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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 508 · 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 31 children, 22 play chess, 12 play carrom and 6 play both. How many play only carrom?
  2. 2.In a group of 23 children, 18 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 57 children, 25 play chess, 26 play carrom and 9 play both. How many play neither of the two?
  4. 4.In a group of 41 children, 12 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  5. 5.In a group of 32 children, 11 like mangoes, 21 like bananas and 4 like both. How many like neither of the two?
  6. 6.In a group of 21 children, 10 play cricket, 11 play football and 5 play both. How many play exactly one of the two?
  7. 7.In a group of 53 children, 26 sing Hindi songs, 27 sing English songs and 10 sing both. How many sing only English songs?
  8. 8.In a group of 46 children, 18 like mangoes, 23 like bananas and 4 like both. How many like neither of the two?
  9. 9.In a group of 30 children, 16 enjoy drawing, 22 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  10. 10.In a group of 26 children, 11 play cricket, 13 play football and 3 play both. How many play only football?
  11. 11.In a group of 34 children, 13 like mangoes, 13 like bananas and 2 like both. How many like only bananas?
  12. 12.In a group of 33 children, 14 play cricket, 6 play football and 2 play both. How many play neither of the two?
  13. 13.In a group of 19 grown-ups, 12 drink tea, 13 drink coffee and 9 drink both. How many drink neither of the two?
  14. 14.In a group of 47 children, 17 sing Hindi songs, 29 sing English songs and 10 sing both. How many sing neither of the two?
  15. 15.In a group of 41 children, 14 like mangoes, 28 like bananas and 11 like both. How many like only mangoes?
  16. 16.In a group of 45 children, 14 sing Hindi songs, 22 sing English songs and 5 sing both. How many sing neither of the two?
  17. 17.In a group of 44 children, 23 enjoy drawing, 20 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  18. 18.In a group of 44 children, 22 play chess, 28 play carrom and 11 play both. How many play exactly one of the two?
  19. 19.In a group of 50 children, 24 sing Hindi songs, 24 sing English songs and 11 sing both. How many sing only Hindi songs?
  20. 20.In a group of 40 children, 27 play cricket, 24 play football and 12 play both. How many play only football?
  21. 21.In a group of 30 children, 18 enjoy drawing, 22 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  22. 22.In a group of 21 children, 12 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  23. 23.In a group of 17 children, 9 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 31 children, 10 like mangoes, 18 like bananas and 3 like both. How many like at least one of the two?
  25. 25.In a group of 33 children, 8 like mangoes, 22 like bananas and 2 like both. How many like exactly one of the two?
  26. 26.In a group of 51 grown-ups, 20 drink tea, 31 drink coffee and 11 drink both. How many drink neither of the two?
  27. 27.In a group of 27 children, 11 play cricket, 16 play football and 6 play both. How many play at least one of the two?
  28. 28.In a group of 34 children, 12 play cricket, 14 play football and 7 play both. How many play exactly one of the two?
  29. 29.In a group of 15 children, 5 play chess, 6 play carrom and 2 play both. How many play only carrom?
  30. 30.In a group of 30 children, 18 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  31. 31.In a group of 35 grown-ups, 8 drink tea, 18 drink coffee and 4 drink both. How many drink neither of the two?
  32. 32.In a group of 37 children, 20 enjoy drawing, 18 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  33. 33.In a group of 48 children, 25 sing Hindi songs, 17 sing English songs and 8 sing both. How many sing only English songs?
  34. 34.In a group of 42 children, 23 play cricket, 10 play football and 4 play both. How many play neither of the two?
  35. 35.In a group of 43 children, 27 play cricket, 18 play football and 10 play both. How many play exactly one of the two?
  36. 36.In a group of 35 children, 10 like mangoes, 17 like bananas and 6 like both. How many like neither of the two?
  37. 37.In a group of 39 children, 22 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing only Hindi songs?
  38. 38.In a group of 30 children, 6 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing only English songs?
  39. 39.In a group of 57 children, 31 sing Hindi songs, 24 sing English songs and 12 sing both. How many sing only English songs?
  40. 40.In a group of 34 children, 15 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy only drawing?

Answer key

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

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