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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 597 · 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 51 children, 17 sing Hindi songs, 28 sing English songs and 9 sing both. How many sing exactly one of the two?
  2. 2.In a group of 45 children, 25 sing Hindi songs, 23 sing English songs and 8 sing both. How many sing exactly one of the two?
  3. 3.In a group of 38 children, 12 enjoy drawing, 21 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  4. 4.In a group of 42 children, 15 play chess, 23 play carrom and 5 play both. How many play at least one of the two?
  5. 5.In a group of 26 children, 19 play cricket, 9 play football and 4 play both. How many play exactly one of the two?
  6. 6.In a group of 42 children, 26 play chess, 21 play carrom and 12 play both. How many play only chess?
  7. 7.In a group of 33 children, 18 play chess, 17 play carrom and 5 play both. How many play exactly one of the two?
  8. 8.In a group of 43 grown-ups, 11 drink tea, 23 drink coffee and 4 drink both. How many drink only coffee?
  9. 9.In a group of 27 children, 17 sing Hindi songs, 12 sing English songs and 5 sing both. How many sing at least one of the two?
  10. 10.In a group of 39 children, 18 play chess, 20 play carrom and 12 play both. How many play only carrom?
  11. 11.In a group of 21 children, 8 play cricket, 13 play football and 5 play both. How many play only football?
  12. 12.In a group of 44 children, 30 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing neither of the two?
  13. 13.In a group of 41 grown-ups, 24 drink tea, 18 drink coffee and 7 drink both. How many drink only coffee?
  14. 14.In a group of 35 children, 8 play cricket, 21 play football and 2 play both. How many play at least one of the two?
  15. 15.In a group of 39 grown-ups, 22 drink tea, 20 drink coffee and 6 drink both. How many drink only coffee?
  16. 16.In a group of 26 children, 17 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing neither of the two?
  17. 17.In a group of 19 children, 10 enjoy drawing, 10 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  18. 18.In a group of 62 children, 28 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing neither of the two?
  19. 19.In a group of 45 children, 24 sing Hindi songs, 26 sing English songs and 8 sing both. How many sing only Hindi songs?
  20. 20.In a group of 30 children, 12 like mangoes, 12 like bananas and 4 like both. How many like only bananas?
  21. 21.In a group of 39 children, 14 like mangoes, 21 like bananas and 6 like both. How many like at least one of the two?
  22. 22.In a group of 42 children, 20 play cricket, 32 play football and 12 play both. How many play only football?
  23. 23.In a group of 34 grown-ups, 14 drink tea, 12 drink coffee and 5 drink both. How many drink only tea?
  24. 24.In a group of 37 children, 18 like mangoes, 18 like bananas and 6 like both. How many like neither of the two?
  25. 25.In a group of 48 children, 27 play cricket, 18 play football and 10 play both. How many play only cricket?
  26. 26.In a group of 36 children, 28 enjoy drawing, 18 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 55 children, 27 like mangoes, 27 like bananas and 8 like both. How many like exactly one of the two?
  28. 28.In a group of 47 children, 28 play cricket, 18 play football and 10 play both. How many play only football?
  29. 29.In a group of 27 grown-ups, 10 drink tea, 11 drink coffee and 7 drink both. How many drink exactly one of the two?
  30. 30.In a group of 30 children, 16 like mangoes, 12 like bananas and 9 like both. How many like only mangoes?
  31. 31.In a group of 47 children, 16 play cricket, 20 play football and 3 play both. How many play only football?
  32. 32.In a group of 43 children, 14 like mangoes, 28 like bananas and 8 like both. How many like neither of the two?
  33. 33.In a group of 42 children, 15 play chess, 20 play carrom and 7 play both. How many play only carrom?
  34. 34.In a group of 48 children, 30 enjoy drawing, 24 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  35. 35.In a group of 37 children, 17 play chess, 22 play carrom and 12 play both. How many play only chess?
  36. 36.In a group of 41 children, 26 sing Hindi songs, 15 sing English songs and 10 sing both. How many sing neither of the two?
  37. 37.In a group of 41 children, 15 enjoy drawing, 22 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  38. 38.In a group of 46 children, 26 like mangoes, 18 like bananas and 10 like both. How many like exactly one of the two?
  39. 39.In a group of 31 children, 16 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  40. 40.In a group of 32 children, 17 like mangoes, 12 like bananas and 4 like both. How many like at least one of the two?

Answer key

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

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