group of 39 children, 18 play cricket, 20 play football and 2 play both. How many play neither of the two?
  4. 4.In a group of 37 children, 16 enjoy drawing, 18 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 29 children, 12 play cricket, 14 play football and 6 play both. How many play only cricket?
  6. 6.In a group of 36 children, 20 enjoy drawing, 20 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 32 children, 8 enjoy drawing, 16 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  8. 8.In a group of 34 children, 15 sing Hindi songs, 12 sing English songs and 4 sing both. How many sing only English songs?
  9. 9.In a group of 20 children, 10 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  10. 10.In a group of 33 children, 17 sing Hindi songs, 13 sing English songs and 5 sing both. How many sing exactly one of the two?
  11. 11.In a group of 34 children, 15 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing exactly one of the two?
  12. 12.In a group of 29 children, 10 play cricket, 15 play football and 3 play both. How many play only cricket?
  13. 13.In a group of 25 children, 20 enjoy drawing, 15 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  14. 14.In a group of 40 children, 28 enjoy drawing, 17 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  15. 15.In a group of 34 children, 18 play cricket, 8 play football and 2 play both. How many play only football?
  16. 16.In a group of 52 children, 25 like mangoes, 23 like bananas and 9 like both. How many like neither of the two?
  17. 17.In a group of 30 children, 16 play cricket, 19 play football and 6 play both. How many play at least one of the two?
  18. 18.In a group of 35 children, 22 play cricket, 17 play football and 9 play both. How many play at least one of the two?
  19. 19.In a group of 47 children, 18 enjoy drawing, 26 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  20. 20.In a group of 44 children, 19 like mangoes, 20 like bananas and 9 like both. How many like only mangoes?
  21. 21.In a group of 31 children, 10 play cricket, 16 play football and 6 play both. How many play only football?
  22. 22.In a group of 39 children, 21 enjoy drawing, 26 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 46 grown-ups, 21 drink tea, 28 drink coffee and 11 drink both. How many drink at least one of the two?
  24. 24.In a group of 41 children, 24 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  25. 25.In a group of 30 children, 10 sing Hindi songs, 22 sing English songs and 3 sing both. How many sing only English songs?
  26. 26.In a group of 47 children, 18 play cricket, 19 play football and 4 play both. How many play exactly one of the two?
  27. 27.In a group of 40 children, 20 play cricket, 20 play football and 8 play both. How many play only football?
  28. 28.In a group of 40 children, 31 play cricket, 17 play football and 12 play both. How many play at least one of the two?
  29. 29.In a group of 41 children, 13 play cricket, 21 play football and 2 play both. How many play at least one of the two?
  30. 30.In a group of 36 children, 17 play cricket, 20 play football and 12 play both. How many play neither of the two?
  31. 31.In a group of 48 children, 26 play cricket, 26 play football and 8 play both. How many play exactly one of the two?
  32. 32.In a group of 33 children, 18 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing at least one of the two?
  33. 33.In a group of 50 children, 29 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 19 children, 9 play cricket, 7 play football and 2 play both. How many play only cricket?
  35. 35.In a group of 39 children, 17 like mangoes, 17 like bananas and 6 like both. How many like exactly one of the two?
  36. 36.In a group of 23 children, 13 sing Hindi songs, 15 sing English songs and 8 sing both. How many sing only English songs?
  37. 37.In a group of 38 children, 25 sing Hindi songs, 17 sing English songs and 12 sing both. How many sing neither of the two?
  38. 38.In a group of 33 children, 8 like mangoes, 23 like bananas and 3 like both. How many like exactly one of the two?
  39. 39.In a group of 33 children, 16 play cricket, 11 play football and 5 play both. How many play at least one of the two?
  40. 40.In a group of 38 children, 26 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?

Answer key

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

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