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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 284 · 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 22 children, 11 enjoy drawing, 10 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 41 children, 24 like mangoes, 13 like bananas and 10 like both. How many like neither of the two?
  3. 3.In a group of 45 children, 25 like mangoes, 22 like bananas and 8 like both. How many like only mangoes?
  4. 4.In a group of 31 children, 17 play chess, 21 play carrom and 10 play both. How many play neither of the two?
  5. 5.In a group of 16 children, 6 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  6. 6.In a group of 29 children, 17 like mangoes, 18 like bananas and 7 like both. How many like only mangoes?
  7. 7.In a group of 27 children, 11 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing neither of the two?
  8. 8.In a group of 30 children, 8 like mangoes, 17 like bananas and 5 like both. How many like exactly one of the two?
  9. 9.In a group of 26 children, 9 like mangoes, 9 like bananas and 2 like both. How many like only mangoes?
  10. 10.In a group of 28 children, 6 like mangoes, 19 like bananas and 2 like both. How many like only mangoes?
  11. 11.In a group of 24 children, 9 sing Hindi songs, 11 sing English songs and 4 sing both. How many sing only Hindi songs?
  12. 12.In a group of 40 children, 25 enjoy drawing, 14 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  13. 13.In a group of 34 children, 18 like mangoes, 17 like bananas and 12 like both. How many like exactly one of the two?
  14. 14.In a group of 41 children, 15 sing Hindi songs, 22 sing English songs and 3 sing both. How many sing only English songs?
  15. 15.In a group of 22 children, 5 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 36 grown-ups, 20 drink tea, 13 drink coffee and 7 drink both. How many drink only coffee?
  17. 17.In a group of 39 children, 18 play chess, 24 play carrom and 7 play both. How many play neither of the two?
  18. 18.In a group of 28 children, 13 play chess, 12 play carrom and 6 play both. How many play only chess?
  19. 19.In a group of 40 children, 18 enjoy drawing, 19 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 32 children, 25 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  21. 21.In a group of 47 children, 14 play chess, 29 play carrom and 9 play both. How many play neither of the two?
  22. 22.In a group of 37 children, 15 sing Hindi songs, 22 sing English songs and 8 sing both. How many sing only Hindi songs?
  23. 23.In a group of 41 children, 16 play chess, 27 play carrom and 9 play both. How many play only carrom?
  24. 24.In a group of 24 grown-ups, 12 drink tea, 12 drink coffee and 3 drink both. How many drink at least one of the two?
  25. 25.In a group of 37 children, 21 enjoy drawing, 19 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  26. 26.In a group of 27 children, 17 sing Hindi songs, 16 sing English songs and 8 sing both. How many sing only Hindi songs?
  27. 27.In a group of 26 children, 13 like mangoes, 8 like bananas and 4 like both. How many like only bananas?
  28. 28.In a group of 47 grown-ups, 22 drink tea, 31 drink coffee and 12 drink both. How many drink only tea?
  29. 29.In a group of 30 children, 9 like mangoes, 22 like bananas and 6 like both. How many like at least one of the two?
  30. 30.In a group of 28 children, 15 sing Hindi songs, 21 sing English songs and 12 sing both. How many sing only English songs?
  31. 31.In a group of 34 grown-ups, 11 drink tea, 19 drink coffee and 8 drink both. How many drink only tea?
  32. 32.In a group of 37 children, 17 sing Hindi songs, 25 sing English songs and 10 sing both. How many sing exactly one of the two?
  33. 33.In a group of 35 children, 24 play chess, 9 play carrom and 6 play both. How many play only chess?
  34. 34.In a group of 35 children, 24 play cricket, 14 play football and 7 play both. How many play only football?
  35. 35.In a group of 44 children, 12 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  36. 36.In a group of 49 children, 25 like mangoes, 24 like bananas and 7 like both. How many like neither of the two?
  37. 37.In a group of 34 children, 25 play chess, 10 play carrom and 6 play both. How many play only chess?
  38. 38.In a group of 37 children, 20 play chess, 11 play carrom and 6 play both. How many play at least one of the two?
  39. 39.In a group of 34 children, 19 play chess, 9 play carrom and 3 play both. How many play only carrom?
  40. 40.In a group of 15 grown-ups, 8 drink tea, 8 drink coffee and 2 drink both. How many drink exactly one of the two?

Answer key

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

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