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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 396 · 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 26 children, 15 play cricket, 18 play football and 9 play both. How many play exactly one of the two?
  2. 2.In a group of 38 children, 26 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 32 children, 8 play cricket, 13 play football and 2 play both. How many play only cricket?
  4. 4.In a group of 27 grown-ups, 14 drink tea, 12 drink coffee and 9 drink both. How many drink only coffee?
  5. 5.In a group of 39 children, 17 play cricket, 19 play football and 5 play both. How many play at least one of the two?
  6. 6.In a group of 40 children, 15 like mangoes, 24 like bananas and 7 like both. How many like neither of the two?
  7. 7.In a group of 41 grown-ups, 12 drink tea, 20 drink coffee and 6 drink both. How many drink only coffee?
  8. 8.In a group of 26 children, 13 play chess, 16 play carrom and 5 play both. How many play only chess?
  9. 9.In a group of 58 children, 26 enjoy drawing, 25 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  10. 10.In a group of 42 children, 20 sing Hindi songs, 22 sing English songs and 12 sing both. How many sing only Hindi songs?
  11. 11.In a group of 49 children, 16 play chess, 20 play carrom and 2 play both. How many play exactly one of the two?
  12. 12.In a group of 42 children, 20 like mangoes, 19 like bananas and 8 like both. How many like neither of the two?
  13. 13.In a group of 45 children, 20 sing Hindi songs, 31 sing English songs and 11 sing both. How many sing only English songs?
  14. 14.In a group of 31 children, 15 like mangoes, 20 like bananas and 8 like both. How many like only mangoes?
  15. 15.In a group of 33 children, 8 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  16. 16.In a group of 43 children, 18 play cricket, 22 play football and 9 play both. How many play only football?
  17. 17.In a group of 28 children, 15 sing Hindi songs, 17 sing English songs and 12 sing both. How many sing exactly one of the two?
  18. 18.In a group of 48 children, 28 play cricket, 24 play football and 10 play both. How many play neither of the two?
  19. 19.In a group of 37 children, 19 sing Hindi songs, 12 sing English songs and 9 sing both. How many sing only English songs?
  20. 20.In a group of 35 children, 13 like mangoes, 20 like bananas and 8 like both. How many like neither of the two?
  21. 21.In a group of 34 children, 17 play chess, 8 play carrom and 3 play both. How many play only carrom?
  22. 22.In a group of 34 children, 14 play chess, 23 play carrom and 7 play both. How many play only chess?
  23. 23.In a group of 40 children, 25 play chess, 18 play carrom and 9 play both. How many play exactly one of the two?
  24. 24.In a group of 39 children, 14 like mangoes, 21 like bananas and 11 like both. How many like neither of the two?
  25. 25.In a group of 34 children, 17 play chess, 10 play carrom and 5 play both. How many play exactly one of the two?
  26. 26.In a group of 49 children, 18 play cricket, 28 play football and 12 play both. How many play neither of the two?
  27. 27.In a group of 27 children, 11 play cricket, 16 play football and 5 play both. How many play neither of the two?
  28. 28.In a group of 37 children, 25 sing Hindi songs, 8 sing English songs and 5 sing both. How many sing only Hindi songs?
  29. 29.In a group of 40 children, 30 sing Hindi songs, 19 sing English songs and 11 sing both. How many sing exactly one of the two?
  30. 30.In a group of 18 children, 8 like mangoes, 11 like bananas and 5 like both. How many like exactly one of the two?
  31. 31.In a group of 38 children, 17 enjoy drawing, 25 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  32. 32.In a group of 41 children, 20 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing neither of the two?
  33. 33.In a group of 42 children, 28 like mangoes, 16 like bananas and 10 like both. How many like only mangoes?
  34. 34.In a group of 17 children, 5 like mangoes, 7 like bananas and 2 like both. How many like only bananas?
  35. 35.In a group of 37 children, 14 sing Hindi songs, 20 sing English songs and 8 sing both. How many sing neither of the two?
  36. 36.In a group of 37 children, 19 sing Hindi songs, 25 sing English songs and 10 sing both. How many sing neither of the two?
  37. 37.In a group of 38 children, 8 enjoy drawing, 23 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  38. 38.In a group of 26 children, 15 like mangoes, 8 like bananas and 2 like both. How many like neither of the two?
  39. 39.In a group of 43 children, 29 enjoy drawing, 24 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  40. 40.In a group of 36 children, 12 play chess, 21 play carrom and 7 play both. How many play at least one of the two?

Answer key

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

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