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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 569 · 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 39 children, 14 play cricket, 13 play football and 2 play both. How many play only cricket?
  2. 2.In a group of 29 children, 13 sing Hindi songs, 13 sing English songs and 2 sing both. How many sing only English songs?
  3. 3.In a group of 34 children, 6 like mangoes, 17 like bananas and 3 like both. How many like at least one of the two?
  4. 4.In a group of 38 children, 21 enjoy drawing, 16 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  5. 5.In a group of 22 children, 13 play cricket, 8 play football and 4 play both. How many play neither of the two?
  6. 6.In a group of 47 children, 14 play chess, 27 play carrom and 8 play both. How many play exactly one of the two?
  7. 7.In a group of 36 grown-ups, 18 drink tea, 20 drink coffee and 12 drink both. How many drink exactly one of the two?
  8. 8.In a group of 33 children, 16 enjoy drawing, 18 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  9. 9.In a group of 48 children, 30 play chess, 15 play carrom and 11 play both. How many play exactly one of the two?
  10. 10.In a group of 28 children, 7 play chess, 21 play carrom and 4 play both. How many play exactly one of the two?
  11. 11.In a group of 30 children, 16 play cricket, 22 play football and 12 play both. How many play neither of the two?
  12. 12.In a group of 43 children, 25 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  13. 13.In a group of 35 children, 15 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  14. 14.In a group of 43 children, 16 play cricket, 27 play football and 8 play both. How many play only cricket?
  15. 15.In a group of 47 children, 26 enjoy drawing, 27 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 37 grown-ups, 22 drink tea, 17 drink coffee and 11 drink both. How many drink neither of the two?
  17. 17.In a group of 18 children, 10 play chess, 10 play carrom and 5 play both. How many play only chess?
  18. 18.In a group of 36 children, 6 enjoy drawing, 19 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  19. 19.In a group of 43 children, 16 play cricket, 30 play football and 10 play both. How many play only football?
  20. 20.In a group of 51 children, 19 like mangoes, 23 like bananas and 4 like both. How many like at least one of the two?
  21. 21.In a group of 42 children, 14 like mangoes, 25 like bananas and 9 like both. How many like only bananas?
  22. 22.In a group of 39 children, 18 like mangoes, 12 like bananas and 3 like both. How many like at least one of the two?
  23. 23.In a group of 38 children, 15 play cricket, 29 play football and 9 play both. How many play at least one of the two?
  24. 24.In a group of 30 children, 12 like mangoes, 23 like bananas and 9 like both. How many like only mangoes?
  25. 25.In a group of 33 children, 20 play cricket, 15 play football and 11 play both. How many play only cricket?
  26. 26.In a group of 31 children, 17 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 47 children, 22 play cricket, 15 play football and 2 play both. How many play only football?
  28. 28.In a group of 36 children, 19 sing Hindi songs, 18 sing English songs and 3 sing both. How many sing exactly one of the two?
  29. 29.In a group of 26 grown-ups, 11 drink tea, 11 drink coffee and 8 drink both. How many drink neither of the two?
  30. 30.In a group of 43 grown-ups, 22 drink tea, 31 drink coffee and 11 drink both. How many drink only tea?
  31. 31.In a group of 37 grown-ups, 21 drink tea, 16 drink coffee and 4 drink both. How many drink exactly one of the two?
  32. 32.In a group of 50 children, 21 play chess, 22 play carrom and 6 play both. How many play only chess?
  33. 33.In a group of 41 children, 21 play cricket, 14 play football and 9 play both. How many play neither of the two?
  34. 34.In a group of 28 children, 18 play chess, 8 play carrom and 3 play both. How many play only chess?
  35. 35.In a group of 46 children, 16 enjoy drawing, 26 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  36. 36.In a group of 18 children, 9 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 53 children, 29 play cricket, 24 play football and 10 play both. How many play neither of the two?
  38. 38.In a group of 49 children, 21 sing Hindi songs, 23 sing English songs and 6 sing both. How many sing exactly one of the two?
  39. 39.In a group of 49 children, 26 like mangoes, 24 like bananas and 7 like both. How many like exactly one of the two?
  40. 40.In a group of 40 children, 27 play chess, 12 play carrom and 9 play both. How many play neither of the two?

Answer key

  1. 12
  2. 11
  3. 20
  4. 11
  5. 5
  6. 25
  7. 14
  8. 9
  9. 23
  10. 20
  11. 4
  12. 12
  13. 10
  14. 8
  15. 43
  16. 9
  17. 5
  18. 21
  19. 20
  20. 38
  21. 16
  22. 27
  23. 35
  24. 3
  25. 9
  26. 15
  27. 13
  28. 31
  29. 12
  30. 11
  31. 29
  32. 15
  33. 15
  34. 15
  35. 14
  36. 11
  37. 10
  38. 32
  39. 36
  40. 10

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