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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 258 · 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 39 grown-ups, 23 drink tea, 21 drink coffee and 9 drink both. How many drink neither of the two?
  2. 2.In a group of 19 children, 10 play cricket, 11 play football and 5 play both. How many play exactly one of the two?
  3. 3.In a group of 46 grown-ups, 19 drink tea, 27 drink coffee and 10 drink both. How many drink only tea?
  4. 4.In a group of 27 children, 17 like mangoes, 21 like bananas and 12 like both. How many like at least one of the two?
  5. 5.In a group of 36 grown-ups, 20 drink tea, 18 drink coffee and 6 drink both. How many drink only coffee?
  6. 6.In a group of 51 children, 28 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  7. 7.In a group of 49 children, 26 play cricket, 25 play football and 9 play both. How many play neither of the two?
  8. 8.In a group of 25 children, 13 play cricket, 14 play football and 9 play both. How many play exactly one of the two?
  9. 9.In a group of 38 children, 11 play chess, 20 play carrom and 4 play both. How many play only chess?
  10. 10.In a group of 33 children, 21 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  11. 11.In a group of 40 children, 20 enjoy drawing, 20 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  12. 12.In a group of 45 children, 27 play chess, 25 play carrom and 9 play both. How many play only chess?
  13. 13.In a group of 31 children, 16 enjoy drawing, 8 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  14. 14.In a group of 34 children, 12 play chess, 11 play carrom and 3 play both. How many play at least one of the two?
  15. 15.In a group of 42 children, 22 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 35 children, 19 enjoy drawing, 12 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 37 children, 18 play cricket, 11 play football and 7 play both. How many play at least one of the two?
  18. 18.In a group of 45 grown-ups, 11 drink tea, 22 drink coffee and 3 drink both. How many drink only tea?
  19. 19.In a group of 35 children, 9 play cricket, 25 play football and 5 play both. How many play only cricket?
  20. 20.In a group of 43 children, 19 play cricket, 23 play football and 12 play both. How many play only football?
  21. 21.In a group of 24 children, 15 sing Hindi songs, 14 sing English songs and 11 sing both. How many sing neither of the two?
  22. 22.In a group of 54 grown-ups, 30 drink tea, 29 drink coffee and 12 drink both. How many drink at least one of the two?
  23. 23.In a group of 49 children, 17 enjoy drawing, 27 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 32 grown-ups, 20 drink tea, 13 drink coffee and 7 drink both. How many drink exactly one of the two?
  25. 25.In a group of 20 children, 9 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing neither of the two?
  26. 26.In a group of 28 children, 17 enjoy drawing, 12 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 28 children, 22 play chess, 10 play carrom and 6 play both. How many play exactly one of the two?
  28. 28.In a group of 27 children, 17 enjoy drawing, 11 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  29. 29.In a group of 44 children, 20 sing Hindi songs, 16 sing English songs and 4 sing both. How many sing only English songs?
  30. 30.In a group of 45 children, 23 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  31. 31.In a group of 34 children, 17 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  32. 32.In a group of 50 children, 22 like mangoes, 21 like bananas and 8 like both. How many like at least one of the two?
  33. 33.In a group of 12 grown-ups, 6 drink tea, 6 drink coffee and 3 drink both. How many drink only tea?
  34. 34.In a group of 39 children, 24 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  35. 35.In a group of 38 children, 12 sing Hindi songs, 21 sing English songs and 4 sing both. How many sing at least one of the two?
  36. 36.In a group of 35 children, 10 like mangoes, 16 like bananas and 6 like both. How many like exactly one of the two?
  37. 37.In a group of 35 children, 17 like mangoes, 13 like bananas and 10 like both. How many like at least one of the two?
  38. 38.In a group of 27 grown-ups, 14 drink tea, 8 drink coffee and 5 drink both. How many drink exactly one of the two?
  39. 39.In a group of 39 children, 20 enjoy drawing, 12 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  40. 40.In a group of 48 grown-ups, 26 drink tea, 29 drink coffee and 11 drink both. How many drink at least one of the two?

Answer key

  1. 4
  2. 11
  3. 9
  4. 26
  5. 12
  6. 12
  7. 7
  8. 9
  9. 7
  10. 11
  11. 10
  12. 18
  13. 12
  14. 20
  15. 40
  16. 10
  17. 22
  18. 8
  19. 4
  20. 11
  21. 6
  22. 47
  23. 30
  24. 19
  25. 5
  26. 11
  27. 20
  28. 25
  29. 12
  30. 32
  31. 9
  32. 35
  33. 3
  34. 5
  35. 29
  36. 14
  37. 20
  38. 12
  39. 24
  40. 44

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