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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 615 · 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 47 children, 19 play chess, 18 play carrom and 4 play both. How many play only chess?
  2. 2.In a group of 33 children, 26 play cricket, 15 play football and 10 play both. How many play at least one of the two?
  3. 3.In a group of 49 children, 22 play chess, 17 play carrom and 5 play both. How many play only carrom?
  4. 4.In a group of 27 children, 16 sing Hindi songs, 16 sing English songs and 7 sing both. How many sing exactly one of the two?
  5. 5.In a group of 31 children, 13 like mangoes, 12 like bananas and 6 like both. How many like neither of the two?
  6. 6.In a group of 21 children, 14 play cricket, 13 play football and 7 play both. How many play exactly one of the two?
  7. 7.In a group of 32 children, 21 play chess, 22 play carrom and 12 play both. How many play at least one of the two?
  8. 8.In a group of 31 children, 24 like mangoes, 9 like bananas and 5 like both. How many like only bananas?
  9. 9.In a group of 51 children, 29 play chess, 21 play carrom and 9 play both. How many play only chess?
  10. 10.In a group of 32 grown-ups, 13 drink tea, 16 drink coffee and 4 drink both. How many drink at least one of the two?
  11. 11.In a group of 44 children, 20 play cricket, 22 play football and 7 play both. How many play exactly one of the two?
  12. 12.In a group of 29 children, 18 like mangoes, 21 like bananas and 12 like both. How many like exactly one of the two?
  13. 13.In a group of 35 children, 13 enjoy drawing, 20 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  14. 14.In a group of 35 children, 13 enjoy drawing, 13 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  15. 15.In a group of 29 children, 14 play cricket, 23 play football and 11 play both. How many play only football?
  16. 16.In a group of 37 grown-ups, 20 drink tea, 15 drink coffee and 7 drink both. How many drink at least one of the two?
  17. 17.In a group of 40 children, 18 play cricket, 16 play football and 8 play both. How many play exactly one of the two?
  18. 18.In a group of 46 children, 30 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  19. 19.In a group of 37 children, 17 like mangoes, 21 like bananas and 10 like both. How many like at least one of the two?
  20. 20.In a group of 15 children, 8 play cricket, 10 play football and 5 play both. How many play only football?
  21. 21.In a group of 46 children, 15 sing Hindi songs, 24 sing English songs and 4 sing both. How many sing only English songs?
  22. 22.In a group of 40 grown-ups, 16 drink tea, 16 drink coffee and 2 drink both. How many drink at least one of the two?
  23. 23.In a group of 40 children, 16 play chess, 18 play carrom and 9 play both. How many play neither of the two?
  24. 24.In a group of 35 grown-ups, 11 drink tea, 16 drink coffee and 3 drink both. How many drink exactly one of the two?
  25. 25.In a group of 38 children, 20 like mangoes, 24 like bananas and 10 like both. How many like only bananas?
  26. 26.In a group of 51 children, 31 enjoy drawing, 25 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  27. 27.In a group of 32 children, 16 play cricket, 10 play football and 6 play both. How many play only cricket?
  28. 28.In a group of 32 grown-ups, 14 drink tea, 15 drink coffee and 7 drink both. How many drink neither of the two?
  29. 29.In a group of 31 children, 19 play chess, 12 play carrom and 3 play both. How many play only chess?
  30. 30.In a group of 40 children, 21 play chess, 11 play carrom and 3 play both. How many play only carrom?
  31. 31.In a group of 27 children, 18 like mangoes, 7 like bananas and 4 like both. How many like at least one of the two?
  32. 32.In a group of 23 children, 12 sing Hindi songs, 8 sing English songs and 2 sing both. How many sing only English songs?
  33. 33.In a group of 36 children, 14 sing Hindi songs, 24 sing English songs and 10 sing both. How many sing exactly one of the two?
  34. 34.In a group of 52 children, 18 like mangoes, 29 like bananas and 10 like both. How many like exactly one of the two?
  35. 35.In a group of 23 children, 5 like mangoes, 19 like bananas and 2 like both. How many like only mangoes?
  36. 36.In a group of 51 children, 23 enjoy drawing, 20 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 19 children, 6 like mangoes, 11 like bananas and 2 like both. How many like neither of the two?
  38. 38.In a group of 41 children, 21 play chess, 15 play carrom and 10 play both. How many play only chess?
  39. 39.In a group of 34 children, 15 sing Hindi songs, 22 sing English songs and 7 sing both. How many sing only Hindi songs?
  40. 40.In a group of 36 children, 17 sing Hindi songs, 19 sing English songs and 10 sing both. How many sing exactly one of the two?

Answer key

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

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