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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 449 · 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 45 children, 21 enjoy drawing, 22 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 39 children, 21 sing Hindi songs, 20 sing English songs and 4 sing both. How many sing only Hindi songs?
  3. 3.In a group of 50 children, 28 sing Hindi songs, 24 sing English songs and 9 sing both. How many sing only English songs?
  4. 4.In a group of 51 children, 27 enjoy drawing, 28 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 45 children, 14 play chess, 23 play carrom and 7 play both. How many play neither of the two?
  6. 6.In a group of 26 children, 5 play cricket, 22 play football and 2 play both. How many play only cricket?
  7. 7.In a group of 49 children, 18 sing Hindi songs, 26 sing English songs and 9 sing both. How many sing exactly one of the two?
  8. 8.In a group of 50 children, 31 play cricket, 28 play football and 12 play both. How many play exactly one of the two?
  9. 9.In a group of 39 children, 21 like mangoes, 13 like bananas and 9 like both. How many like at least one of the two?
  10. 10.In a group of 49 children, 20 like mangoes, 30 like bananas and 12 like both. How many like exactly one of the two?
  11. 11.In a group of 42 children, 9 enjoy drawing, 20 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  12. 12.In a group of 28 children, 7 play cricket, 22 play football and 4 play both. How many play exactly one of the two?
  13. 13.In a group of 33 children, 19 enjoy drawing, 16 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 38 children, 21 play chess, 11 play carrom and 8 play both. How many play only carrom?
  15. 15.In a group of 39 grown-ups, 28 drink tea, 17 drink coffee and 10 drink both. How many drink only tea?
  16. 16.In a group of 30 children, 9 sing Hindi songs, 17 sing English songs and 6 sing both. How many sing neither of the two?
  17. 17.In a group of 43 children, 17 play chess, 15 play carrom and 2 play both. How many play exactly one of the two?
  18. 18.In a group of 38 children, 17 like mangoes, 13 like bananas and 6 like both. How many like only mangoes?
  19. 19.In a group of 17 children, 9 sing Hindi songs, 10 sing English songs and 3 sing both. How many sing at least one of the two?
  20. 20.In a group of 42 children, 28 play cricket, 13 play football and 8 play both. How many play only cricket?
  21. 21.In a group of 36 children, 12 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing at least one of the two?
  22. 22.In a group of 35 children, 19 like mangoes, 22 like bananas and 9 like both. How many like only mangoes?
  23. 23.In a group of 26 children, 13 like mangoes, 13 like bananas and 9 like both. How many like at least one of the two?
  24. 24.In a group of 34 children, 16 sing Hindi songs, 20 sing English songs and 5 sing both. How many sing at least one of the two?
  25. 25.In a group of 35 children, 23 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing neither of the two?
  26. 26.In a group of 25 children, 15 sing Hindi songs, 10 sing English songs and 2 sing both. How many sing at least one of the two?
  27. 27.In a group of 35 children, 24 play chess, 20 play carrom and 10 play both. How many play only chess?
  28. 28.In a group of 32 children, 18 sing Hindi songs, 17 sing English songs and 12 sing both. How many sing neither of the two?
  29. 29.In a group of 31 children, 14 like mangoes, 19 like bananas and 6 like both. How many like neither of the two?
  30. 30.In a group of 41 children, 13 like mangoes, 25 like bananas and 7 like both. How many like neither of the two?
  31. 31.In a group of 30 grown-ups, 13 drink tea, 12 drink coffee and 2 drink both. How many drink exactly one of the two?
  32. 32.In a group of 27 children, 16 sing Hindi songs, 18 sing English songs and 8 sing both. How many sing neither of the two?
  33. 33.In a group of 49 children, 22 play chess, 23 play carrom and 4 play both. How many play neither of the two?
  34. 34.In a group of 32 children, 18 play cricket, 16 play football and 7 play both. How many play exactly one of the two?
  35. 35.In a group of 39 children, 15 enjoy drawing, 19 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  36. 36.In a group of 23 grown-ups, 13 drink tea, 6 drink coffee and 3 drink both. How many drink at least one of the two?
  37. 37.In a group of 33 children, 10 play cricket, 25 play football and 6 play both. How many play neither of the two?
  38. 38.In a group of 28 children, 10 enjoy drawing, 13 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  39. 39.In a group of 25 grown-ups, 6 drink tea, 8 drink coffee and 3 drink both. How many drink at least one of the two?
  40. 40.In a group of 48 children, 18 play chess, 20 play carrom and 3 play both. How many play neither of the two?

Answer key

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

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