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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 425 · 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 42 children, 27 enjoy drawing, 24 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  2. 2.In a group of 24 children, 12 play cricket, 14 play football and 5 play both. How many play exactly one of the two?
  3. 3.In a group of 37 children, 15 play chess, 22 play carrom and 4 play both. How many play neither of the two?
  4. 4.In a group of 40 grown-ups, 24 drink tea, 17 drink coffee and 11 drink both. How many drink only coffee?
  5. 5.In a group of 29 children, 15 play chess, 8 play carrom and 2 play both. How many play neither of the two?
  6. 6.In a group of 49 children, 19 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing only English songs?
  7. 7.In a group of 31 children, 17 sing Hindi songs, 10 sing English songs and 7 sing both. How many sing exactly one of the two?
  8. 8.In a group of 45 grown-ups, 19 drink tea, 26 drink coffee and 7 drink both. How many drink only coffee?
  9. 9.In a group of 43 children, 15 enjoy drawing, 19 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  10. 10.In a group of 37 children, 17 play chess, 13 play carrom and 4 play both. How many play at least one of the two?
  11. 11.In a group of 46 children, 18 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  12. 12.In a group of 36 grown-ups, 25 drink tea, 13 drink coffee and 6 drink both. How many drink only tea?
  13. 13.In a group of 32 children, 12 play chess, 23 play carrom and 8 play both. How many play only chess?
  14. 14.In a group of 43 children, 22 play cricket, 22 play football and 3 play both. How many play exactly one of the two?
  15. 15.In a group of 38 children, 11 play chess, 20 play carrom and 4 play both. How many play only carrom?
  16. 16.In a group of 39 children, 27 play cricket, 18 play football and 12 play both. How many play neither of the two?
  17. 17.In a group of 26 children, 19 enjoy drawing, 9 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 39 children, 24 play chess, 11 play carrom and 7 play both. How many play exactly one of the two?
  19. 19.In a group of 46 children, 32 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 36 children, 29 enjoy drawing, 13 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 27 children, 13 sing Hindi songs, 14 sing English songs and 5 sing both. How many sing neither of the two?
  22. 22.In a group of 40 children, 26 like mangoes, 12 like bananas and 9 like both. How many like only bananas?
  23. 23.In a group of 20 children, 10 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing neither of the two?
  24. 24.In a group of 52 children, 17 sing Hindi songs, 30 sing English songs and 10 sing both. How many sing at least one of the two?
  25. 25.In a group of 46 children, 24 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  26. 26.In a group of 37 children, 23 enjoy drawing, 16 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 54 children, 27 play cricket, 22 play football and 9 play both. How many play exactly one of the two?
  28. 28.In a group of 35 children, 20 sing Hindi songs, 20 sing English songs and 8 sing both. How many sing only English songs?
  29. 29.In a group of 30 children, 13 enjoy drawing, 20 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 49 children, 29 play chess, 25 play carrom and 10 play both. How many play neither of the two?
  31. 31.In a group of 38 children, 22 sing Hindi songs, 16 sing English songs and 5 sing both. How many sing only Hindi songs?
  32. 32.In a group of 49 children, 28 like mangoes, 24 like bananas and 12 like both. How many like neither of the two?
  33. 33.In a group of 20 children, 10 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing only English songs?
  34. 34.In a group of 40 children, 19 play chess, 21 play carrom and 4 play both. How many play exactly one of the two?
  35. 35.In a group of 31 children, 20 like mangoes, 14 like bananas and 8 like both. How many like only mangoes?
  36. 36.In a group of 27 children, 22 play chess, 14 play carrom and 11 play both. How many play neither of the two?
  37. 37.In a group of 30 children, 14 enjoy drawing, 23 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 44 children, 28 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing only English songs?
  39. 39.In a group of 25 children, 13 like mangoes, 13 like bananas and 9 like both. How many like neither of the two?
  40. 40.In a group of 20 children, 12 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing only Hindi songs?

Answer key

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

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