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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 87 · 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, 8 play cricket, 24 play football and 5 play both. How many play only cricket?
  2. 2.In a group of 23 children, 13 like mangoes, 18 like bananas and 10 like both. How many like at least one of the two?
  3. 3.In a group of 36 grown-ups, 20 drink tea, 15 drink coffee and 2 drink both. How many drink exactly one of the two?
  4. 4.In a group of 27 children, 8 sing Hindi songs, 20 sing English songs and 2 sing both. How many sing only Hindi songs?
  5. 5.In a group of 42 children, 29 play cricket, 21 play football and 10 play both. How many play exactly one of the two?
  6. 6.In a group of 41 grown-ups, 25 drink tea, 20 drink coffee and 8 drink both. How many drink exactly one of the two?
  7. 7.In a group of 41 children, 20 play cricket, 19 play football and 10 play both. How many play at least one of the two?
  8. 8.In a group of 46 children, 21 play chess, 18 play carrom and 6 play both. How many play exactly one of the two?
  9. 9.In a group of 38 grown-ups, 14 drink tea, 17 drink coffee and 5 drink both. How many drink only tea?
  10. 10.In a group of 15 children, 5 play chess, 9 play carrom and 2 play both. How many play neither of the two?
  11. 11.In a group of 33 children, 19 play chess, 8 play carrom and 2 play both. How many play only carrom?
  12. 12.In a group of 56 children, 30 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 53 children, 25 sing Hindi songs, 26 sing English songs and 9 sing both. How many sing only Hindi songs?
  14. 14.In a group of 41 grown-ups, 11 drink tea, 28 drink coffee and 8 drink both. How many drink only tea?
  15. 15.In a group of 24 children, 12 play chess, 14 play carrom and 8 play both. How many play only carrom?
  16. 16.In a group of 44 children, 25 sing Hindi songs, 26 sing English songs and 10 sing both. How many sing only Hindi songs?
  17. 17.In a group of 43 children, 27 play chess, 23 play carrom and 11 play both. How many play exactly one of the two?
  18. 18.In a group of 11 children, 6 play cricket, 5 play football and 2 play both. How many play only football?
  19. 19.In a group of 30 children, 21 play cricket, 11 play football and 3 play both. How many play only football?
  20. 20.In a group of 40 children, 15 sing Hindi songs, 24 sing English songs and 11 sing both. How many sing only Hindi songs?
  21. 21.In a group of 20 grown-ups, 16 drink tea, 8 drink coffee and 5 drink both. How many drink only coffee?
  22. 22.In a group of 55 grown-ups, 27 drink tea, 23 drink coffee and 7 drink both. How many drink neither of the two?
  23. 23.In a group of 41 children, 17 sing Hindi songs, 25 sing English songs and 10 sing both. How many sing only English songs?
  24. 24.In a group of 35 children, 18 play chess, 24 play carrom and 12 play both. How many play only chess?
  25. 25.In a group of 35 children, 15 like mangoes, 22 like bananas and 12 like both. How many like exactly one of the two?
  26. 26.In a group of 41 children, 27 like mangoes, 16 like bananas and 11 like both. How many like neither of the two?
  27. 27.In a group of 45 children, 28 like mangoes, 24 like bananas and 11 like both. How many like only bananas?
  28. 28.In a group of 46 grown-ups, 16 drink tea, 30 drink coffee and 10 drink both. How many drink at least one of the two?
  29. 29.In a group of 41 children, 14 play cricket, 21 play football and 4 play both. How many play at least one of the two?
  30. 30.In a group of 50 children, 16 play cricket, 31 play football and 12 play both. How many play only football?
  31. 31.In a group of 27 children, 16 like mangoes, 16 like bananas and 12 like both. How many like at least one of the two?
  32. 32.In a group of 55 children, 27 play chess, 21 play carrom and 7 play both. How many play only carrom?
  33. 33.In a group of 28 children, 13 like mangoes, 17 like bananas and 4 like both. How many like neither of the two?
  34. 34.In a group of 36 grown-ups, 16 drink tea, 16 drink coffee and 7 drink both. How many drink exactly one of the two?
  35. 35.In a group of 47 children, 22 enjoy drawing, 24 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  36. 36.In a group of 27 grown-ups, 16 drink tea, 14 drink coffee and 11 drink both. How many drink exactly one of the two?
  37. 37.In a group of 41 children, 30 enjoy drawing, 17 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  38. 38.In a group of 52 children, 31 play chess, 18 play carrom and 12 play both. How many play neither of the two?
  39. 39.In a group of 48 children, 24 play chess, 22 play carrom and 8 play both. How many play only carrom?
  40. 40.In a group of 29 children, 17 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?

Answer key

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

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