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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 311 · 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 27 children, 16 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing at least one of the two?
  2. 2.In a group of 36 children, 12 enjoy drawing, 23 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 42 children, 24 like mangoes, 18 like bananas and 9 like both. How many like at least one of the two?
  4. 4.In a group of 37 children, 24 play chess, 19 play carrom and 7 play both. How many play only carrom?
  5. 5.In a group of 28 children, 17 play chess, 9 play carrom and 6 play both. How many play only chess?
  6. 6.In a group of 54 children, 30 sing Hindi songs, 28 sing English songs and 11 sing both. How many sing only English songs?
  7. 7.In a group of 31 grown-ups, 18 drink tea, 12 drink coffee and 2 drink both. How many drink exactly one of the two?
  8. 8.In a group of 14 grown-ups, 9 drink tea, 7 drink coffee and 3 drink both. How many drink at least one of the two?
  9. 9.In a group of 17 children, 6 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  10. 10.In a group of 49 children, 17 play cricket, 25 play football and 8 play both. How many play neither of the two?
  11. 11.In a group of 30 children, 25 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  12. 12.In a group of 35 grown-ups, 23 drink tea, 10 drink coffee and 3 drink both. How many drink neither of the two?
  13. 13.In a group of 34 children, 9 play cricket, 19 play football and 5 play both. How many play at least one of the two?
  14. 14.In a group of 55 children, 27 play cricket, 29 play football and 9 play both. How many play at least one of the two?
  15. 15.In a group of 37 children, 10 play chess, 20 play carrom and 5 play both. How many play at least one of the two?
  16. 16.In a group of 33 children, 15 like mangoes, 9 like bananas and 6 like both. How many like only bananas?
  17. 17.In a group of 39 children, 17 enjoy drawing, 25 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  18. 18.In a group of 49 grown-ups, 15 drink tea, 28 drink coffee and 9 drink both. How many drink exactly one of the two?
  19. 19.In a group of 44 children, 16 like mangoes, 20 like bananas and 6 like both. How many like neither of the two?
  20. 20.In a group of 61 children, 31 enjoy drawing, 28 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 34 children, 19 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing at least one of the two?
  22. 22.In a group of 49 children, 21 like mangoes, 23 like bananas and 7 like both. How many like at least one of the two?
  23. 23.In a group of 30 children, 21 sing Hindi songs, 12 sing English songs and 7 sing both. How many sing at least one of the two?
  24. 24.In a group of 29 children, 18 enjoy drawing, 7 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  25. 25.In a group of 38 children, 17 sing Hindi songs, 16 sing English songs and 4 sing both. How many sing only Hindi songs?
  26. 26.In a group of 24 children, 13 sing Hindi songs, 18 sing English songs and 8 sing both. How many sing at least one of the two?
  27. 27.In a group of 42 grown-ups, 13 drink tea, 24 drink coffee and 7 drink both. How many drink only coffee?
  28. 28.In a group of 38 children, 12 like mangoes, 29 like bananas and 9 like both. How many like neither of the two?
  29. 29.In a group of 47 children, 26 like mangoes, 21 like bananas and 8 like both. How many like neither of the two?
  30. 30.In a group of 54 children, 28 enjoy drawing, 24 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  31. 31.In a group of 26 grown-ups, 16 drink tea, 9 drink coffee and 3 drink both. How many drink neither of the two?
  32. 32.In a group of 36 children, 22 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  33. 33.In a group of 30 children, 12 play chess, 15 play carrom and 5 play both. How many play exactly one of the two?
  34. 34.In a group of 34 children, 23 like mangoes, 12 like bananas and 3 like both. How many like exactly one of the two?
  35. 35.In a group of 32 children, 22 enjoy drawing, 16 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 35 children, 17 play chess, 15 play carrom and 9 play both. How many play at least one of the two?
  37. 37.In a group of 23 children, 14 play chess, 14 play carrom and 8 play both. How many play exactly one of the two?
  38. 38.In a group of 37 children, 22 play cricket, 13 play football and 7 play both. How many play at least one of the two?
  39. 39.In a group of 18 children, 7 play cricket, 12 play football and 4 play both. How many play only football?
  40. 40.In a group of 23 grown-ups, 8 drink tea, 7 drink coffee and 3 drink both. How many drink only tea?

Answer key

  1. 23
  2. 19
  3. 33
  4. 12
  5. 11
  6. 17
  7. 26
  8. 13
  9. 10
  10. 15
  11. 18
  12. 5
  13. 23
  14. 47
  15. 25
  16. 3
  17. 34
  18. 25
  19. 14
  20. 48
  21. 24
  22. 37
  23. 26
  24. 17
  25. 13
  26. 23
  27. 17
  28. 6
  29. 8
  30. 13
  31. 4
  32. 32
  33. 17
  34. 29
  35. 31
  36. 23
  37. 12
  38. 28
  39. 8
  40. 5

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