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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 142 · 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 35 children, 23 play cricket, 17 play football and 6 play both. How many play neither of the two?
  2. 2.In a group of 33 children, 11 sing Hindi songs, 15 sing English songs and 6 sing both. How many sing exactly one of the two?
  3. 3.In a group of 31 children, 14 play cricket, 18 play football and 10 play both. How many play neither of the two?
  4. 4.In a group of 45 children, 19 like mangoes, 22 like bananas and 2 like both. How many like only mangoes?
  5. 5.In a group of 37 children, 11 play cricket, 21 play football and 6 play both. How many play only football?
  6. 6.In a group of 30 children, 18 play chess, 17 play carrom and 12 play both. How many play only chess?
  7. 7.In a group of 29 children, 18 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing neither of the two?
  8. 8.In a group of 27 children, 11 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  9. 9.In a group of 32 children, 11 play chess, 15 play carrom and 3 play both. How many play neither of the two?
  10. 10.In a group of 28 children, 10 like mangoes, 16 like bananas and 3 like both. How many like exactly one of the two?
  11. 11.In a group of 40 grown-ups, 16 drink tea, 19 drink coffee and 4 drink both. How many drink exactly one of the two?
  12. 12.In a group of 36 children, 24 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  13. 13.In a group of 52 children, 31 play cricket, 27 play football and 12 play both. How many play only football?
  14. 14.In a group of 34 children, 21 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  15. 15.In a group of 40 children, 19 sing Hindi songs, 19 sing English songs and 9 sing both. How many sing exactly one of the two?
  16. 16.In a group of 43 grown-ups, 28 drink tea, 18 drink coffee and 10 drink both. How many drink only tea?
  17. 17.In a group of 59 grown-ups, 31 drink tea, 24 drink coffee and 11 drink both. How many drink exactly one of the two?
  18. 18.In a group of 23 grown-ups, 7 drink tea, 14 drink coffee and 3 drink both. How many drink only coffee?
  19. 19.In a group of 26 children, 12 play chess, 14 play carrom and 9 play both. How many play only chess?
  20. 20.In a group of 39 children, 25 play cricket, 17 play football and 10 play both. How many play only cricket?
  21. 21.In a group of 36 children, 16 play cricket, 28 play football and 10 play both. How many play exactly one of the two?
  22. 22.In a group of 25 children, 14 like mangoes, 18 like bananas and 8 like both. How many like exactly one of the two?
  23. 23.In a group of 53 children, 28 like mangoes, 24 like bananas and 12 like both. How many like neither of the two?
  24. 24.In a group of 42 children, 25 play cricket, 22 play football and 12 play both. How many play only football?
  25. 25.In a group of 28 children, 17 play chess, 11 play carrom and 8 play both. How many play only chess?
  26. 26.In a group of 27 children, 19 sing Hindi songs, 16 sing English songs and 9 sing both. How many sing only English songs?
  27. 27.In a group of 42 children, 24 play cricket, 9 play football and 4 play both. How many play only football?
  28. 28.In a group of 41 children, 12 enjoy drawing, 26 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 42 children, 26 enjoy drawing, 14 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 48 grown-ups, 21 drink tea, 30 drink coffee and 11 drink both. How many drink only coffee?
  31. 31.In a group of 46 children, 21 play chess, 24 play carrom and 8 play both. How many play at least one of the two?
  32. 32.In a group of 39 children, 22 sing Hindi songs, 12 sing English songs and 7 sing both. How many sing only English songs?
  33. 33.In a group of 56 children, 25 like mangoes, 31 like bananas and 12 like both. How many like exactly one of the two?
  34. 34.In a group of 25 grown-ups, 13 drink tea, 14 drink coffee and 6 drink both. How many drink only tea?
  35. 35.In a group of 59 children, 27 sing Hindi songs, 31 sing English songs and 11 sing both. How many sing neither of the two?
  36. 36.In a group of 56 children, 28 play chess, 24 play carrom and 8 play both. How many play only carrom?
  37. 37.In a group of 53 grown-ups, 22 drink tea, 23 drink coffee and 5 drink both. How many drink exactly one of the two?
  38. 38.In a group of 36 grown-ups, 23 drink tea, 12 drink coffee and 4 drink both. How many drink neither of the two?
  39. 39.In a group of 24 children, 6 sing Hindi songs, 12 sing English songs and 3 sing both. How many sing neither of the two?
  40. 40.In a group of 50 children, 17 like mangoes, 27 like bananas and 7 like both. How many like neither of the two?

Answer key

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

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