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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 105 · 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 23 children, 17 play cricket, 15 play football and 12 play both. How many play exactly one of the two?
  2. 2.In a group of 38 grown-ups, 20 drink tea, 13 drink coffee and 6 drink both. How many drink exactly one of the two?
  3. 3.In a group of 46 children, 18 play cricket, 21 play football and 5 play both. How many play at least one of the two?
  4. 4.In a group of 45 children, 29 like mangoes, 19 like bananas and 12 like both. How many like at least one of the two?
  5. 5.In a group of 52 children, 27 play chess, 22 play carrom and 11 play both. How many play at least one of the two?
  6. 6.In a group of 36 grown-ups, 22 drink tea, 14 drink coffee and 11 drink both. How many drink exactly one of the two?
  7. 7.In a group of 28 children, 12 enjoy drawing, 11 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 38 grown-ups, 11 drink tea, 15 drink coffee and 2 drink both. How many drink only tea?
  9. 9.In a group of 28 children, 18 like mangoes, 14 like bananas and 8 like both. How many like neither of the two?
  10. 10.In a group of 52 grown-ups, 27 drink tea, 24 drink coffee and 10 drink both. How many drink neither of the two?
  11. 11.In a group of 54 children, 23 like mangoes, 25 like bananas and 8 like both. How many like at least one of the two?
  12. 12.In a group of 45 children, 24 play chess, 19 play carrom and 12 play both. How many play at least one of the two?
  13. 13.In a group of 27 children, 13 play chess, 14 play carrom and 9 play both. How many play at least one of the two?
  14. 14.In a group of 37 grown-ups, 13 drink tea, 12 drink coffee and 2 drink both. How many drink at least one of the two?
  15. 15.In a group of 33 children, 11 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 32 children, 12 like mangoes, 21 like bananas and 5 like both. How many like exactly one of the two?
  17. 17.In a group of 38 children, 21 play chess, 17 play carrom and 4 play both. How many play only carrom?
  18. 18.In a group of 31 children, 15 enjoy drawing, 15 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 35 children, 22 play cricket, 13 play football and 4 play both. How many play only cricket?
  20. 20.In a group of 31 children, 10 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  21. 21.In a group of 26 grown-ups, 17 drink tea, 16 drink coffee and 8 drink both. How many drink at least one of the two?
  22. 22.In a group of 36 children, 18 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  23. 23.In a group of 17 children, 7 like mangoes, 10 like bananas and 3 like both. How many like neither of the two?
  24. 24.In a group of 56 children, 25 sing Hindi songs, 25 sing English songs and 9 sing both. How many sing only English songs?
  25. 25.In a group of 51 children, 29 like mangoes, 22 like bananas and 12 like both. How many like at least one of the two?
  26. 26.In a group of 34 children, 20 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  27. 27.In a group of 40 children, 19 enjoy drawing, 23 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  28. 28.In a group of 48 children, 17 play cricket, 29 play football and 12 play both. How many play only football?
  29. 29.In a group of 30 children, 10 like mangoes, 20 like bananas and 4 like both. How many like neither of the two?
  30. 30.In a group of 44 children, 29 play cricket, 16 play football and 9 play both. How many play only football?
  31. 31.In a group of 36 children, 14 play cricket, 19 play football and 10 play both. How many play only football?
  32. 32.In a group of 25 children, 11 play chess, 11 play carrom and 4 play both. How many play exactly one of the two?
  33. 33.In a group of 38 children, 19 play cricket, 27 play football and 9 play both. How many play exactly one of the two?
  34. 34.In a group of 33 children, 14 like mangoes, 21 like bananas and 9 like both. How many like neither of the two?
  35. 35.In a group of 35 children, 16 sing Hindi songs, 20 sing English songs and 4 sing both. How many sing only English songs?
  36. 36.In a group of 36 grown-ups, 9 drink tea, 21 drink coffee and 3 drink both. How many drink only tea?
  37. 37.In a group of 51 children, 25 play cricket, 21 play football and 9 play both. How many play only football?
  38. 38.In a group of 22 children, 12 play cricket, 8 play football and 5 play both. How many play only cricket?
  39. 39.In a group of 39 children, 12 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  40. 40.In a group of 25 children, 9 sing Hindi songs, 8 sing English songs and 4 sing both. How many sing only Hindi songs?

Answer key

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

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