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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 399 · 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 46 children, 26 play cricket, 15 play football and 8 play both. How many play exactly one of the two?
  2. 2.In a group of 50 children, 27 play cricket, 29 play football and 11 play both. How many play only cricket?
  3. 3.In a group of 16 grown-ups, 8 drink tea, 9 drink coffee and 3 drink both. How many drink at least one of the two?
  4. 4.In a group of 33 children, 7 like mangoes, 20 like bananas and 2 like both. How many like only bananas?
  5. 5.In a group of 20 children, 11 play cricket, 11 play football and 4 play both. How many play exactly one of the two?
  6. 6.In a group of 31 children, 10 play chess, 21 play carrom and 4 play both. How many play neither of the two?
  7. 7.In a group of 32 grown-ups, 21 drink tea, 19 drink coffee and 12 drink both. How many drink at least one of the two?
  8. 8.In a group of 41 grown-ups, 22 drink tea, 20 drink coffee and 8 drink both. How many drink only tea?
  9. 9.In a group of 28 children, 16 play chess, 12 play carrom and 7 play both. How many play neither of the two?
  10. 10.In a group of 28 children, 11 play chess, 17 play carrom and 5 play both. How many play at least one of the two?
  11. 11.In a group of 53 grown-ups, 32 drink tea, 20 drink coffee and 12 drink both. How many drink only tea?
  12. 12.In a group of 25 children, 10 play chess, 15 play carrom and 7 play both. How many play neither of the two?
  13. 13.In a group of 46 children, 21 enjoy drawing, 21 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  14. 14.In a group of 25 children, 11 sing Hindi songs, 19 sing English songs and 7 sing both. How many sing neither of the two?
  15. 15.In a group of 37 children, 10 play cricket, 17 play football and 5 play both. How many play only football?
  16. 16.In a group of 42 children, 22 sing Hindi songs, 29 sing English songs and 11 sing both. How many sing exactly one of the two?
  17. 17.In a group of 43 children, 19 sing Hindi songs, 19 sing English songs and 2 sing both. How many sing neither of the two?
  18. 18.In a group of 54 grown-ups, 27 drink tea, 30 drink coffee and 10 drink both. How many drink neither of the two?
  19. 19.In a group of 35 children, 16 play chess, 28 play carrom and 10 play both. How many play exactly one of the two?
  20. 20.In a group of 49 children, 22 enjoy drawing, 20 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  21. 21.In a group of 32 children, 16 play cricket, 24 play football and 9 play both. How many play at least one of the two?
  22. 22.In a group of 23 children, 15 sing Hindi songs, 10 sing English songs and 5 sing both. How many sing only English songs?
  23. 23.In a group of 26 children, 13 play chess, 9 play carrom and 5 play both. How many play only chess?
  24. 24.In a group of 40 children, 22 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  25. 25.In a group of 40 children, 23 enjoy drawing, 17 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  26. 26.In a group of 35 children, 20 enjoy drawing, 13 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  27. 27.In a group of 33 grown-ups, 10 drink tea, 17 drink coffee and 6 drink both. How many drink only tea?
  28. 28.In a group of 39 children, 11 enjoy drawing, 25 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  29. 29.In a group of 35 children, 15 enjoy drawing, 20 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  30. 30.In a group of 26 children, 7 sing Hindi songs, 15 sing English songs and 2 sing both. How many sing only Hindi songs?
  31. 31.In a group of 31 grown-ups, 11 drink tea, 20 drink coffee and 5 drink both. How many drink exactly one of the two?
  32. 32.In a group of 48 children, 23 like mangoes, 20 like bananas and 9 like both. How many like neither of the two?
  33. 33.In a group of 28 children, 12 play chess, 15 play carrom and 6 play both. How many play neither of the two?
  34. 34.In a group of 18 children, 10 sing Hindi songs, 9 sing English songs and 3 sing both. How many sing only English songs?
  35. 35.In a group of 28 children, 10 enjoy drawing, 14 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  36. 36.In a group of 29 children, 17 play chess, 18 play carrom and 10 play both. How many play at least one of the two?
  37. 37.In a group of 41 children, 24 play chess, 14 play carrom and 9 play both. How many play exactly one of the two?
  38. 38.In a group of 41 children, 16 sing Hindi songs, 24 sing English songs and 4 sing both. How many sing exactly one of the two?
  39. 39.In a group of 38 children, 22 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  40. 40.In a group of 45 children, 18 sing Hindi songs, 17 sing English songs and 4 sing both. How many sing at least one of the two?

Answer key

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

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