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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 93 · 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, 7 play cricket, 9 play football and 2 play both. How many play neither of the two?
  2. 2.In a group of 39 children, 18 play cricket, 14 play football and 8 play both. How many play at least one of the two?
  3. 3.In a group of 41 children, 25 sing Hindi songs, 17 sing English songs and 7 sing both. How many sing neither of the two?
  4. 4.In a group of 50 children, 15 play cricket, 23 play football and 3 play both. How many play exactly one of the two?
  5. 5.In a group of 21 children, 11 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  6. 6.In a group of 44 children, 17 play cricket, 27 play football and 7 play both. How many play only football?
  7. 7.In a group of 33 children, 17 play chess, 20 play carrom and 12 play both. How many play exactly one of the two?
  8. 8.In a group of 23 children, 14 like mangoes, 17 like bananas and 10 like both. How many like neither of the two?
  9. 9.In a group of 34 children, 18 play chess, 20 play carrom and 11 play both. How many play neither of the two?
  10. 10.In a group of 42 children, 23 enjoy drawing, 27 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  11. 11.In a group of 45 children, 16 enjoy drawing, 25 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 33 children, 19 like mangoes, 12 like bananas and 6 like both. How many like at least one of the two?
  13. 13.In a group of 25 children, 13 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing at least one of the two?
  14. 14.In a group of 49 children, 23 play chess, 19 play carrom and 4 play both. How many play exactly one of the two?
  15. 15.In a group of 24 children, 15 play chess, 13 play carrom and 9 play both. How many play only chess?
  16. 16.In a group of 41 children, 15 play cricket, 28 play football and 11 play both. How many play only football?
  17. 17.In a group of 41 children, 26 like mangoes, 19 like bananas and 6 like both. How many like only bananas?
  18. 18.In a group of 46 grown-ups, 15 drink tea, 27 drink coffee and 7 drink both. How many drink only tea?
  19. 19.In a group of 44 children, 24 sing Hindi songs, 16 sing English songs and 6 sing both. How many sing exactly one of the two?
  20. 20.In a group of 17 children, 11 play cricket, 8 play football and 3 play both. How many play only football?
  21. 21.In a group of 22 grown-ups, 10 drink tea, 11 drink coffee and 6 drink both. How many drink at least one of the two?
  22. 22.In a group of 30 children, 10 play chess, 12 play carrom and 4 play both. How many play only carrom?
  23. 23.In a group of 42 children, 20 enjoy drawing, 32 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  24. 24.In a group of 23 grown-ups, 7 drink tea, 18 drink coffee and 4 drink both. How many drink exactly one of the two?
  25. 25.In a group of 40 children, 16 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 28 children, 15 enjoy drawing, 16 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 41 grown-ups, 18 drink tea, 28 drink coffee and 9 drink both. How many drink exactly one of the two?
  28. 28.In a group of 39 children, 19 enjoy drawing, 18 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 53 children, 28 play chess, 23 play carrom and 9 play both. How many play neither of the two?
  30. 30.In a group of 23 children, 14 sing Hindi songs, 13 sing English songs and 6 sing both. How many sing only English songs?
  31. 31.In a group of 40 children, 15 play cricket, 15 play football and 5 play both. How many play at least one of the two?
  32. 32.In a group of 44 children, 20 like mangoes, 21 like bananas and 6 like both. How many like at least one of the two?
  33. 33.In a group of 27 children, 7 sing Hindi songs, 9 sing English songs and 4 sing both. How many sing exactly one of the two?
  34. 34.In a group of 17 grown-ups, 5 drink tea, 5 drink coffee and 2 drink both. How many drink exactly one of the two?
  35. 35.In a group of 27 children, 9 play chess, 8 play carrom and 3 play both. How many play only chess?
  36. 36.In a group of 36 children, 21 play cricket, 23 play football and 12 play both. How many play neither of the two?
  37. 37.In a group of 43 children, 22 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing neither of the two?
  38. 38.In a group of 47 children, 28 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing only Hindi songs?
  39. 39.In a group of 34 children, 15 sing Hindi songs, 21 sing English songs and 10 sing both. How many sing only Hindi songs?
  40. 40.In a group of 28 children, 23 like mangoes, 7 like bananas and 4 like both. How many like neither of the two?

Answer key

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

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