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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 423 · 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 32 children, 18 sing Hindi songs, 20 sing English songs and 7 sing both. How many sing only English songs?
  2. 2.In a group of 35 children, 18 play cricket, 14 play football and 2 play both. How many play at least one of the two?
  3. 3.In a group of 27 children, 6 like mangoes, 20 like bananas and 3 like both. How many like at least one of the two?
  4. 4.In a group of 34 grown-ups, 18 drink tea, 17 drink coffee and 8 drink both. How many drink neither of the two?
  5. 5.In a group of 27 children, 12 sing Hindi songs, 9 sing English songs and 5 sing both. How many sing exactly one of the two?
  6. 6.In a group of 46 children, 22 like mangoes, 27 like bananas and 7 like both. How many like only bananas?
  7. 7.In a group of 36 children, 18 sing Hindi songs, 18 sing English songs and 6 sing both. How many sing exactly one of the two?
  8. 8.In a group of 46 children, 18 play cricket, 22 play football and 4 play both. How many play exactly one of the two?
  9. 9.In a group of 38 children, 17 like mangoes, 27 like bananas and 11 like both. How many like only bananas?
  10. 10.In a group of 34 children, 14 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  11. 11.In a group of 41 children, 19 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing neither of the two?
  12. 12.In a group of 49 children, 20 play cricket, 28 play football and 11 play both. How many play only football?
  13. 13.In a group of 37 children, 21 sing Hindi songs, 18 sing English songs and 10 sing both. How many sing only Hindi songs?
  14. 14.In a group of 49 children, 21 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing only Hindi songs?
  15. 15.In a group of 42 children, 11 enjoy drawing, 20 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 33 children, 16 play chess, 17 play carrom and 10 play both. How many play at least one of the two?
  17. 17.In a group of 34 children, 21 like mangoes, 11 like bananas and 8 like both. How many like only mangoes?
  18. 18.In a group of 35 children, 18 sing Hindi songs, 8 sing English songs and 4 sing both. How many sing at least one of the two?
  19. 19.In a group of 24 children, 20 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing exactly one of the two?
  20. 20.In a group of 30 children, 16 play chess, 19 play carrom and 12 play both. How many play neither of the two?
  21. 21.In a group of 44 children, 19 play cricket, 15 play football and 3 play both. How many play neither of the two?
  22. 22.In a group of 42 children, 19 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing only English songs?
  23. 23.In a group of 31 children, 12 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 19 children, 7 play cricket, 14 play football and 3 play both. How many play only cricket?
  25. 25.In a group of 53 children, 24 play cricket, 29 play football and 12 play both. How many play only football?
  26. 26.In a group of 36 children, 10 enjoy drawing, 26 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 29 children, 10 sing Hindi songs, 22 sing English songs and 6 sing both. How many sing only English songs?
  28. 28.In a group of 32 children, 17 enjoy drawing, 19 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  29. 29.In a group of 45 children, 12 play chess, 24 play carrom and 6 play both. How many play only carrom?
  30. 30.In a group of 38 children, 11 enjoy drawing, 18 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 20 grown-ups, 8 drink tea, 14 drink coffee and 3 drink both. How many drink only tea?
  32. 32.In a group of 46 children, 16 enjoy drawing, 28 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  33. 33.In a group of 42 grown-ups, 16 drink tea, 14 drink coffee and 3 drink both. How many drink only coffee?
  34. 34.In a group of 30 children, 15 like mangoes, 21 like bananas and 7 like both. How many like only mangoes?
  35. 35.In a group of 38 grown-ups, 27 drink tea, 11 drink coffee and 7 drink both. How many drink neither of the two?
  36. 36.In a group of 31 children, 19 like mangoes, 11 like bananas and 8 like both. How many like at least one of the two?
  37. 37.In a group of 17 children, 5 sing Hindi songs, 10 sing English songs and 2 sing both. How many sing neither of the two?
  38. 38.In a group of 30 children, 17 sing Hindi songs, 20 sing English songs and 8 sing both. How many sing neither of the two?
  39. 39.In a group of 24 children, 8 sing Hindi songs, 8 sing English songs and 5 sing both. How many sing at least one of the two?
  40. 40.In a group of 41 children, 13 like mangoes, 30 like bananas and 10 like both. How many like neither of the two?

Answer key

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

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