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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 495 · 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 35 children, 11 enjoy drawing, 21 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 45 children, 20 sing Hindi songs, 23 sing English songs and 10 sing both. How many sing neither of the two?
  3. 3.In a group of 55 grown-ups, 24 drink tea, 25 drink coffee and 6 drink both. How many drink at least one of the two?
  4. 4.In a group of 30 children, 12 sing Hindi songs, 23 sing English songs and 7 sing both. How many sing only English songs?
  5. 5.In a group of 24 children, 5 play chess, 8 play carrom and 2 play both. How many play neither of the two?
  6. 6.In a group of 24 children, 12 like mangoes, 9 like bananas and 2 like both. How many like only mangoes?
  7. 7.In a group of 42 children, 9 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing only English songs?
  8. 8.In a group of 49 grown-ups, 26 drink tea, 27 drink coffee and 12 drink both. How many drink only tea?
  9. 9.In a group of 17 children, 8 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  10. 10.In a group of 37 children, 25 sing Hindi songs, 20 sing English songs and 10 sing both. How many sing only English songs?
  11. 11.In a group of 44 grown-ups, 21 drink tea, 27 drink coffee and 11 drink both. How many drink only coffee?
  12. 12.In a group of 33 children, 13 play cricket, 16 play football and 10 play both. How many play at least one of the two?
  13. 13.In a group of 42 children, 23 play cricket, 12 play football and 8 play both. How many play at least one of the two?
  14. 14.In a group of 37 children, 11 play cricket, 20 play football and 6 play both. How many play only football?
  15. 15.In a group of 35 children, 21 play cricket, 7 play football and 4 play both. How many play neither of the two?
  16. 16.In a group of 43 children, 23 play chess, 15 play carrom and 8 play both. How many play at least one of the two?
  17. 17.In a group of 28 children, 10 play cricket, 20 play football and 4 play both. How many play only cricket?
  18. 18.In a group of 39 grown-ups, 19 drink tea, 27 drink coffee and 11 drink both. How many drink neither of the two?
  19. 19.In a group of 36 children, 20 like mangoes, 6 like bananas and 3 like both. How many like at least one of the two?
  20. 20.In a group of 52 children, 17 enjoy drawing, 22 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  21. 21.In a group of 48 children, 21 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing only Hindi songs?
  22. 22.In a group of 54 children, 28 play chess, 29 play carrom and 12 play both. How many play exactly one of the two?
  23. 23.In a group of 35 children, 14 play chess, 10 play carrom and 2 play both. How many play exactly one of the two?
  24. 24.In a group of 37 children, 8 sing Hindi songs, 20 sing English songs and 2 sing both. How many sing only Hindi songs?
  25. 25.In a group of 46 children, 28 play chess, 24 play carrom and 12 play both. How many play only chess?
  26. 26.In a group of 46 children, 19 sing Hindi songs, 24 sing English songs and 8 sing both. How many sing neither of the two?
  27. 27.In a group of 24 grown-ups, 12 drink tea, 17 drink coffee and 7 drink both. How many drink neither of the two?
  28. 28.In a group of 52 children, 20 sing Hindi songs, 25 sing English songs and 7 sing both. How many sing at least one of the two?
  29. 29.In a group of 41 grown-ups, 21 drink tea, 11 drink coffee and 4 drink both. How many drink at least one of the two?
  30. 30.In a group of 43 children, 12 sing Hindi songs, 20 sing English songs and 4 sing both. How many sing neither of the two?
  31. 31.In a group of 44 children, 20 sing Hindi songs, 24 sing English songs and 4 sing both. How many sing only English songs?
  32. 32.In a group of 36 children, 17 play chess, 17 play carrom and 2 play both. How many play neither of the two?
  33. 33.In a group of 29 children, 18 play chess, 13 play carrom and 8 play both. How many play only carrom?
  34. 34.In a group of 54 children, 29 like mangoes, 23 like bananas and 12 like both. How many like only bananas?
  35. 35.In a group of 36 children, 12 play cricket, 27 play football and 8 play both. How many play exactly one of the two?
  36. 36.In a group of 40 children, 24 play chess, 16 play carrom and 9 play both. How many play at least one of the two?
  37. 37.In a group of 13 children, 6 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing only Hindi songs?
  38. 38.In a group of 27 grown-ups, 18 drink tea, 16 drink coffee and 8 drink both. How many drink neither of the two?
  39. 39.In a group of 31 children, 15 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  40. 40.In a group of 34 children, 20 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?

Answer key

  1. 16
  2. 12
  3. 43
  4. 16
  5. 13
  6. 10
  7. 20
  8. 14
  9. 2
  10. 10
  11. 16
  12. 19
  13. 27
  14. 14
  15. 11
  16. 30
  17. 6
  18. 4
  19. 23
  20. 35
  21. 19
  22. 33
  23. 20
  24. 6
  25. 16
  26. 11
  27. 2
  28. 38
  29. 28
  30. 15
  31. 20
  32. 4
  33. 5
  34. 11
  35. 23
  36. 31
  37. 4
  38. 1
  39. 15
  40. 7

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