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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 410 · 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 42 children, 18 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 33 children, 14 like mangoes, 9 like bananas and 2 like both. How many like only mangoes?
  3. 3.In a group of 23 grown-ups, 9 drink tea, 13 drink coffee and 2 drink both. How many drink at least one of the two?
  4. 4.In a group of 55 children, 24 play chess, 20 play carrom and 4 play both. How many play exactly one of the two?
  5. 5.In a group of 44 children, 13 enjoy drawing, 20 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  6. 6.In a group of 36 children, 22 play cricket, 18 play football and 8 play both. How many play neither of the two?
  7. 7.In a group of 33 children, 18 play chess, 10 play carrom and 2 play both. How many play only chess?
  8. 8.In a group of 40 children, 26 sing Hindi songs, 14 sing English songs and 6 sing both. How many sing at least one of the two?
  9. 9.In a group of 46 children, 23 play chess, 21 play carrom and 3 play both. How many play at least one of the two?
  10. 10.In a group of 45 grown-ups, 18 drink tea, 21 drink coffee and 8 drink both. How many drink only tea?
  11. 11.In a group of 41 children, 15 like mangoes, 24 like bananas and 7 like both. How many like only mangoes?
  12. 12.In a group of 22 grown-ups, 8 drink tea, 9 drink coffee and 2 drink both. How many drink at least one of the two?
  13. 13.In a group of 25 children, 11 play cricket, 7 play football and 2 play both. How many play at least one of the two?
  14. 14.In a group of 34 children, 14 play chess, 28 play carrom and 9 play both. How many play only carrom?
  15. 15.In a group of 31 children, 15 play chess, 16 play carrom and 2 play both. How many play only carrom?
  16. 16.In a group of 51 children, 26 play cricket, 25 play football and 6 play both. How many play only cricket?
  17. 17.In a group of 46 children, 23 enjoy drawing, 26 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  18. 18.In a group of 48 grown-ups, 20 drink tea, 18 drink coffee and 4 drink both. How many drink exactly one of the two?
  19. 19.In a group of 16 children, 11 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  20. 20.In a group of 37 children, 16 sing Hindi songs, 21 sing English songs and 10 sing both. How many sing exactly one of the two?
  21. 21.In a group of 29 children, 21 like mangoes, 10 like bananas and 7 like both. How many like at least one of the two?
  22. 22.In a group of 34 children, 27 enjoy drawing, 13 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  23. 23.In a group of 18 children, 14 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  24. 24.In a group of 42 grown-ups, 21 drink tea, 28 drink coffee and 9 drink both. How many drink neither of the two?
  25. 25.In a group of 39 children, 25 sing Hindi songs, 20 sing English songs and 8 sing both. How many sing at least one of the two?
  26. 26.In a group of 32 children, 11 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 28 children, 14 like mangoes, 17 like bananas and 10 like both. How many like exactly one of the two?
  28. 28.In a group of 49 grown-ups, 24 drink tea, 21 drink coffee and 6 drink both. How many drink only tea?
  29. 29.In a group of 34 children, 14 like mangoes, 17 like bananas and 6 like both. How many like only bananas?
  30. 30.In a group of 35 children, 24 sing Hindi songs, 17 sing English songs and 7 sing both. How many sing exactly one of the two?
  31. 31.In a group of 44 children, 26 play chess, 20 play carrom and 10 play both. How many play neither of the two?
  32. 32.In a group of 36 children, 20 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing neither of the two?
  33. 33.In a group of 32 children, 18 play chess, 18 play carrom and 5 play both. How many play only chess?
  34. 34.In a group of 33 children, 17 enjoy drawing, 7 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  35. 35.In a group of 52 children, 20 sing Hindi songs, 25 sing English songs and 5 sing both. How many sing neither of the two?
  36. 36.In a group of 53 children, 24 play chess, 23 play carrom and 5 play both. How many play only chess?
  37. 37.In a group of 31 children, 21 play chess, 13 play carrom and 4 play both. How many play at least one of the two?
  38. 38.In a group of 37 children, 20 sing Hindi songs, 14 sing English songs and 6 sing both. How many sing neither of the two?
  39. 39.In a group of 39 children, 16 sing Hindi songs, 20 sing English songs and 8 sing both. How many sing only Hindi songs?
  40. 40.In a group of 30 grown-ups, 9 drink tea, 21 drink coffee and 6 drink both. How many drink exactly one of the two?

Answer key

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

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