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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 611 · 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 50 children, 29 play chess, 20 play carrom and 12 play both. How many play only chess?
  2. 2.In a group of 27 children, 15 enjoy drawing, 18 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  3. 3.In a group of 35 children, 19 like mangoes, 11 like bananas and 6 like both. How many like only mangoes?
  4. 4.In a group of 29 grown-ups, 15 drink tea, 13 drink coffee and 4 drink both. How many drink only tea?
  5. 5.In a group of 30 children, 24 play cricket, 10 play football and 6 play both. How many play exactly one of the two?
  6. 6.In a group of 30 children, 13 like mangoes, 13 like bananas and 7 like both. How many like at least one of the two?
  7. 7.In a group of 41 grown-ups, 11 drink tea, 22 drink coffee and 2 drink both. How many drink exactly one of the two?
  8. 8.In a group of 21 children, 17 enjoy drawing, 15 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 30 children, 10 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing at least one of the two?
  10. 10.In a group of 41 children, 26 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  11. 11.In a group of 38 grown-ups, 16 drink tea, 18 drink coffee and 4 drink both. How many drink only tea?
  12. 12.In a group of 55 children, 28 play cricket, 28 play football and 10 play both. How many play only cricket?
  13. 13.In a group of 28 children, 10 like mangoes, 18 like bananas and 2 like both. How many like only bananas?
  14. 14.In a group of 40 children, 18 enjoy drawing, 20 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  15. 15.In a group of 36 children, 10 play cricket, 20 play football and 5 play both. How many play only cricket?
  16. 16.In a group of 51 children, 25 like mangoes, 28 like bananas and 8 like both. How many like exactly one of the two?
  17. 17.In a group of 30 children, 18 play chess, 8 play carrom and 4 play both. How many play exactly one of the two?
  18. 18.In a group of 25 children, 19 play cricket, 15 play football and 12 play both. How many play only cricket?
  19. 19.In a group of 48 children, 29 enjoy drawing, 30 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 45 children, 19 play chess, 19 play carrom and 2 play both. How many play only carrom?
  21. 21.In a group of 33 children, 22 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing only Hindi songs?
  22. 22.In a group of 35 children, 14 sing Hindi songs, 17 sing English songs and 9 sing both. How many sing neither of the two?
  23. 23.In a group of 34 grown-ups, 14 drink tea, 18 drink coffee and 8 drink both. How many drink neither of the two?
  24. 24.In a group of 33 grown-ups, 8 drink tea, 21 drink coffee and 2 drink both. How many drink only coffee?
  25. 25.In a group of 26 children, 6 play cricket, 15 play football and 2 play both. How many play at least one of the two?
  26. 26.In a group of 61 children, 27 enjoy drawing, 26 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  27. 27.In a group of 37 children, 12 play chess, 14 play carrom and 3 play both. How many play neither of the two?
  28. 28.In a group of 39 grown-ups, 9 drink tea, 21 drink coffee and 4 drink both. How many drink only tea?
  29. 29.In a group of 32 grown-ups, 8 drink tea, 11 drink coffee and 2 drink both. How many drink exactly one of the two?
  30. 30.In a group of 49 children, 22 play chess, 21 play carrom and 2 play both. How many play at least one of the two?
  31. 31.In a group of 38 children, 16 play cricket, 15 play football and 3 play both. How many play exactly one of the two?
  32. 32.In a group of 32 children, 11 sing Hindi songs, 23 sing English songs and 4 sing both. How many sing neither of the two?
  33. 33.In a group of 30 children, 18 sing Hindi songs, 14 sing English songs and 3 sing both. How many sing only English songs?
  34. 34.In a group of 25 children, 7 enjoy drawing, 11 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  35. 35.In a group of 28 children, 14 like mangoes, 18 like bananas and 11 like both. How many like neither of the two?
  36. 36.In a group of 40 children, 19 play cricket, 12 play football and 4 play both. How many play at least one of the two?
  37. 37.In a group of 46 grown-ups, 19 drink tea, 24 drink coffee and 7 drink both. How many drink at least one of the two?
  38. 38.In a group of 45 children, 26 sing Hindi songs, 18 sing English songs and 7 sing both. How many sing at least one of the two?
  39. 39.In a group of 45 children, 21 enjoy drawing, 23 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  40. 40.In a group of 36 grown-ups, 16 drink tea, 17 drink coffee and 12 drink both. How many drink neither of the two?

Answer key

  1. 17
  2. 17
  3. 13
  4. 11
  5. 22
  6. 19
  7. 29
  8. 3
  9. 25
  10. 8
  11. 12
  12. 18
  13. 16
  14. 34
  15. 5
  16. 37
  17. 18
  18. 7
  19. 17
  20. 17
  21. 20
  22. 13
  23. 10
  24. 19
  25. 19
  26. 15
  27. 14
  28. 5
  29. 15
  30. 41
  31. 25
  32. 2
  33. 11
  34. 4
  35. 7
  36. 27
  37. 36
  38. 37
  39. 8
  40. 15

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