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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 660 · 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 47 children, 27 enjoy drawing, 28 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 48 children, 19 play cricket, 30 play football and 12 play both. How many play only cricket?
  3. 3.In a group of 28 children, 17 sing Hindi songs, 14 sing English songs and 6 sing both. How many sing neither of the two?
  4. 4.In a group of 41 children, 31 play cricket, 16 play football and 11 play both. How many play exactly one of the two?
  5. 5.In a group of 18 children, 10 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing only Hindi songs?
  6. 6.In a group of 31 grown-ups, 17 drink tea, 18 drink coffee and 12 drink both. How many drink only tea?
  7. 7.In a group of 25 children, 8 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing only Hindi songs?
  8. 8.In a group of 29 children, 14 play cricket, 15 play football and 9 play both. How many play neither of the two?
  9. 9.In a group of 38 children, 16 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 29 children, 21 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  11. 11.In a group of 38 children, 12 enjoy drawing, 26 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  12. 12.In a group of 49 children, 19 like mangoes, 30 like bananas and 10 like both. How many like neither of the two?
  13. 13.In a group of 51 children, 23 like mangoes, 24 like bananas and 7 like both. How many like only mangoes?
  14. 14.In a group of 43 children, 18 play cricket, 26 play football and 8 play both. How many play at least one of the two?
  15. 15.In a group of 35 children, 12 play cricket, 23 play football and 6 play both. How many play exactly one of the two?
  16. 16.In a group of 20 children, 13 play cricket, 5 play football and 2 play both. How many play only cricket?
  17. 17.In a group of 62 children, 31 enjoy drawing, 32 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  18. 18.In a group of 48 children, 15 like mangoes, 28 like bananas and 8 like both. How many like at least one of the two?
  19. 19.In a group of 31 children, 15 sing Hindi songs, 17 sing English songs and 6 sing both. How many sing neither of the two?
  20. 20.In a group of 29 children, 19 play chess, 6 play carrom and 3 play both. How many play only chess?
  21. 21.In a group of 28 grown-ups, 6 drink tea, 23 drink coffee and 3 drink both. How many drink exactly one of the two?
  22. 22.In a group of 30 children, 24 like mangoes, 11 like bananas and 6 like both. How many like only bananas?
  23. 23.In a group of 32 children, 16 like mangoes, 12 like bananas and 9 like both. How many like exactly one of the two?
  24. 24.In a group of 28 children, 20 play cricket, 18 play football and 11 play both. How many play at least one of the two?
  25. 25.In a group of 42 children, 28 sing Hindi songs, 21 sing English songs and 8 sing both. How many sing only Hindi songs?
  26. 26.In a group of 41 children, 17 sing Hindi songs, 22 sing English songs and 3 sing both. How many sing only Hindi songs?
  27. 27.In a group of 27 children, 12 like mangoes, 7 like bananas and 3 like both. How many like neither of the two?
  28. 28.In a group of 41 children, 23 like mangoes, 15 like bananas and 4 like both. How many like exactly one of the two?
  29. 29.In a group of 37 children, 20 play chess, 25 play carrom and 11 play both. How many play only chess?
  30. 30.In a group of 40 children, 31 play chess, 16 play carrom and 11 play both. How many play exactly one of the two?
  31. 31.In a group of 36 children, 24 play cricket, 15 play football and 6 play both. How many play only football?
  32. 32.In a group of 49 children, 27 enjoy drawing, 21 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  33. 33.In a group of 34 grown-ups, 16 drink tea, 23 drink coffee and 6 drink both. How many drink exactly one of the two?
  34. 34.In a group of 34 children, 15 like mangoes, 8 like bananas and 3 like both. How many like neither of the two?
  35. 35.In a group of 46 children, 23 like mangoes, 14 like bananas and 5 like both. How many like only bananas?
  36. 36.In a group of 26 children, 19 enjoy drawing, 16 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  37. 37.In a group of 32 grown-ups, 18 drink tea, 9 drink coffee and 4 drink both. How many drink neither of the two?
  38. 38.In a group of 38 children, 17 play chess, 24 play carrom and 5 play both. How many play exactly one of the two?
  39. 39.In a group of 47 children, 25 play chess, 22 play carrom and 6 play both. How many play only chess?
  40. 40.In a group of 38 children, 15 play chess, 13 play carrom and 4 play both. How many play exactly one of the two?

Answer key

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

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