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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 551 · 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 37 children, 22 like mangoes, 14 like bananas and 4 like both. How many like at least one of the two?
  2. 2.In a group of 42 children, 27 like mangoes, 14 like bananas and 10 like both. How many like only mangoes?
  3. 3.In a group of 52 children, 20 play chess, 25 play carrom and 5 play both. How many play only chess?
  4. 4.In a group of 30 grown-ups, 6 drink tea, 11 drink coffee and 2 drink both. How many drink only coffee?
  5. 5.In a group of 28 children, 15 play chess, 13 play carrom and 2 play both. How many play only chess?
  6. 6.In a group of 37 children, 13 play cricket, 13 play football and 4 play both. How many play neither of the two?
  7. 7.In a group of 33 children, 13 play cricket, 8 play football and 3 play both. How many play only cricket?
  8. 8.In a group of 29 children, 17 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  9. 9.In a group of 31 children, 23 like mangoes, 14 like bananas and 10 like both. How many like only bananas?
  10. 10.In a group of 46 children, 20 play cricket, 21 play football and 8 play both. How many play exactly one of the two?
  11. 11.In a group of 33 children, 20 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 45 children, 14 enjoy drawing, 26 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  13. 13.In a group of 43 grown-ups, 15 drink tea, 29 drink coffee and 10 drink both. How many drink exactly one of the two?
  14. 14.In a group of 33 children, 12 play cricket, 20 play football and 6 play both. How many play at least one of the two?
  15. 15.In a group of 57 children, 28 like mangoes, 30 like bananas and 12 like both. How many like exactly one of the two?
  16. 16.In a group of 32 children, 13 enjoy drawing, 16 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  17. 17.In a group of 29 children, 7 play chess, 20 play carrom and 3 play both. How many play exactly one of the two?
  18. 18.In a group of 40 grown-ups, 22 drink tea, 22 drink coffee and 8 drink both. How many drink at least one of the two?
  19. 19.In a group of 59 children, 30 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing only English songs?
  20. 20.In a group of 40 grown-ups, 21 drink tea, 13 drink coffee and 5 drink both. How many drink only tea?
  21. 21.In a group of 36 children, 13 enjoy drawing, 18 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  22. 22.In a group of 40 children, 16 like mangoes, 25 like bananas and 6 like both. How many like at least one of the two?
  23. 23.In a group of 23 children, 8 sing Hindi songs, 17 sing English songs and 3 sing both. How many sing only English songs?
  24. 24.In a group of 21 children, 14 sing Hindi songs, 6 sing English songs and 3 sing both. How many sing exactly one of the two?
  25. 25.In a group of 25 children, 9 sing Hindi songs, 21 sing English songs and 6 sing both. How many sing neither of the two?
  26. 26.In a group of 23 children, 14 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  27. 27.In a group of 38 children, 15 sing Hindi songs, 24 sing English songs and 7 sing both. How many sing neither of the two?
  28. 28.In a group of 35 children, 19 play cricket, 17 play football and 4 play both. How many play only football?
  29. 29.In a group of 43 children, 17 play cricket, 23 play football and 4 play both. How many play only cricket?
  30. 30.In a group of 29 children, 10 play chess, 19 play carrom and 2 play both. How many play only carrom?
  31. 31.In a group of 37 children, 30 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  32. 32.In a group of 43 children, 12 play cricket, 27 play football and 7 play both. How many play only cricket?
  33. 33.In a group of 32 children, 20 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing only English songs?
  34. 34.In a group of 31 grown-ups, 18 drink tea, 21 drink coffee and 12 drink both. How many drink neither of the two?
  35. 35.In a group of 41 children, 20 sing Hindi songs, 23 sing English songs and 7 sing both. How many sing neither of the two?
  36. 36.In a group of 39 children, 18 play chess, 24 play carrom and 9 play both. How many play only chess?
  37. 37.In a group of 37 children, 8 sing Hindi songs, 23 sing English songs and 4 sing both. How many sing neither of the two?
  38. 38.In a group of 29 children, 10 like mangoes, 20 like bananas and 4 like both. How many like only bananas?
  39. 39.In a group of 21 children, 6 play chess, 8 play carrom and 3 play both. How many play only carrom?
  40. 40.In a group of 36 grown-ups, 25 drink tea, 14 drink coffee and 10 drink both. How many drink at least one of the two?

Answer key

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

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