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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 19 · 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 45 grown-ups, 25 drink tea, 25 drink coffee and 7 drink both. How many drink at least one of the two?
  2. 2.In a group of 54 children, 27 play cricket, 22 play football and 7 play both. How many play only cricket?
  3. 3.In a group of 39 children, 16 play cricket, 24 play football and 9 play both. How many play only cricket?
  4. 4.In a group of 48 children, 21 play cricket, 17 play football and 5 play both. How many play only cricket?
  5. 5.In a group of 45 children, 25 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  6. 6.In a group of 46 children, 20 sing Hindi songs, 15 sing English songs and 2 sing both. How many sing only English songs?
  7. 7.In a group of 17 children, 8 play chess, 5 play carrom and 2 play both. How many play only chess?
  8. 8.In a group of 26 children, 15 play cricket, 13 play football and 10 play both. How many play exactly one of the two?
  9. 9.In a group of 21 children, 9 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 49 children, 19 play cricket, 22 play football and 6 play both. How many play at least one of the two?
  11. 11.In a group of 41 grown-ups, 16 drink tea, 26 drink coffee and 6 drink both. How many drink only coffee?
  12. 12.In a group of 36 grown-ups, 13 drink tea, 18 drink coffee and 7 drink both. How many drink exactly one of the two?
  13. 13.In a group of 35 grown-ups, 23 drink tea, 20 drink coffee and 9 drink both. How many drink only tea?
  14. 14.In a group of 28 grown-ups, 11 drink tea, 21 drink coffee and 6 drink both. How many drink only coffee?
  15. 15.In a group of 24 children, 9 play chess, 9 play carrom and 2 play both. How many play neither of the two?
  16. 16.In a group of 30 children, 7 like mangoes, 19 like bananas and 2 like both. How many like only bananas?
  17. 17.In a group of 64 children, 31 like mangoes, 31 like bananas and 12 like both. How many like exactly one of the two?
  18. 18.In a group of 32 children, 15 play cricket, 26 play football and 10 play both. How many play at least one of the two?
  19. 19.In a group of 24 children, 6 enjoy drawing, 7 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 38 children, 16 sing Hindi songs, 18 sing English songs and 11 sing both. How many sing only Hindi songs?
  21. 21.In a group of 33 children, 12 play chess, 19 play carrom and 5 play both. How many play exactly one of the two?
  22. 22.In a group of 33 children, 17 like mangoes, 15 like bananas and 2 like both. How many like only mangoes?
  23. 23.In a group of 54 children, 25 play cricket, 27 play football and 12 play both. How many play only cricket?
  24. 24.In a group of 47 children, 27 enjoy drawing, 22 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  25. 25.In a group of 40 children, 30 play chess, 17 play carrom and 12 play both. How many play only carrom?
  26. 26.In a group of 34 grown-ups, 14 drink tea, 15 drink coffee and 7 drink both. How many drink neither of the two?
  27. 27.In a group of 26 children, 12 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  28. 28.In a group of 48 children, 24 like mangoes, 22 like bananas and 5 like both. How many like only mangoes?
  29. 29.In a group of 29 children, 10 like mangoes, 13 like bananas and 2 like both. How many like exactly one of the two?
  30. 30.In a group of 36 children, 16 play cricket, 17 play football and 2 play both. How many play only cricket?
  31. 31.In a group of 41 children, 20 like mangoes, 26 like bananas and 7 like both. How many like neither of the two?
  32. 32.In a group of 51 children, 23 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  33. 33.In a group of 49 children, 27 enjoy drawing, 27 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 50 children, 24 like mangoes, 19 like bananas and 8 like both. How many like exactly one of the two?
  35. 35.In a group of 24 children, 10 play cricket, 14 play football and 2 play both. How many play exactly one of the two?
  36. 36.In a group of 41 children, 21 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 35 children, 14 play cricket, 20 play football and 9 play both. How many play neither of the two?
  38. 38.In a group of 40 children, 10 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  39. 39.In a group of 28 children, 12 like mangoes, 16 like bananas and 4 like both. How many like at least one of the two?
  40. 40.In a group of 47 children, 31 enjoy drawing, 18 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?

Answer key

  1. 43
  2. 20
  3. 7
  4. 16
  5. 36
  6. 13
  7. 6
  8. 8
  9. 14
  10. 35
  11. 20
  12. 17
  13. 14
  14. 15
  15. 8
  16. 17
  17. 38
  18. 31
  19. 11
  20. 5
  21. 21
  22. 15
  23. 13
  24. 10
  25. 5
  26. 12
  27. 6
  28. 19
  29. 19
  30. 14
  31. 2
  32. 42
  33. 16
  34. 27
  35. 20
  36. 26
  37. 10
  38. 15
  39. 24
  40. 38

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