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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 598 · 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 38 children, 23 enjoy drawing, 12 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 45 children, 29 like mangoes, 14 like bananas and 10 like both. How many like neither of the two?
  3. 3.In a group of 41 grown-ups, 27 drink tea, 24 drink coffee and 11 drink both. How many drink at least one of the two?
  4. 4.In a group of 33 grown-ups, 18 drink tea, 16 drink coffee and 2 drink both. How many drink exactly one of the two?
  5. 5.In a group of 31 children, 18 enjoy drawing, 20 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  6. 6.In a group of 31 children, 8 like mangoes, 12 like bananas and 3 like both. How many like only mangoes?
  7. 7.In a group of 30 children, 17 play cricket, 19 play football and 8 play both. How many play at least one of the two?
  8. 8.In a group of 32 children, 12 sing Hindi songs, 26 sing English songs and 8 sing both. How many sing exactly one of the two?
  9. 9.In a group of 33 children, 15 play chess, 25 play carrom and 11 play both. How many play neither of the two?
  10. 10.In a group of 36 children, 13 play chess, 14 play carrom and 3 play both. How many play only carrom?
  11. 11.In a group of 29 children, 7 like mangoes, 11 like bananas and 2 like both. How many like only bananas?
  12. 12.In a group of 41 children, 11 play cricket, 23 play football and 7 play both. How many play neither of the two?
  13. 13.In a group of 40 children, 21 play cricket, 8 play football and 4 play both. How many play only football?
  14. 14.In a group of 30 grown-ups, 21 drink tea, 20 drink coffee and 12 drink both. How many drink only tea?
  15. 15.In a group of 17 children, 6 enjoy drawing, 6 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 31 children, 13 sing Hindi songs, 19 sing English songs and 6 sing both. How many sing exactly one of the two?
  17. 17.In a group of 44 children, 25 like mangoes, 12 like bananas and 7 like both. How many like exactly one of the two?
  18. 18.In a group of 22 children, 13 sing Hindi songs, 16 sing English songs and 8 sing both. How many sing only Hindi songs?
  19. 19.In a group of 33 grown-ups, 18 drink tea, 24 drink coffee and 11 drink both. How many drink neither of the two?
  20. 20.In a group of 30 children, 17 play cricket, 13 play football and 2 play both. How many play at least one of the two?
  21. 21.In a group of 28 children, 7 sing Hindi songs, 21 sing English songs and 4 sing both. How many sing only English songs?
  22. 22.In a group of 40 children, 16 enjoy drawing, 27 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 25 children, 16 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  24. 24.In a group of 33 grown-ups, 10 drink tea, 17 drink coffee and 4 drink both. How many drink only tea?
  25. 25.In a group of 35 children, 16 play cricket, 25 play football and 11 play both. How many play only cricket?
  26. 26.In a group of 36 children, 16 play chess, 10 play carrom and 3 play both. How many play neither of the two?
  27. 27.In a group of 38 children, 20 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 38 children, 25 play chess, 15 play carrom and 12 play both. How many play only chess?
  29. 29.In a group of 39 children, 16 sing Hindi songs, 23 sing English songs and 8 sing both. How many sing only English songs?
  30. 30.In a group of 55 children, 26 play cricket, 23 play football and 8 play both. How many play exactly one of the two?
  31. 31.In a group of 33 children, 15 enjoy drawing, 15 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 40 children, 20 play cricket, 26 play football and 9 play both. How many play neither of the two?
  33. 33.In a group of 29 children, 23 sing Hindi songs, 8 sing English songs and 4 sing both. How many sing only Hindi songs?
  34. 34.In a group of 40 children, 25 play cricket, 21 play football and 9 play both. How many play only football?
  35. 35.In a group of 23 children, 8 play chess, 17 play carrom and 3 play both. How many play neither of the two?
  36. 36.In a group of 31 children, 23 play cricket, 9 play football and 5 play both. How many play only cricket?
  37. 37.In a group of 53 children, 26 play cricket, 29 play football and 9 play both. How many play only cricket?
  38. 38.In a group of 32 children, 22 play cricket, 15 play football and 7 play both. How many play exactly one of the two?
  39. 39.In a group of 53 children, 23 play chess, 28 play carrom and 11 play both. How many play only carrom?
  40. 40.In a group of 45 children, 18 sing Hindi songs, 29 sing English songs and 11 sing both. How many sing only Hindi songs?

Answer key

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

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