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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 448 · 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 31 children, 13 play chess, 9 play carrom and 2 play both. How many play only chess?
  2. 2.In a group of 53 children, 29 play chess, 22 play carrom and 12 play both. How many play only chess?
  3. 3.In a group of 28 children, 9 enjoy drawing, 16 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  4. 4.In a group of 36 grown-ups, 9 drink tea, 19 drink coffee and 4 drink both. How many drink only coffee?
  5. 5.In a group of 25 children, 17 enjoy drawing, 5 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  6. 6.In a group of 41 children, 21 enjoy drawing, 29 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  7. 7.In a group of 49 children, 26 play chess, 30 play carrom and 12 play both. How many play at least one of the two?
  8. 8.In a group of 38 grown-ups, 19 drink tea, 26 drink coffee and 9 drink both. How many drink at least one of the two?
  9. 9.In a group of 22 grown-ups, 11 drink tea, 14 drink coffee and 7 drink both. How many drink exactly one of the two?
  10. 10.In a group of 51 children, 22 enjoy drawing, 23 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  11. 11.In a group of 24 children, 17 play cricket, 17 play football and 11 play both. How many play at least one of the two?
  12. 12.In a group of 33 children, 21 enjoy drawing, 17 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 23 children, 13 play cricket, 13 play football and 4 play both. How many play at least one of the two?
  14. 14.In a group of 29 children, 17 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  15. 15.In a group of 36 children, 19 enjoy drawing, 7 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  16. 16.In a group of 42 children, 24 play chess, 17 play carrom and 11 play both. How many play only chess?
  17. 17.In a group of 35 children, 25 enjoy drawing, 8 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  18. 18.In a group of 33 children, 12 like mangoes, 23 like bananas and 5 like both. How many like at least one of the two?
  19. 19.In a group of 40 children, 11 sing Hindi songs, 27 sing English songs and 7 sing both. How many sing at least one of the two?
  20. 20.In a group of 42 children, 22 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing at least one of the two?
  21. 21.In a group of 30 children, 25 like mangoes, 13 like bananas and 9 like both. How many like neither of the two?
  22. 22.In a group of 41 children, 15 play cricket, 24 play football and 6 play both. How many play only cricket?
  23. 23.In a group of 46 children, 24 like mangoes, 17 like bananas and 9 like both. How many like exactly one of the two?
  24. 24.In a group of 48 children, 21 like mangoes, 27 like bananas and 10 like both. How many like only bananas?
  25. 25.In a group of 31 children, 18 enjoy drawing, 11 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  26. 26.In a group of 41 grown-ups, 21 drink tea, 15 drink coffee and 8 drink both. How many drink only tea?
  27. 27.In a group of 43 children, 10 enjoy drawing, 22 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 43 children, 15 sing Hindi songs, 18 sing English songs and 4 sing both. How many sing only Hindi songs?
  29. 29.In a group of 18 children, 5 play chess, 8 play carrom and 2 play both. How many play only chess?
  30. 30.In a group of 28 children, 8 play cricket, 10 play football and 2 play both. How many play only cricket?
  31. 31.In a group of 46 children, 23 like mangoes, 22 like bananas and 6 like both. How many like only mangoes?
  32. 32.In a group of 48 children, 22 sing Hindi songs, 24 sing English songs and 12 sing both. How many sing at least one of the two?
  33. 33.In a group of 46 children, 21 enjoy drawing, 24 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  34. 34.In a group of 58 children, 25 like mangoes, 24 like bananas and 5 like both. How many like exactly one of the two?
  35. 35.In a group of 41 grown-ups, 17 drink tea, 24 drink coffee and 8 drink both. How many drink neither of the two?
  36. 36.In a group of 40 children, 19 play cricket, 15 play football and 5 play both. How many play exactly one of the two?
  37. 37.In a group of 33 children, 17 like mangoes, 25 like bananas and 12 like both. How many like exactly one of the two?
  38. 38.In a group of 32 children, 18 play chess, 12 play carrom and 5 play both. How many play exactly one of the two?
  39. 39.In a group of 36 children, 14 play chess, 20 play carrom and 10 play both. How many play only carrom?
  40. 40.In a group of 42 children, 25 enjoy drawing, 9 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?

Answer key

  1. 11
  2. 17
  3. 7
  4. 15
  5. 3
  6. 10
  7. 44
  8. 36
  9. 11
  10. 18
  11. 23
  12. 18
  13. 22
  14. 5
  15. 15
  16. 13
  17. 20
  18. 30
  19. 31
  20. 29
  21. 1
  22. 9
  23. 23
  24. 17
  25. 25
  26. 13
  27. 28
  28. 11
  29. 3
  30. 6
  31. 17
  32. 34
  33. 11
  34. 39
  35. 8
  36. 24
  37. 18
  38. 20
  39. 10
  40. 14

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