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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 400 · 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 33 children, 21 play cricket, 7 play football and 3 play both. How many play exactly one of the two?
  2. 2.In a group of 38 grown-ups, 11 drink tea, 19 drink coffee and 6 drink both. How many drink only tea?
  3. 3.In a group of 29 children, 16 sing Hindi songs, 13 sing English songs and 5 sing both. How many sing exactly one of the two?
  4. 4.In a group of 24 children, 17 play cricket, 11 play football and 6 play both. How many play at least one of the two?
  5. 5.In a group of 16 children, 5 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  6. 6.In a group of 41 children, 21 like mangoes, 18 like bananas and 3 like both. How many like only mangoes?
  7. 7.In a group of 51 children, 26 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing exactly one of the two?
  8. 8.In a group of 43 children, 17 like mangoes, 21 like bananas and 10 like both. How many like only mangoes?
  9. 9.In a group of 21 children, 10 play cricket, 12 play football and 6 play both. How many play only football?
  10. 10.In a group of 46 children, 11 enjoy drawing, 24 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  11. 11.In a group of 54 children, 20 play chess, 28 play carrom and 9 play both. How many play only carrom?
  12. 12.In a group of 33 children, 17 play chess, 18 play carrom and 6 play both. How many play at least one of the two?
  13. 13.In a group of 22 children, 6 play cricket, 6 play football and 3 play both. How many play at least one of the two?
  14. 14.In a group of 30 children, 22 play cricket, 13 play football and 8 play both. How many play neither of the two?
  15. 15.In a group of 43 children, 11 play cricket, 24 play football and 5 play both. How many play at least one of the two?
  16. 16.In a group of 49 children, 31 play chess, 28 play carrom and 12 play both. How many play only chess?
  17. 17.In a group of 40 children, 12 like mangoes, 28 like bananas and 9 like both. How many like neither of the two?
  18. 18.In a group of 35 children, 17 enjoy drawing, 19 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  19. 19.In a group of 38 children, 27 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 41 children, 24 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  21. 21.In a group of 26 children, 13 play chess, 18 play carrom and 6 play both. How many play at least one of the two?
  22. 22.In a group of 51 children, 23 sing Hindi songs, 19 sing English songs and 5 sing both. How many sing only Hindi songs?
  23. 23.In a group of 31 grown-ups, 12 drink tea, 18 drink coffee and 7 drink both. How many drink at least one of the two?
  24. 24.In a group of 27 grown-ups, 9 drink tea, 21 drink coffee and 5 drink both. How many drink neither of the two?
  25. 25.In a group of 40 children, 20 sing Hindi songs, 24 sing English songs and 8 sing both. How many sing only Hindi songs?
  26. 26.In a group of 39 children, 7 enjoy drawing, 21 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 41 grown-ups, 23 drink tea, 20 drink coffee and 4 drink both. How many drink at least one of the two?
  28. 28.In a group of 34 children, 12 like mangoes, 19 like bananas and 8 like both. How many like neither of the two?
  29. 29.In a group of 33 children, 15 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing only English songs?
  30. 30.In a group of 32 grown-ups, 16 drink tea, 24 drink coffee and 11 drink both. How many drink only coffee?
  31. 31.In a group of 33 children, 15 play cricket, 20 play football and 4 play both. How many play only football?
  32. 32.In a group of 42 children, 14 like mangoes, 22 like bananas and 5 like both. How many like exactly one of the two?
  33. 33.In a group of 45 children, 19 enjoy drawing, 22 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  34. 34.In a group of 31 grown-ups, 13 drink tea, 16 drink coffee and 2 drink both. How many drink neither of the two?
  35. 35.In a group of 28 children, 22 sing Hindi songs, 12 sing English songs and 9 sing both. How many sing exactly one of the two?
  36. 36.In a group of 50 grown-ups, 22 drink tea, 28 drink coffee and 9 drink both. How many drink at least one of the two?
  37. 37.In a group of 53 grown-ups, 21 drink tea, 31 drink coffee and 12 drink both. How many drink at least one of the two?
  38. 38.In a group of 41 children, 29 sing Hindi songs, 19 sing English songs and 11 sing both. How many sing only English songs?
  39. 39.In a group of 39 grown-ups, 22 drink tea, 20 drink coffee and 7 drink both. How many drink at least one of the two?
  40. 40.In a group of 41 children, 20 play cricket, 13 play football and 4 play both. How many play only football?

Answer key

  1. 22
  2. 5
  3. 19
  4. 22
  5. 7
  6. 18
  7. 37
  8. 7
  9. 6
  10. 7
  11. 19
  12. 29
  13. 9
  14. 3
  15. 30
  16. 19
  17. 9
  18. 9
  19. 19
  20. 24
  21. 25
  22. 18
  23. 23
  24. 2
  25. 12
  26. 19
  27. 39
  28. 11
  29. 5
  30. 13
  31. 16
  32. 26
  33. 39
  34. 4
  35. 16
  36. 41
  37. 40
  38. 8
  39. 35
  40. 9

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