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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 114 · 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 24 children, 15 play chess, 12 play carrom and 7 play both. How many play at least one of the two?
  2. 2.In a group of 37 children, 24 sing Hindi songs, 13 sing English songs and 6 sing both. How many sing at least one of the two?
  3. 3.In a group of 28 grown-ups, 19 drink tea, 17 drink coffee and 10 drink both. How many drink only tea?
  4. 4.In a group of 32 grown-ups, 19 drink tea, 20 drink coffee and 11 drink both. How many drink only coffee?
  5. 5.In a group of 40 children, 22 enjoy drawing, 13 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  6. 6.In a group of 21 children, 5 play cricket, 9 play football and 2 play both. How many play only cricket?
  7. 7.In a group of 47 children, 20 enjoy drawing, 24 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  8. 8.In a group of 27 children, 15 sing Hindi songs, 19 sing English songs and 9 sing both. How many sing only Hindi songs?
  9. 9.In a group of 44 children, 27 play cricket, 17 play football and 11 play both. How many play exactly one of the two?
  10. 10.In a group of 53 children, 30 play cricket, 27 play football and 10 play both. How many play only football?
  11. 11.In a group of 44 children, 11 sing Hindi songs, 22 sing English songs and 4 sing both. How many sing only English songs?
  12. 12.In a group of 39 grown-ups, 13 drink tea, 21 drink coffee and 6 drink both. How many drink only tea?
  13. 13.In a group of 23 children, 8 play cricket, 9 play football and 5 play both. How many play only cricket?
  14. 14.In a group of 40 children, 16 play cricket, 30 play football and 11 play both. How many play only football?
  15. 15.In a group of 27 children, 7 play cricket, 10 play football and 3 play both. How many play only cricket?
  16. 16.In a group of 35 children, 17 enjoy drawing, 16 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 29 grown-ups, 19 drink tea, 17 drink coffee and 11 drink both. How many drink exactly one of the two?
  18. 18.In a group of 43 children, 16 enjoy drawing, 24 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  19. 19.In a group of 30 children, 22 play cricket, 17 play football and 10 play both. How many play only cricket?
  20. 20.In a group of 46 children, 25 play chess, 19 play carrom and 8 play both. How many play only carrom?
  21. 21.In a group of 18 children, 13 play cricket, 12 play football and 8 play both. How many play only football?
  22. 22.In a group of 46 children, 25 play chess, 30 play carrom and 10 play both. How many play neither of the two?
  23. 23.In a group of 39 children, 22 sing Hindi songs, 12 sing English songs and 2 sing both. How many sing exactly one of the two?
  24. 24.In a group of 51 children, 29 play chess, 17 play carrom and 10 play both. How many play only carrom?
  25. 25.In a group of 33 children, 16 enjoy drawing, 10 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  26. 26.In a group of 52 children, 29 enjoy drawing, 31 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 26 grown-ups, 11 drink tea, 9 drink coffee and 5 drink both. How many drink only coffee?
  28. 28.In a group of 30 children, 22 like mangoes, 13 like bananas and 6 like both. How many like only bananas?
  29. 29.In a group of 32 children, 18 enjoy drawing, 21 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  30. 30.In a group of 32 children, 22 play chess, 9 play carrom and 4 play both. How many play at least one of the two?
  31. 31.In a group of 37 children, 20 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing only English songs?
  32. 32.In a group of 23 children, 9 sing Hindi songs, 14 sing English songs and 4 sing both. How many sing neither of the two?
  33. 33.In a group of 38 children, 22 sing Hindi songs, 22 sing English songs and 7 sing both. How many sing neither of the two?
  34. 34.In a group of 43 children, 10 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  35. 35.In a group of 45 children, 19 play cricket, 27 play football and 12 play both. How many play only cricket?
  36. 36.In a group of 31 grown-ups, 17 drink tea, 13 drink coffee and 4 drink both. How many drink at least one of the two?
  37. 37.In a group of 20 children, 9 sing Hindi songs, 8 sing English songs and 2 sing both. How many sing at least one of the two?
  38. 38.In a group of 37 children, 18 play cricket, 14 play football and 4 play both. How many play only football?
  39. 39.In a group of 46 children, 28 enjoy drawing, 13 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  40. 40.In a group of 43 children, 19 enjoy drawing, 31 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?

Answer key

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

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