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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 685 · 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 34 children, 12 enjoy drawing, 11 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 34 grown-ups, 8 drink tea, 20 drink coffee and 4 drink both. How many drink only coffee?
  3. 3.In a group of 23 children, 14 play chess, 10 play carrom and 7 play both. How many play only carrom?
  4. 4.In a group of 23 grown-ups, 9 drink tea, 9 drink coffee and 3 drink both. How many drink only tea?
  5. 5.In a group of 23 grown-ups, 9 drink tea, 11 drink coffee and 3 drink both. How many drink neither of the two?
  6. 6.In a group of 47 children, 19 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing exactly one of the two?
  7. 7.In a group of 37 children, 15 play cricket, 27 play football and 9 play both. How many play neither of the two?
  8. 8.In a group of 35 grown-ups, 22 drink tea, 18 drink coffee and 9 drink both. How many drink neither of the two?
  9. 9.In a group of 33 grown-ups, 12 drink tea, 21 drink coffee and 2 drink both. How many drink only tea?
  10. 10.In a group of 26 children, 6 enjoy drawing, 16 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  11. 11.In a group of 44 children, 28 enjoy drawing, 25 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  12. 12.In a group of 57 children, 26 like mangoes, 26 like bananas and 6 like both. How many like at least one of the two?
  13. 13.In a group of 35 children, 17 like mangoes, 16 like bananas and 4 like both. How many like only bananas?
  14. 14.In a group of 40 children, 23 play chess, 16 play carrom and 12 play both. How many play only chess?
  15. 15.In a group of 35 children, 8 play chess, 22 play carrom and 3 play both. How many play neither of the two?
  16. 16.In a group of 28 children, 10 play cricket, 12 play football and 6 play both. How many play only football?
  17. 17.In a group of 30 children, 17 play cricket, 18 play football and 12 play both. How many play exactly one of the two?
  18. 18.In a group of 38 children, 22 sing Hindi songs, 18 sing English songs and 5 sing both. How many sing only Hindi songs?
  19. 19.In a group of 47 children, 23 play cricket, 12 play football and 3 play both. How many play exactly one of the two?
  20. 20.In a group of 31 children, 16 play cricket, 19 play football and 6 play both. How many play only cricket?
  21. 21.In a group of 30 children, 7 play chess, 12 play carrom and 3 play both. How many play only carrom?
  22. 22.In a group of 36 children, 10 like mangoes, 19 like bananas and 5 like both. How many like at least one of the two?
  23. 23.In a group of 23 children, 7 play cricket, 12 play football and 2 play both. How many play exactly one of the two?
  24. 24.In a group of 41 children, 24 sing Hindi songs, 9 sing English songs and 4 sing both. How many sing at least one of the two?
  25. 25.In a group of 29 children, 22 play cricket, 6 play football and 3 play both. How many play at least one of the two?
  26. 26.In a group of 40 children, 27 like mangoes, 21 like bananas and 11 like both. How many like at least one of the two?
  27. 27.In a group of 23 grown-ups, 15 drink tea, 12 drink coffee and 9 drink both. How many drink exactly one of the two?
  28. 28.In a group of 50 children, 27 enjoy drawing, 29 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  29. 29.In a group of 37 children, 13 play cricket, 20 play football and 5 play both. How many play only football?
  30. 30.In a group of 37 children, 23 enjoy drawing, 21 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 24 children, 18 play chess, 17 play carrom and 12 play both. How many play exactly one of the two?
  32. 32.In a group of 46 children, 13 enjoy drawing, 22 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  33. 33.In a group of 35 children, 18 sing Hindi songs, 15 sing English songs and 2 sing both. How many sing only Hindi songs?
  34. 34.In a group of 58 children, 30 play cricket, 30 play football and 11 play both. How many play only cricket?
  35. 35.In a group of 35 children, 18 like mangoes, 23 like bananas and 7 like both. How many like neither of the two?
  36. 36.In a group of 39 grown-ups, 13 drink tea, 13 drink coffee and 2 drink both. How many drink exactly one of the two?
  37. 37.In a group of 39 grown-ups, 30 drink tea, 17 drink coffee and 11 drink both. How many drink exactly one of the two?
  38. 38.In a group of 33 grown-ups, 19 drink tea, 21 drink coffee and 9 drink both. How many drink neither of the two?
  39. 39.In a group of 33 children, 22 like mangoes, 18 like bananas and 11 like both. How many like exactly one of the two?
  40. 40.In a group of 63 grown-ups, 29 drink tea, 28 drink coffee and 9 drink both. How many drink neither of the two?

Answer key

  1. 13
  2. 16
  3. 3
  4. 6
  5. 6
  6. 30
  7. 4
  8. 4
  9. 10
  10. 4
  11. 31
  12. 46
  13. 12
  14. 11
  15. 8
  16. 6
  17. 11
  18. 17
  19. 29
  20. 10
  21. 9
  22. 24
  23. 15
  24. 29
  25. 25
  26. 37
  27. 9
  28. 17
  29. 15
  30. 13
  31. 11
  32. 33
  33. 16
  34. 19
  35. 1
  36. 22
  37. 25
  38. 2
  39. 18
  40. 15

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