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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 614 · 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, 15 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  2. 2.In a group of 25 children, 10 play cricket, 12 play football and 3 play both. How many play neither of the two?
  3. 3.In a group of 35 children, 14 sing Hindi songs, 20 sing English songs and 5 sing both. How many sing only English songs?
  4. 4.In a group of 35 children, 15 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  5. 5.In a group of 27 children, 13 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  6. 6.In a group of 32 children, 14 play chess, 21 play carrom and 9 play both. How many play only chess?
  7. 7.In a group of 48 grown-ups, 16 drink tea, 20 drink coffee and 3 drink both. How many drink only coffee?
  8. 8.In a group of 37 grown-ups, 13 drink tea, 23 drink coffee and 9 drink both. How many drink exactly one of the two?
  9. 9.In a group of 28 children, 12 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  10. 10.In a group of 37 grown-ups, 16 drink tea, 13 drink coffee and 2 drink both. How many drink neither of the two?
  11. 11.In a group of 22 children, 13 play chess, 14 play carrom and 9 play both. How many play exactly one of the two?
  12. 12.In a group of 41 children, 18 sing Hindi songs, 23 sing English songs and 7 sing both. How many sing only Hindi songs?
  13. 13.In a group of 34 children, 16 like mangoes, 23 like bananas and 6 like both. How many like at least one of the two?
  14. 14.In a group of 33 children, 10 enjoy drawing, 21 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  15. 15.In a group of 24 children, 12 play chess, 14 play carrom and 7 play both. How many play only chess?
  16. 16.In a group of 35 children, 20 sing Hindi songs, 17 sing English songs and 10 sing both. How many sing only English songs?
  17. 17.In a group of 39 children, 12 play cricket, 25 play football and 5 play both. How many play only cricket?
  18. 18.In a group of 24 grown-ups, 9 drink tea, 6 drink coffee and 2 drink both. How many drink neither of the two?
  19. 19.In a group of 41 children, 18 enjoy drawing, 29 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  20. 20.In a group of 35 children, 20 play cricket, 8 play football and 5 play both. How many play only cricket?
  21. 21.In a group of 33 children, 24 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  22. 22.In a group of 50 children, 25 like mangoes, 22 like bananas and 8 like both. How many like neither of the two?
  23. 23.In a group of 33 children, 22 enjoy drawing, 10 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  24. 24.In a group of 40 children, 16 play chess, 14 play carrom and 3 play both. How many play neither of the two?
  25. 25.In a group of 40 children, 24 like mangoes, 22 like bananas and 7 like both. How many like at least one of the two?
  26. 26.In a group of 41 children, 26 play chess, 14 play carrom and 10 play both. How many play only chess?
  27. 27.In a group of 47 grown-ups, 17 drink tea, 22 drink coffee and 3 drink both. How many drink only tea?
  28. 28.In a group of 31 children, 18 play chess, 13 play carrom and 8 play both. How many play neither of the two?
  29. 29.In a group of 44 children, 24 like mangoes, 12 like bananas and 7 like both. How many like neither of the two?
  30. 30.In a group of 44 grown-ups, 24 drink tea, 26 drink coffee and 10 drink both. How many drink only coffee?
  31. 31.In a group of 38 children, 24 sing Hindi songs, 21 sing English songs and 12 sing both. How many sing only English songs?
  32. 32.In a group of 29 children, 14 play cricket, 8 play football and 3 play both. How many play exactly one of the two?
  33. 33.In a group of 46 children, 25 like mangoes, 20 like bananas and 11 like both. How many like exactly one of the two?
  34. 34.In a group of 44 children, 20 enjoy drawing, 21 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  35. 35.In a group of 24 children, 16 play chess, 19 play carrom and 12 play both. How many play neither of the two?
  36. 36.In a group of 37 children, 16 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 39 children, 10 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing at least one of the two?
  38. 38.In a group of 25 children, 18 play chess, 8 play carrom and 4 play both. How many play only carrom?
  39. 39.In a group of 35 children, 21 play cricket, 14 play football and 6 play both. How many play only football?
  40. 40.In a group of 16 children, 6 enjoy drawing, 11 enjoy dancing and 2 enjoy both. How many enjoy only drawing?

Answer key

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

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