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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 120 · 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 30 children, 19 like mangoes, 12 like bananas and 3 like both. How many like at least one of the two?
  2. 2.In a group of 39 children, 22 play chess, 28 play carrom and 12 play both. How many play only carrom?
  3. 3.In a group of 24 children, 8 play chess, 13 play carrom and 2 play both. How many play only carrom?
  4. 4.In a group of 29 children, 16 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  5. 5.In a group of 43 children, 14 enjoy drawing, 26 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  6. 6.In a group of 49 grown-ups, 21 drink tea, 16 drink coffee and 2 drink both. How many drink only coffee?
  7. 7.In a group of 33 children, 22 like mangoes, 12 like bananas and 2 like both. How many like only mangoes?
  8. 8.In a group of 39 children, 21 play chess, 20 play carrom and 6 play both. How many play neither of the two?
  9. 9.In a group of 47 children, 24 play cricket, 29 play football and 9 play both. How many play only cricket?
  10. 10.In a group of 34 children, 19 enjoy drawing, 15 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  11. 11.In a group of 22 children, 7 sing Hindi songs, 9 sing English songs and 4 sing both. How many sing neither of the two?
  12. 12.In a group of 46 grown-ups, 25 drink tea, 12 drink coffee and 6 drink both. How many drink exactly one of the two?
  13. 13.In a group of 49 children, 16 play chess, 25 play carrom and 7 play both. How many play exactly one of the two?
  14. 14.In a group of 27 grown-ups, 13 drink tea, 13 drink coffee and 6 drink both. How many drink exactly one of the two?
  15. 15.In a group of 45 children, 19 play chess, 21 play carrom and 9 play both. How many play exactly one of the two?
  16. 16.In a group of 35 children, 17 like mangoes, 25 like bananas and 9 like both. How many like exactly one of the two?
  17. 17.In a group of 41 children, 22 enjoy drawing, 24 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  18. 18.In a group of 33 children, 16 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 41 children, 12 play cricket, 23 play football and 5 play both. How many play only football?
  20. 20.In a group of 33 children, 18 like mangoes, 11 like bananas and 8 like both. How many like neither of the two?
  21. 21.In a group of 35 children, 22 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing at least one of the two?
  22. 22.In a group of 41 children, 28 like mangoes, 16 like bananas and 12 like both. How many like at least one of the two?
  23. 23.In a group of 34 children, 13 enjoy drawing, 14 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  24. 24.In a group of 48 children, 16 sing Hindi songs, 26 sing English songs and 6 sing both. How many sing at least one of the two?
  25. 25.In a group of 29 grown-ups, 16 drink tea, 13 drink coffee and 5 drink both. How many drink neither of the two?
  26. 26.In a group of 35 children, 19 sing Hindi songs, 12 sing English songs and 8 sing both. How many sing only English songs?
  27. 27.In a group of 47 children, 23 play cricket, 23 play football and 5 play both. How many play only football?
  28. 28.In a group of 35 children, 5 enjoy drawing, 20 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  29. 29.In a group of 42 children, 19 play chess, 20 play carrom and 11 play both. How many play neither of the two?
  30. 30.In a group of 38 children, 21 play cricket, 15 play football and 3 play both. How many play neither of the two?
  31. 31.In a group of 30 children, 8 play chess, 11 play carrom and 4 play both. How many play at least one of the two?
  32. 32.In a group of 38 children, 29 play chess, 15 play carrom and 10 play both. How many play at least one of the two?
  33. 33.In a group of 43 children, 11 play cricket, 26 play football and 6 play both. How many play neither of the two?
  34. 34.In a group of 39 children, 16 sing Hindi songs, 21 sing English songs and 9 sing both. How many sing only Hindi songs?
  35. 35.In a group of 49 children, 25 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing only English songs?
  36. 36.In a group of 41 children, 14 play chess, 27 play carrom and 8 play both. How many play neither of the two?
  37. 37.In a group of 35 grown-ups, 13 drink tea, 28 drink coffee and 8 drink both. How many drink only coffee?
  38. 38.In a group of 38 children, 22 sing Hindi songs, 8 sing English songs and 2 sing both. How many sing neither of the two?
  39. 39.In a group of 49 children, 23 play cricket, 29 play football and 12 play both. How many play only cricket?
  40. 40.In a group of 51 children, 21 play chess, 26 play carrom and 10 play both. How many play neither of the two?

Answer key

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

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