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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 47 · 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 36 children, 29 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  2. 2.In a group of 39 children, 15 enjoy drawing, 22 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 56 children, 27 enjoy drawing, 26 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 36 grown-ups, 18 drink tea, 17 drink coffee and 8 drink both. How many drink exactly one of the two?
  5. 5.In a group of 37 children, 25 play cricket, 19 play football and 8 play both. How many play at least one of the two?
  6. 6.In a group of 36 children, 25 play chess, 18 play carrom and 9 play both. How many play neither of the two?
  7. 7.In a group of 39 children, 13 enjoy drawing, 25 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 28 children, 9 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 38 children, 20 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 40 children, 15 like mangoes, 23 like bananas and 8 like both. How many like at least one of the two?
  11. 11.In a group of 37 children, 23 like mangoes, 15 like bananas and 3 like both. How many like only bananas?
  12. 12.In a group of 31 children, 10 play cricket, 23 play football and 4 play both. How many play only football?
  13. 13.In a group of 36 children, 21 play chess, 7 play carrom and 3 play both. How many play only carrom?
  14. 14.In a group of 21 children, 14 play chess, 8 play carrom and 2 play both. How many play only carrom?
  15. 15.In a group of 31 children, 7 play chess, 16 play carrom and 2 play both. How many play only chess?
  16. 16.In a group of 39 children, 19 play cricket, 18 play football and 6 play both. How many play neither of the two?
  17. 17.In a group of 26 children, 20 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing only English songs?
  18. 18.In a group of 22 children, 14 sing Hindi songs, 10 sing English songs and 7 sing both. How many sing only Hindi songs?
  19. 19.In a group of 39 children, 18 enjoy drawing, 29 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 33 children, 19 enjoy drawing, 17 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  21. 21.In a group of 29 children, 22 play chess, 5 play carrom and 2 play both. How many play exactly one of the two?
  22. 22.In a group of 47 children, 16 enjoy drawing, 24 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 41 children, 30 play chess, 17 play carrom and 11 play both. How many play only carrom?
  24. 24.In a group of 39 children, 21 play chess, 16 play carrom and 10 play both. How many play only chess?
  25. 25.In a group of 33 children, 9 play cricket, 15 play football and 5 play both. How many play at least one of the two?
  26. 26.In a group of 39 children, 14 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing only English songs?
  27. 27.In a group of 34 children, 13 like mangoes, 19 like bananas and 2 like both. How many like at least one of the two?
  28. 28.In a group of 37 children, 14 play chess, 21 play carrom and 3 play both. How many play only carrom?
  29. 29.In a group of 37 children, 19 enjoy drawing, 24 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 29 children, 23 play cricket, 13 play football and 8 play both. How many play only football?
  31. 31.In a group of 41 children, 12 play cricket, 17 play football and 3 play both. How many play only cricket?
  32. 32.In a group of 35 children, 10 play cricket, 13 play football and 3 play both. How many play exactly one of the two?
  33. 33.In a group of 30 grown-ups, 15 drink tea, 21 drink coffee and 9 drink both. How many drink at least one of the two?
  34. 34.In a group of 29 children, 16 play chess, 10 play carrom and 3 play both. How many play at least one of the two?
  35. 35.In a group of 31 grown-ups, 16 drink tea, 18 drink coffee and 4 drink both. How many drink at least one of the two?
  36. 36.In a group of 47 children, 22 sing Hindi songs, 24 sing English songs and 8 sing both. How many sing at least one of the two?
  37. 37.In a group of 36 children, 14 like mangoes, 19 like bananas and 10 like both. How many like exactly one of the two?
  38. 38.In a group of 44 children, 22 sing Hindi songs, 16 sing English songs and 2 sing both. How many sing exactly one of the two?
  39. 39.In a group of 29 children, 16 play chess, 17 play carrom and 7 play both. How many play at least one of the two?
  40. 40.In a group of 35 children, 14 like mangoes, 23 like bananas and 10 like both. How many like only mangoes?

Answer key

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

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