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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 537 · 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 21 children, 6 play cricket, 8 play football and 2 play both. How many play only cricket?
  2. 2.In a group of 31 children, 24 like mangoes, 10 like bananas and 6 like both. How many like exactly one of the two?
  3. 3.In a group of 29 children, 7 play chess, 16 play carrom and 3 play both. How many play only carrom?
  4. 4.In a group of 37 children, 12 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 39 children, 19 like mangoes, 23 like bananas and 7 like both. How many like only mangoes?
  6. 6.In a group of 35 children, 17 play chess, 26 play carrom and 12 play both. How many play only chess?
  7. 7.In a group of 29 children, 12 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 40 children, 15 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 39 children, 22 play cricket, 20 play football and 10 play both. How many play at least one of the two?
  10. 10.In a group of 44 children, 19 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  11. 11.In a group of 34 children, 18 like mangoes, 8 like bananas and 2 like both. How many like at least one of the two?
  12. 12.In a group of 52 children, 24 sing Hindi songs, 32 sing English songs and 12 sing both. How many sing exactly one of the two?
  13. 13.In a group of 31 children, 12 sing Hindi songs, 18 sing English songs and 8 sing both. How many sing only English songs?
  14. 14.In a group of 35 children, 23 like mangoes, 13 like bananas and 7 like both. How many like neither of the two?
  15. 15.In a group of 30 children, 8 like mangoes, 25 like bananas and 5 like both. How many like exactly one of the two?
  16. 16.In a group of 32 children, 24 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  17. 17.In a group of 31 children, 12 like mangoes, 14 like bananas and 8 like both. How many like exactly one of the two?
  18. 18.In a group of 39 children, 19 play chess, 27 play carrom and 10 play both. How many play neither of the two?
  19. 19.In a group of 47 children, 24 play cricket, 27 play football and 7 play both. How many play only cricket?
  20. 20.In a group of 25 children, 12 play chess, 7 play carrom and 2 play both. How many play neither of the two?
  21. 21.In a group of 26 children, 10 play chess, 20 play carrom and 6 play both. How many play neither of the two?
  22. 22.In a group of 38 grown-ups, 7 drink tea, 21 drink coffee and 3 drink both. How many drink only tea?
  23. 23.In a group of 29 children, 18 play cricket, 14 play football and 5 play both. How many play at least one of the two?
  24. 24.In a group of 30 children, 11 enjoy drawing, 7 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  25. 25.In a group of 44 children, 23 enjoy drawing, 22 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 42 children, 21 play chess, 18 play carrom and 9 play both. How many play at least one of the two?
  27. 27.In a group of 44 grown-ups, 22 drink tea, 29 drink coffee and 10 drink both. How many drink only coffee?
  28. 28.In a group of 47 children, 31 play cricket, 25 play football and 12 play both. How many play only football?
  29. 29.In a group of 43 children, 27 enjoy drawing, 25 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  30. 30.In a group of 37 grown-ups, 14 drink tea, 27 drink coffee and 9 drink both. How many drink only coffee?
  31. 31.In a group of 39 children, 29 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  32. 32.In a group of 45 children, 11 play cricket, 22 play football and 2 play both. How many play at least one of the two?
  33. 33.In a group of 31 children, 23 play chess, 14 play carrom and 7 play both. How many play only chess?
  34. 34.In a group of 46 children, 23 play cricket, 13 play football and 4 play both. How many play only cricket?
  35. 35.In a group of 36 children, 18 play chess, 20 play carrom and 4 play both. How many play at least one of the two?
  36. 36.In a group of 55 children, 28 play cricket, 25 play football and 11 play both. How many play at least one of the two?
  37. 37.In a group of 48 children, 22 enjoy drawing, 25 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  38. 38.In a group of 43 children, 27 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  39. 39.In a group of 36 children, 15 play cricket, 30 play football and 12 play both. How many play only cricket?
  40. 40.In a group of 11 children, 6 like mangoes, 6 like bananas and 2 like both. How many like only mangoes?

Answer key

  1. 4
  2. 22
  3. 13
  4. 25
  5. 12
  6. 5
  7. 3
  8. 10
  9. 32
  10. 15
  11. 24
  12. 32
  13. 10
  14. 6
  15. 23
  16. 28
  17. 10
  18. 3
  19. 17
  20. 8
  21. 2
  22. 4
  23. 27
  24. 12
  25. 10
  26. 30
  27. 19
  28. 13
  29. 40
  30. 18
  31. 4
  32. 31
  33. 16
  34. 19
  35. 34
  36. 42
  37. 8
  38. 11
  39. 3
  40. 4

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