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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 590 · 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 30 children, 15 enjoy drawing, 11 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  2. 2.In a group of 32 children, 17 play chess, 20 play carrom and 11 play both. How many play neither of the two?
  3. 3.In a group of 36 children, 20 enjoy drawing, 17 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 38 children, 18 play cricket, 12 play football and 6 play both. How many play only cricket?
  5. 5.In a group of 28 children, 19 like mangoes, 8 like bananas and 5 like both. How many like exactly one of the two?
  6. 6.In a group of 27 children, 14 play cricket, 15 play football and 8 play both. How many play only football?
  7. 7.In a group of 54 children, 25 play cricket, 26 play football and 9 play both. How many play only cricket?
  8. 8.In a group of 38 children, 23 like mangoes, 19 like bananas and 8 like both. How many like at least one of the two?
  9. 9.In a group of 23 children, 16 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing only Hindi songs?
  10. 10.In a group of 43 grown-ups, 24 drink tea, 23 drink coffee and 9 drink both. How many drink neither of the two?
  11. 11.In a group of 39 children, 26 play chess, 13 play carrom and 8 play both. How many play neither of the two?
  12. 12.In a group of 38 grown-ups, 16 drink tea, 17 drink coffee and 10 drink both. How many drink only tea?
  13. 13.In a group of 34 children, 20 enjoy drawing, 6 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 38 children, 17 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing neither of the two?
  15. 15.In a group of 37 children, 28 enjoy drawing, 18 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 25 children, 15 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  17. 17.In a group of 40 children, 26 sing Hindi songs, 21 sing English songs and 9 sing both. How many sing neither of the two?
  18. 18.In a group of 34 children, 21 like mangoes, 16 like bananas and 6 like both. How many like only mangoes?
  19. 19.In a group of 36 children, 13 like mangoes, 21 like bananas and 4 like both. How many like neither of the two?
  20. 20.In a group of 37 children, 21 like mangoes, 14 like bananas and 6 like both. How many like only mangoes?
  21. 21.In a group of 28 grown-ups, 18 drink tea, 11 drink coffee and 6 drink both. How many drink only tea?
  22. 22.In a group of 41 children, 25 enjoy drawing, 14 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  23. 23.In a group of 34 children, 12 like mangoes, 19 like bananas and 4 like both. How many like exactly one of the two?
  24. 24.In a group of 26 children, 13 sing Hindi songs, 15 sing English songs and 7 sing both. How many sing exactly one of the two?
  25. 25.In a group of 34 grown-ups, 11 drink tea, 13 drink coffee and 5 drink both. How many drink neither of the two?
  26. 26.In a group of 35 children, 11 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  27. 27.In a group of 35 children, 16 sing Hindi songs, 24 sing English songs and 11 sing both. How many sing only English songs?
  28. 28.In a group of 52 children, 29 play chess, 20 play carrom and 9 play both. How many play only chess?
  29. 29.In a group of 32 children, 9 sing Hindi songs, 24 sing English songs and 5 sing both. How many sing at least one of the two?
  30. 30.In a group of 28 children, 12 play cricket, 13 play football and 5 play both. How many play neither of the two?
  31. 31.In a group of 35 children, 20 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing only Hindi songs?
  32. 32.In a group of 23 children, 11 play chess, 18 play carrom and 8 play both. How many play only carrom?
  33. 33.In a group of 43 children, 27 play cricket, 24 play football and 11 play both. How many play neither of the two?
  34. 34.In a group of 42 grown-ups, 20 drink tea, 29 drink coffee and 11 drink both. How many drink exactly one of the two?
  35. 35.In a group of 27 grown-ups, 11 drink tea, 19 drink coffee and 7 drink both. How many drink only tea?
  36. 36.In a group of 24 children, 10 play chess, 10 play carrom and 6 play both. How many play exactly one of the two?
  37. 37.In a group of 22 children, 18 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  38. 38.In a group of 36 children, 28 play cricket, 15 play football and 9 play both. How many play neither of the two?
  39. 39.In a group of 42 children, 23 play cricket, 25 play football and 10 play both. How many play only football?
  40. 40.In a group of 36 grown-ups, 25 drink tea, 10 drink coffee and 5 drink both. How many drink exactly one of the two?

Answer key

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

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