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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 66 · 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 36 children, 18 play cricket, 24 play football and 8 play both. How many play exactly one of the two?
  2. 2.In a group of 19 children, 7 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing at least one of the two?
  3. 3.In a group of 61 children, 28 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing neither of the two?
  4. 4.In a group of 24 children, 11 play cricket, 13 play football and 7 play both. How many play at least one of the two?
  5. 5.In a group of 39 children, 20 sing Hindi songs, 22 sing English songs and 11 sing both. How many sing only Hindi songs?
  6. 6.In a group of 45 children, 18 sing Hindi songs, 22 sing English songs and 2 sing both. How many sing exactly one of the two?
  7. 7.In a group of 50 grown-ups, 29 drink tea, 30 drink coffee and 11 drink both. How many drink neither of the two?
  8. 8.In a group of 23 children, 14 like mangoes, 9 like bananas and 4 like both. How many like only mangoes?
  9. 9.In a group of 28 children, 15 play cricket, 23 play football and 11 play both. How many play at least one of the two?
  10. 10.In a group of 29 children, 14 play chess, 8 play carrom and 4 play both. How many play at least one of the two?
  11. 11.In a group of 37 children, 17 play cricket, 16 play football and 6 play both. How many play only football?
  12. 12.In a group of 25 children, 6 enjoy drawing, 19 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  13. 13.In a group of 32 grown-ups, 15 drink tea, 22 drink coffee and 8 drink both. How many drink neither of the two?
  14. 14.In a group of 27 children, 9 play cricket, 12 play football and 4 play both. How many play at least one of the two?
  15. 15.In a group of 23 children, 11 sing Hindi songs, 16 sing English songs and 8 sing both. How many sing at least one of the two?
  16. 16.In a group of 35 children, 19 play cricket, 14 play football and 6 play both. How many play only football?
  17. 17.In a group of 41 children, 15 like mangoes, 21 like bananas and 7 like both. How many like neither of the two?
  18. 18.In a group of 17 children, 10 sing Hindi songs, 9 sing English songs and 3 sing both. How many sing at least one of the two?
  19. 19.In a group of 34 children, 15 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  20. 20.In a group of 30 children, 11 like mangoes, 14 like bananas and 8 like both. How many like exactly one of the two?
  21. 21.In a group of 49 children, 24 sing Hindi songs, 17 sing English songs and 7 sing both. How many sing at least one of the two?
  22. 22.In a group of 33 children, 29 play chess, 13 play carrom and 10 play both. How many play exactly one of the two?
  23. 23.In a group of 49 children, 29 sing Hindi songs, 16 sing English songs and 10 sing both. How many sing exactly one of the two?
  24. 24.In a group of 43 children, 18 enjoy drawing, 13 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  25. 25.In a group of 39 children, 24 sing Hindi songs, 14 sing English songs and 8 sing both. How many sing exactly one of the two?
  26. 26.In a group of 33 children, 17 sing Hindi songs, 19 sing English songs and 8 sing both. How many sing neither of the two?
  27. 27.In a group of 58 grown-ups, 25 drink tea, 32 drink coffee and 12 drink both. How many drink at least one of the two?
  28. 28.In a group of 25 children, 8 play chess, 7 play carrom and 4 play both. How many play at least one of the two?
  29. 29.In a group of 44 children, 24 play chess, 21 play carrom and 12 play both. How many play at least one of the two?
  30. 30.In a group of 41 children, 26 sing Hindi songs, 24 sing English songs and 10 sing both. How many sing exactly one of the two?
  31. 31.In a group of 32 grown-ups, 15 drink tea, 15 drink coffee and 11 drink both. How many drink only coffee?
  32. 32.In a group of 17 children, 13 play cricket, 6 play football and 3 play both. How many play at least one of the two?
  33. 33.In a group of 38 children, 32 play cricket, 15 play football and 12 play both. How many play exactly one of the two?
  34. 34.In a group of 49 children, 26 like mangoes, 27 like bananas and 10 like both. How many like neither of the two?
  35. 35.In a group of 28 children, 17 play chess, 16 play carrom and 6 play both. How many play only chess?
  36. 36.In a group of 25 children, 7 play chess, 16 play carrom and 2 play both. How many play neither of the two?
  37. 37.In a group of 43 children, 21 play cricket, 25 play football and 11 play both. How many play at least one of the two?
  38. 38.In a group of 50 children, 23 play chess, 30 play carrom and 10 play both. How many play only carrom?
  39. 39.In a group of 37 children, 11 like mangoes, 17 like bananas and 5 like both. How many like only mangoes?
  40. 40.In a group of 33 children, 22 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?

Answer key

  1. 26
  2. 10
  3. 14
  4. 17
  5. 9
  6. 36
  7. 2
  8. 10
  9. 27
  10. 18
  11. 10
  12. 4
  13. 3
  14. 17
  15. 19
  16. 8
  17. 12
  18. 16
  19. 18
  20. 9
  21. 34
  22. 22
  23. 25
  24. 10
  25. 22
  26. 5
  27. 45
  28. 11
  29. 33
  30. 30
  31. 4
  32. 16
  33. 23
  34. 6
  35. 11
  36. 4
  37. 35
  38. 20
  39. 6
  40. 22

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