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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 384 · 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 36 children, 16 play cricket, 24 play football and 9 play both. How many play exactly one of the two?
  2. 2.In a group of 45 children, 12 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  3. 3.In a group of 42 children, 14 play cricket, 20 play football and 3 play both. How many play only football?
  4. 4.In a group of 57 children, 23 play chess, 24 play carrom and 4 play both. How many play only carrom?
  5. 5.In a group of 58 children, 25 sing Hindi songs, 24 sing English songs and 6 sing both. How many sing only Hindi songs?
  6. 6.In a group of 40 grown-ups, 19 drink tea, 16 drink coffee and 2 drink both. How many drink at least one of the two?
  7. 7.In a group of 37 children, 26 play chess, 18 play carrom and 10 play both. How many play at least one of the two?
  8. 8.In a group of 42 children, 9 play chess, 22 play carrom and 2 play both. How many play only chess?
  9. 9.In a group of 50 children, 29 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  10. 10.In a group of 45 children, 18 play chess, 29 play carrom and 12 play both. How many play only carrom?
  11. 11.In a group of 23 children, 16 enjoy drawing, 9 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  12. 12.In a group of 18 grown-ups, 12 drink tea, 12 drink coffee and 7 drink both. How many drink only tea?
  13. 13.In a group of 21 grown-ups, 9 drink tea, 8 drink coffee and 3 drink both. How many drink only coffee?
  14. 14.In a group of 38 children, 16 like mangoes, 13 like bananas and 3 like both. How many like only bananas?
  15. 15.In a group of 47 children, 30 sing Hindi songs, 17 sing English songs and 12 sing both. How many sing neither of the two?
  16. 16.In a group of 49 children, 25 enjoy drawing, 21 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 44 children, 21 play cricket, 29 play football and 11 play both. How many play only football?
  18. 18.In a group of 49 children, 28 like mangoes, 26 like bananas and 8 like both. How many like exactly one of the two?
  19. 19.In a group of 47 children, 21 play chess, 26 play carrom and 10 play both. How many play only carrom?
  20. 20.In a group of 52 children, 29 sing Hindi songs, 31 sing English songs and 11 sing both. How many sing at least one of the two?
  21. 21.In a group of 18 grown-ups, 10 drink tea, 7 drink coffee and 4 drink both. How many drink neither of the two?
  22. 22.In a group of 40 grown-ups, 10 drink tea, 25 drink coffee and 6 drink both. How many drink only tea?
  23. 23.In a group of 26 children, 13 play chess, 14 play carrom and 9 play both. How many play only chess?
  24. 24.In a group of 50 children, 24 play cricket, 23 play football and 6 play both. How many play neither of the two?
  25. 25.In a group of 53 children, 29 play cricket, 26 play football and 12 play both. How many play exactly one of the two?
  26. 26.In a group of 55 children, 26 like mangoes, 20 like bananas and 6 like both. How many like neither of the two?
  27. 27.In a group of 36 children, 20 sing Hindi songs, 22 sing English songs and 12 sing both. How many sing exactly one of the two?
  28. 28.In a group of 31 children, 16 play cricket, 16 play football and 2 play both. How many play only cricket?
  29. 29.In a group of 40 children, 17 enjoy drawing, 29 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  30. 30.In a group of 54 children, 21 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing only Hindi songs?
  31. 31.In a group of 23 children, 12 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 41 children, 13 enjoy drawing, 19 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  33. 33.In a group of 29 children, 18 play cricket, 11 play football and 8 play both. How many play only cricket?
  34. 34.In a group of 28 children, 15 play chess, 10 play carrom and 4 play both. How many play at least one of the two?
  35. 35.In a group of 28 children, 9 sing Hindi songs, 10 sing English songs and 4 sing both. How many sing at least one of the two?
  36. 36.In a group of 51 grown-ups, 24 drink tea, 21 drink coffee and 6 drink both. How many drink only coffee?
  37. 37.In a group of 39 children, 12 sing Hindi songs, 18 sing English songs and 3 sing both. How many sing neither of the two?
  38. 38.In a group of 45 children, 18 like mangoes, 24 like bananas and 11 like both. How many like only mangoes?
  39. 39.In a group of 41 children, 15 sing Hindi songs, 25 sing English songs and 10 sing both. How many sing neither of the two?
  40. 40.In a group of 37 children, 10 play chess, 14 play carrom and 2 play both. How many play exactly one of the two?

Answer key

  1. 22
  2. 3
  3. 17
  4. 20
  5. 19
  6. 33
  7. 34
  8. 7
  9. 18
  10. 17
  11. 15
  12. 5
  13. 5
  14. 10
  15. 12
  16. 13
  17. 18
  18. 38
  19. 16
  20. 49
  21. 5
  22. 4
  23. 4
  24. 9
  25. 31
  26. 15
  27. 18
  28. 14
  29. 18
  30. 9
  31. 5
  32. 26
  33. 10
  34. 21
  35. 15
  36. 15
  37. 12
  38. 7
  39. 11
  40. 20

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