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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 214 · 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, 14 play cricket, 25 play football and 5 play both. How many play exactly one of the two?
  2. 2.In a group of 38 children, 14 play cricket, 11 play football and 2 play both. How many play neither of the two?
  3. 3.In a group of 28 children, 18 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing at least one of the two?
  4. 4.In a group of 40 children, 18 play cricket, 24 play football and 4 play both. How many play exactly one of the two?
  5. 5.In a group of 54 children, 22 like mangoes, 31 like bananas and 12 like both. How many like only bananas?
  6. 6.In a group of 44 children, 20 enjoy drawing, 29 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  7. 7.In a group of 45 children, 31 enjoy drawing, 15 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 39 children, 25 play cricket, 12 play football and 6 play both. How many play at least one of the two?
  9. 9.In a group of 44 children, 18 enjoy drawing, 26 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  10. 10.In a group of 26 children, 18 like mangoes, 16 like bananas and 11 like both. How many like only mangoes?
  11. 11.In a group of 42 children, 21 play cricket, 18 play football and 10 play both. How many play neither of the two?
  12. 12.In a group of 24 children, 9 play chess, 17 play carrom and 3 play both. How many play exactly one of the two?
  13. 13.In a group of 22 children, 14 play cricket, 15 play football and 8 play both. How many play neither of the two?
  14. 14.In a group of 38 children, 15 play cricket, 22 play football and 6 play both. How many play neither of the two?
  15. 15.In a group of 47 children, 17 enjoy drawing, 28 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 44 children, 20 play cricket, 14 play football and 3 play both. How many play neither of the two?
  17. 17.In a group of 30 children, 18 play cricket, 19 play football and 10 play both. How many play at least one of the two?
  18. 18.In a group of 32 children, 11 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  19. 19.In a group of 40 children, 21 play cricket, 19 play football and 2 play both. How many play neither of the two?
  20. 20.In a group of 45 grown-ups, 22 drink tea, 19 drink coffee and 5 drink both. How many drink neither of the two?
  21. 21.In a group of 38 children, 19 sing Hindi songs, 23 sing English songs and 8 sing both. How many sing only English songs?
  22. 22.In a group of 47 children, 29 play chess, 17 play carrom and 10 play both. How many play only chess?
  23. 23.In a group of 44 children, 20 play cricket, 14 play football and 4 play both. How many play neither of the two?
  24. 24.In a group of 53 children, 21 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing only Hindi songs?
  25. 25.In a group of 43 children, 23 play chess, 20 play carrom and 6 play both. How many play only chess?
  26. 26.In a group of 30 children, 9 enjoy drawing, 16 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 14 children, 10 play cricket, 7 play football and 4 play both. How many play at least one of the two?
  28. 28.In a group of 17 grown-ups, 11 drink tea, 11 drink coffee and 6 drink both. How many drink exactly one of the two?
  29. 29.In a group of 32 grown-ups, 23 drink tea, 6 drink coffee and 3 drink both. How many drink only tea?
  30. 30.In a group of 40 children, 21 play chess, 19 play carrom and 4 play both. How many play neither of the two?
  31. 31.In a group of 53 children, 32 sing Hindi songs, 24 sing English songs and 12 sing both. How many sing neither of the two?
  32. 32.In a group of 30 grown-ups, 17 drink tea, 15 drink coffee and 11 drink both. How many drink neither of the two?
  33. 33.In a group of 27 children, 15 play chess, 8 play carrom and 4 play both. How many play exactly one of the two?
  34. 34.In a group of 19 grown-ups, 11 drink tea, 6 drink coffee and 3 drink both. How many drink neither of the two?
  35. 35.In a group of 48 children, 27 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 30 children, 10 play chess, 17 play carrom and 6 play both. How many play exactly one of the two?
  37. 37.In a group of 48 children, 30 like mangoes, 28 like bananas and 12 like both. How many like neither of the two?
  38. 38.In a group of 38 children, 22 enjoy drawing, 24 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  39. 39.In a group of 37 children, 17 play chess, 20 play carrom and 4 play both. How many play only chess?
  40. 40.In a group of 55 children, 27 enjoy drawing, 31 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?

Answer key

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

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