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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 70 · 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 30 children, 16 play cricket, 8 play football and 2 play both. How many play at least one of the two?
  2. 2.In a group of 37 children, 19 play cricket, 22 play football and 11 play both. How many play only cricket?
  3. 3.In a group of 33 children, 11 enjoy drawing, 17 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  4. 4.In a group of 48 children, 22 like mangoes, 13 like bananas and 2 like both. How many like only bananas?
  5. 5.In a group of 41 children, 14 play cricket, 20 play football and 7 play both. How many play only football?
  6. 6.In a group of 37 children, 22 play cricket, 15 play football and 10 play both. How many play neither of the two?
  7. 7.In a group of 35 children, 25 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 39 children, 19 play chess, 13 play carrom and 7 play both. How many play only carrom?
  9. 9.In a group of 44 children, 21 play cricket, 29 play football and 10 play both. How many play only cricket?
  10. 10.In a group of 25 children, 15 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing exactly one of the two?
  11. 11.In a group of 39 children, 11 enjoy drawing, 21 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 59 children, 28 sing Hindi songs, 25 sing English songs and 9 sing both. How many sing at least one of the two?
  13. 13.In a group of 39 children, 14 play cricket, 21 play football and 10 play both. How many play only football?
  14. 14.In a group of 50 children, 16 play chess, 26 play carrom and 7 play both. How many play neither of the two?
  15. 15.In a group of 54 children, 30 sing Hindi songs, 29 sing English songs and 12 sing both. How many sing only English songs?
  16. 16.In a group of 45 children, 18 like mangoes, 24 like bananas and 12 like both. How many like neither of the two?
  17. 17.In a group of 44 children, 20 enjoy drawing, 20 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 45 children, 26 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  19. 19.In a group of 62 children, 29 enjoy drawing, 30 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  20. 20.In a group of 31 grown-ups, 14 drink tea, 22 drink coffee and 11 drink both. How many drink only tea?
  21. 21.In a group of 38 children, 13 play cricket, 21 play football and 8 play both. How many play exactly one of the two?
  22. 22.In a group of 39 children, 12 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing only English songs?
  23. 23.In a group of 53 children, 31 play cricket, 22 play football and 11 play both. How many play exactly one of the two?
  24. 24.In a group of 35 children, 24 sing Hindi songs, 19 sing English songs and 10 sing both. How many sing only Hindi songs?
  25. 25.In a group of 23 children, 17 play chess, 7 play carrom and 2 play both. How many play at least one of the two?
  26. 26.In a group of 40 children, 22 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing exactly one of the two?
  27. 27.In a group of 49 children, 25 enjoy drawing, 14 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  28. 28.In a group of 44 children, 26 like mangoes, 28 like bananas and 11 like both. How many like neither of the two?
  29. 29.In a group of 28 grown-ups, 16 drink tea, 16 drink coffee and 6 drink both. How many drink only tea?
  30. 30.In a group of 33 grown-ups, 18 drink tea, 20 drink coffee and 7 drink both. How many drink only coffee?
  31. 31.In a group of 45 children, 27 enjoy drawing, 24 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  32. 32.In a group of 44 children, 30 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing at least one of the two?
  33. 33.In a group of 25 children, 12 play cricket, 16 play football and 4 play both. How many play at least one of the two?
  34. 34.In a group of 26 grown-ups, 11 drink tea, 8 drink coffee and 4 drink both. How many drink only tea?
  35. 35.In a group of 22 children, 6 sing Hindi songs, 6 sing English songs and 3 sing both. How many sing only English songs?
  36. 36.In a group of 30 children, 11 play chess, 14 play carrom and 5 play both. How many play neither of the two?
  37. 37.In a group of 19 children, 6 like mangoes, 10 like bananas and 3 like both. How many like at least one of the two?
  38. 38.In a group of 31 children, 19 play chess, 9 play carrom and 3 play both. How many play only carrom?
  39. 39.In a group of 37 children, 20 play cricket, 9 play football and 5 play both. How many play only football?
  40. 40.In a group of 35 grown-ups, 10 drink tea, 19 drink coffee and 7 drink both. How many drink at least one of the two?

Answer key

  1. 22
  2. 8
  3. 12
  4. 11
  5. 13
  6. 10
  7. 2
  8. 6
  9. 11
  10. 12
  11. 6
  12. 44
  13. 11
  14. 15
  15. 17
  16. 15
  17. 11
  18. 15
  19. 14
  20. 3
  21. 18
  22. 20
  23. 31
  24. 14
  25. 22
  26. 27
  27. 9
  28. 1
  29. 10
  30. 13
  31. 41
  32. 43
  33. 24
  34. 7
  35. 3
  36. 10
  37. 13
  38. 6
  39. 4
  40. 22

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