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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 300 · 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, 16 play chess, 13 play carrom and 6 play both. How many play neither of the two?
  2. 2.In a group of 54 children, 25 enjoy drawing, 24 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 44 children, 23 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing only Hindi songs?
  4. 4.In a group of 38 children, 9 enjoy drawing, 23 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  5. 5.In a group of 33 children, 16 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing only English songs?
  6. 6.In a group of 40 children, 13 sing Hindi songs, 22 sing English songs and 8 sing both. How many sing at least one of the two?
  7. 7.In a group of 29 grown-ups, 15 drink tea, 13 drink coffee and 7 drink both. How many drink only coffee?
  8. 8.In a group of 54 grown-ups, 24 drink tea, 27 drink coffee and 12 drink both. How many drink at least one of the two?
  9. 9.In a group of 25 children, 9 enjoy drawing, 14 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 28 children, 10 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing only Hindi songs?
  11. 11.In a group of 34 children, 18 sing Hindi songs, 15 sing English songs and 3 sing both. How many sing exactly one of the two?
  12. 12.In a group of 39 children, 19 enjoy drawing, 10 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  13. 13.In a group of 37 children, 23 play chess, 16 play carrom and 6 play both. How many play only chess?
  14. 14.In a group of 28 children, 9 sing Hindi songs, 21 sing English songs and 5 sing both. How many sing neither of the two?
  15. 15.In a group of 53 children, 27 sing Hindi songs, 22 sing English songs and 9 sing both. How many sing exactly one of the two?
  16. 16.In a group of 25 children, 17 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  17. 17.In a group of 34 children, 17 play chess, 15 play carrom and 6 play both. How many play at least one of the two?
  18. 18.In a group of 32 children, 8 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  19. 19.In a group of 22 children, 7 play cricket, 16 play football and 4 play both. How many play only football?
  20. 20.In a group of 46 children, 26 like mangoes, 25 like bananas and 12 like both. How many like only mangoes?
  21. 21.In a group of 49 children, 18 play cricket, 27 play football and 10 play both. How many play neither of the two?
  22. 22.In a group of 29 children, 16 like mangoes, 17 like bananas and 12 like both. How many like only mangoes?
  23. 23.In a group of 40 children, 22 enjoy drawing, 11 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 43 children, 28 play chess, 23 play carrom and 12 play both. How many play only chess?
  25. 25.In a group of 45 children, 27 sing Hindi songs, 17 sing English songs and 8 sing both. How many sing only Hindi songs?
  26. 26.In a group of 30 children, 17 like mangoes, 17 like bananas and 9 like both. How many like at least one of the two?
  27. 27.In a group of 30 children, 5 sing Hindi songs, 18 sing English songs and 2 sing both. How many sing only Hindi songs?
  28. 28.In a group of 29 children, 18 sing Hindi songs, 13 sing English songs and 6 sing both. How many sing only English songs?
  29. 29.In a group of 36 children, 15 play cricket, 11 play football and 2 play both. How many play at least one of the two?
  30. 30.In a group of 26 children, 15 play cricket, 16 play football and 6 play both. How many play at least one of the two?
  31. 31.In a group of 31 children, 22 like mangoes, 15 like bananas and 9 like both. How many like neither of the two?
  32. 32.In a group of 31 children, 11 like mangoes, 13 like bananas and 8 like both. How many like at least one of the two?
  33. 33.In a group of 33 children, 12 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 55 children, 28 enjoy drawing, 20 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  35. 35.In a group of 24 children, 11 like mangoes, 14 like bananas and 5 like both. How many like only mangoes?
  36. 36.In a group of 51 children, 29 enjoy drawing, 25 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  37. 37.In a group of 26 children, 13 play cricket, 14 play football and 7 play both. How many play only football?
  38. 38.In a group of 26 grown-ups, 22 drink tea, 5 drink coffee and 2 drink both. How many drink neither of the two?
  39. 39.In a group of 36 children, 21 play chess, 13 play carrom and 4 play both. How many play neither of the two?
  40. 40.In a group of 42 children, 14 play chess, 26 play carrom and 10 play both. How many play only chess?

Answer key

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

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