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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 646 · 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 37 children, 26 enjoy drawing, 18 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  2. 2.In a group of 26 children, 9 play cricket, 19 play football and 6 play both. How many play neither of the two?
  3. 3.In a group of 39 children, 12 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing at least one of the two?
  4. 4.In a group of 20 children, 14 sing Hindi songs, 12 sing English songs and 7 sing both. How many sing exactly one of the two?
  5. 5.In a group of 37 children, 20 play chess, 11 play carrom and 4 play both. How many play only carrom?
  6. 6.In a group of 31 children, 18 play chess, 12 play carrom and 6 play both. How many play exactly one of the two?
  7. 7.In a group of 25 children, 11 enjoy drawing, 15 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  8. 8.In a group of 28 children, 12 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 31 children, 17 sing Hindi songs, 9 sing English songs and 5 sing both. How many sing neither of the two?
  10. 10.In a group of 38 children, 23 play cricket, 14 play football and 4 play both. How many play only cricket?
  11. 11.In a group of 44 children, 21 enjoy drawing, 20 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  12. 12.In a group of 39 children, 20 play cricket, 15 play football and 8 play both. How many play exactly one of the two?
  13. 13.In a group of 40 children, 25 play cricket, 25 play football and 12 play both. How many play neither of the two?
  14. 14.In a group of 27 children, 10 play chess, 21 play carrom and 6 play both. How many play at least one of the two?
  15. 15.In a group of 22 children, 10 play chess, 9 play carrom and 4 play both. How many play neither of the two?
  16. 16.In a group of 50 children, 23 like mangoes, 29 like bananas and 11 like both. How many like only mangoes?
  17. 17.In a group of 32 children, 10 play cricket, 19 play football and 3 play both. How many play only football?
  18. 18.In a group of 49 children, 23 sing Hindi songs, 20 sing English songs and 8 sing both. How many sing exactly one of the two?
  19. 19.In a group of 28 children, 20 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  20. 20.In a group of 42 children, 25 sing Hindi songs, 21 sing English songs and 6 sing both. How many sing exactly one of the two?
  21. 21.In a group of 44 children, 13 play cricket, 25 play football and 5 play both. How many play only football?
  22. 22.In a group of 47 children, 22 sing Hindi songs, 30 sing English songs and 11 sing both. How many sing exactly one of the two?
  23. 23.In a group of 34 children, 23 sing Hindi songs, 12 sing English songs and 8 sing both. How many sing exactly one of the two?
  24. 24.In a group of 27 children, 13 enjoy drawing, 11 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  25. 25.In a group of 28 children, 16 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing only Hindi songs?
  26. 26.In a group of 26 children, 11 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing only Hindi songs?
  27. 27.In a group of 25 children, 13 like mangoes, 9 like bananas and 4 like both. How many like only mangoes?
  28. 28.In a group of 38 grown-ups, 17 drink tea, 26 drink coffee and 12 drink both. How many drink only tea?
  29. 29.In a group of 38 children, 20 play chess, 16 play carrom and 9 play both. How many play exactly one of the two?
  30. 30.In a group of 36 children, 6 play cricket, 21 play football and 3 play both. How many play only cricket?
  31. 31.In a group of 26 children, 13 like mangoes, 14 like bananas and 3 like both. How many like only mangoes?
  32. 32.In a group of 30 children, 18 play chess, 15 play carrom and 10 play both. How many play exactly one of the two?
  33. 33.In a group of 40 children, 20 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  34. 34.In a group of 40 children, 25 sing Hindi songs, 20 sing English songs and 10 sing both. How many sing neither of the two?
  35. 35.In a group of 61 children, 26 enjoy drawing, 31 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 45 children, 22 play chess, 24 play carrom and 8 play both. How many play only carrom?
  37. 37.In a group of 52 children, 20 play cricket, 25 play football and 8 play both. How many play only cricket?
  38. 38.In a group of 28 children, 16 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  39. 39.In a group of 30 children, 21 like mangoes, 12 like bananas and 6 like both. How many like neither of the two?
  40. 40.In a group of 23 grown-ups, 9 drink tea, 6 drink coffee and 2 drink both. How many drink only tea?

Answer key

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

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