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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 356 · 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 31 children, 14 play cricket, 17 play football and 11 play both. How many play exactly one of the two?
  2. 2.In a group of 38 children, 20 play cricket, 22 play football and 12 play both. How many play neither of the two?
  3. 3.In a group of 34 children, 19 like mangoes, 6 like bananas and 3 like both. How many like neither of the two?
  4. 4.In a group of 32 children, 19 play chess, 17 play carrom and 12 play both. How many play at least one of the two?
  5. 5.In a group of 50 children, 30 play chess, 22 play carrom and 12 play both. How many play only chess?
  6. 6.In a group of 34 grown-ups, 18 drink tea, 14 drink coffee and 2 drink both. How many drink neither of the two?
  7. 7.In a group of 36 children, 28 sing Hindi songs, 14 sing English songs and 8 sing both. How many sing at least one of the two?
  8. 8.In a group of 27 children, 11 sing Hindi songs, 19 sing English songs and 7 sing both. How many sing only Hindi songs?
  9. 9.In a group of 35 children, 11 sing Hindi songs, 21 sing English songs and 5 sing both. How many sing only English songs?
  10. 10.In a group of 31 children, 10 like mangoes, 18 like bananas and 2 like both. How many like neither of the two?
  11. 11.In a group of 43 children, 24 enjoy drawing, 24 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 44 children, 23 sing Hindi songs, 18 sing English songs and 8 sing both. How many sing neither of the two?
  13. 13.In a group of 38 children, 18 play chess, 16 play carrom and 2 play both. How many play exactly one of the two?
  14. 14.In a group of 17 grown-ups, 10 drink tea, 8 drink coffee and 3 drink both. How many drink neither of the two?
  15. 15.In a group of 12 children, 7 play cricket, 8 play football and 4 play both. How many play only football?
  16. 16.In a group of 30 children, 16 play chess, 13 play carrom and 4 play both. How many play at least one of the two?
  17. 17.In a group of 44 children, 16 sing Hindi songs, 20 sing English songs and 4 sing both. How many sing neither of the two?
  18. 18.In a group of 45 children, 22 sing Hindi songs, 29 sing English songs and 11 sing both. How many sing at least one of the two?
  19. 19.In a group of 32 children, 9 play cricket, 26 play football and 6 play both. How many play exactly one of the two?
  20. 20.In a group of 43 children, 24 like mangoes, 27 like bananas and 11 like both. How many like neither of the two?
  21. 21.In a group of 39 children, 11 play cricket, 23 play football and 6 play both. How many play at least one of the two?
  22. 22.In a group of 33 children, 14 play chess, 20 play carrom and 9 play both. How many play only carrom?
  23. 23.In a group of 14 grown-ups, 6 drink tea, 6 drink coffee and 2 drink both. How many drink only coffee?
  24. 24.In a group of 38 children, 17 enjoy drawing, 22 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  25. 25.In a group of 36 children, 30 sing Hindi songs, 14 sing English songs and 11 sing both. How many sing only English songs?
  26. 26.In a group of 40 children, 19 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing only English songs?
  27. 27.In a group of 61 children, 30 sing Hindi songs, 32 sing English songs and 12 sing both. How many sing neither of the two?
  28. 28.In a group of 37 children, 24 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  29. 29.In a group of 28 children, 7 like mangoes, 10 like bananas and 3 like both. How many like neither of the two?
  30. 30.In a group of 35 children, 17 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing at least one of the two?
  31. 31.In a group of 32 children, 8 play chess, 15 play carrom and 2 play both. How many play exactly one of the two?
  32. 32.In a group of 29 grown-ups, 18 drink tea, 12 drink coffee and 7 drink both. How many drink only coffee?
  33. 33.In a group of 35 children, 26 play cricket, 14 play football and 11 play both. How many play only cricket?
  34. 34.In a group of 27 children, 20 like mangoes, 9 like bananas and 6 like both. How many like at least one of the two?
  35. 35.In a group of 30 children, 8 like mangoes, 13 like bananas and 3 like both. How many like exactly one of the two?
  36. 36.In a group of 47 children, 23 enjoy drawing, 30 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  37. 37.In a group of 34 children, 14 enjoy drawing, 26 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  38. 38.In a group of 48 children, 30 sing Hindi songs, 14 sing English songs and 10 sing both. How many sing neither of the two?
  39. 39.In a group of 58 children, 29 like mangoes, 29 like bananas and 11 like both. How many like neither of the two?
  40. 40.In a group of 49 grown-ups, 19 drink tea, 20 drink coffee and 4 drink both. How many drink only coffee?

Answer key

  1. 9
  2. 8
  3. 12
  4. 24
  5. 18
  6. 4
  7. 34
  8. 4
  9. 16
  10. 5
  11. 15
  12. 11
  13. 30
  14. 2
  15. 4
  16. 25
  17. 12
  18. 40
  19. 23
  20. 3
  21. 28
  22. 11
  23. 4
  24. 27
  25. 3
  26. 18
  27. 11
  28. 18
  29. 14
  30. 22
  31. 19
  32. 5
  33. 15
  34. 23
  35. 15
  36. 43
  37. 3
  38. 14
  39. 11
  40. 16

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