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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 310 · 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 54 children, 25 play chess, 19 play carrom and 5 play both. How many play only chess?
  2. 2.In a group of 26 children, 10 enjoy drawing, 10 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  3. 3.In a group of 42 children, 18 play chess, 23 play carrom and 9 play both. How many play neither of the two?
  4. 4.In a group of 37 grown-ups, 13 drink tea, 19 drink coffee and 6 drink both. How many drink neither of the two?
  5. 5.In a group of 29 children, 20 play chess, 8 play carrom and 3 play both. How many play only carrom?
  6. 6.In a group of 33 children, 18 sing Hindi songs, 12 sing English songs and 2 sing both. How many sing exactly one of the two?
  7. 7.In a group of 52 children, 25 enjoy drawing, 24 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  8. 8.In a group of 34 children, 12 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  9. 9.In a group of 27 children, 19 sing Hindi songs, 17 sing English songs and 10 sing both. How many sing only English songs?
  10. 10.In a group of 42 children, 26 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  11. 11.In a group of 41 children, 15 like mangoes, 13 like bananas and 2 like both. How many like exactly one of the two?
  12. 12.In a group of 19 children, 14 play cricket, 14 play football and 11 play both. How many play only football?
  13. 13.In a group of 51 children, 27 play chess, 30 play carrom and 11 play both. How many play exactly one of the two?
  14. 14.In a group of 29 children, 17 enjoy drawing, 13 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  15. 15.In a group of 35 children, 14 play cricket, 21 play football and 7 play both. How many play neither of the two?
  16. 16.In a group of 46 grown-ups, 24 drink tea, 20 drink coffee and 12 drink both. How many drink exactly one of the two?
  17. 17.In a group of 33 children, 11 like mangoes, 15 like bananas and 2 like both. How many like neither of the two?
  18. 18.In a group of 55 children, 25 play cricket, 27 play football and 11 play both. How many play only football?
  19. 19.In a group of 32 grown-ups, 22 drink tea, 14 drink coffee and 11 drink both. How many drink at least one of the two?
  20. 20.In a group of 45 children, 21 play cricket, 29 play football and 11 play both. How many play exactly one of the two?
  21. 21.In a group of 42 children, 17 sing Hindi songs, 20 sing English songs and 4 sing both. How many sing only English songs?
  22. 22.In a group of 28 children, 18 like mangoes, 15 like bananas and 6 like both. How many like neither of the two?
  23. 23.In a group of 34 children, 15 enjoy drawing, 21 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  24. 24.In a group of 36 grown-ups, 21 drink tea, 14 drink coffee and 4 drink both. How many drink only coffee?
  25. 25.In a group of 37 children, 25 sing Hindi songs, 16 sing English songs and 5 sing both. How many sing only Hindi songs?
  26. 26.In a group of 53 children, 27 play cricket, 30 play football and 12 play both. How many play exactly one of the two?
  27. 27.In a group of 31 children, 23 play chess, 10 play carrom and 5 play both. How many play exactly one of the two?
  28. 28.In a group of 30 children, 17 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing exactly one of the two?
  29. 29.In a group of 41 children, 9 play chess, 22 play carrom and 2 play both. How many play exactly one of the two?
  30. 30.In a group of 24 children, 15 like mangoes, 5 like bananas and 2 like both. How many like neither of the two?
  31. 31.In a group of 43 children, 25 like mangoes, 18 like bananas and 7 like both. How many like only mangoes?
  32. 32.In a group of 29 children, 12 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  33. 33.In a group of 55 children, 25 play cricket, 24 play football and 8 play both. How many play at least one of the two?
  34. 34.In a group of 37 children, 10 sing Hindi songs, 24 sing English songs and 7 sing both. How many sing exactly one of the two?
  35. 35.In a group of 40 children, 17 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 44 children, 20 enjoy drawing, 30 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 44 children, 22 sing Hindi songs, 25 sing English songs and 8 sing both. How many sing at least one of the two?
  38. 38.In a group of 18 children, 14 play cricket, 9 play football and 6 play both. How many play only cricket?
  39. 39.In a group of 38 children, 25 play cricket, 12 play football and 5 play both. How many play only football?
  40. 40.In a group of 27 children, 18 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy only drawing?

Answer key

  1. 20
  2. 8
  3. 10
  4. 11
  5. 5
  6. 26
  7. 39
  8. 8
  9. 7
  10. 22
  11. 24
  12. 3
  13. 35
  14. 14
  15. 7
  16. 20
  17. 9
  18. 16
  19. 25
  20. 28
  21. 16
  22. 1
  23. 10
  24. 10
  25. 20
  26. 33
  27. 23
  28. 24
  29. 27
  30. 6
  31. 18
  32. 6
  33. 41
  34. 20
  35. 28
  36. 6
  37. 39
  38. 8
  39. 7
  40. 12

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