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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 417 · 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 20 children, 6 enjoy drawing, 13 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  2. 2.In a group of 23 children, 17 like mangoes, 11 like bananas and 6 like both. How many like exactly one of the two?
  3. 3.In a group of 36 children, 14 play chess, 18 play carrom and 4 play both. How many play exactly one of the two?
  4. 4.In a group of 38 children, 20 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  5. 5.In a group of 34 children, 18 play cricket, 14 play football and 5 play both. How many play neither of the two?
  6. 6.In a group of 35 children, 18 play cricket, 15 play football and 8 play both. How many play exactly one of the two?
  7. 7.In a group of 41 children, 22 like mangoes, 28 like bananas and 10 like both. How many like exactly one of the two?
  8. 8.In a group of 34 grown-ups, 16 drink tea, 28 drink coffee and 11 drink both. How many drink neither of the two?
  9. 9.In a group of 46 children, 29 like mangoes, 21 like bananas and 9 like both. How many like exactly one of the two?
  10. 10.In a group of 31 children, 9 sing Hindi songs, 16 sing English songs and 5 sing both. How many sing at least one of the two?
  11. 11.In a group of 28 children, 15 play cricket, 21 play football and 11 play both. How many play exactly one of the two?
  12. 12.In a group of 42 children, 20 enjoy drawing, 24 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  13. 13.In a group of 45 children, 23 play cricket, 21 play football and 6 play both. How many play at least one of the two?
  14. 14.In a group of 37 children, 10 enjoy drawing, 20 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  15. 15.In a group of 33 children, 17 play cricket, 6 play football and 2 play both. How many play at least one of the two?
  16. 16.In a group of 21 children, 8 sing Hindi songs, 14 sing English songs and 2 sing both. How many sing neither of the two?
  17. 17.In a group of 29 children, 20 like mangoes, 14 like bananas and 10 like both. How many like exactly one of the two?
  18. 18.In a group of 34 children, 19 enjoy drawing, 15 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  19. 19.In a group of 50 children, 31 play cricket, 20 play football and 12 play both. How many play at least one of the two?
  20. 20.In a group of 21 children, 15 enjoy drawing, 9 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  21. 21.In a group of 46 children, 14 play cricket, 26 play football and 6 play both. How many play neither of the two?
  22. 22.In a group of 40 grown-ups, 26 drink tea, 20 drink coffee and 8 drink both. How many drink at least one of the two?
  23. 23.In a group of 17 children, 9 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing only Hindi songs?
  24. 24.In a group of 26 children, 15 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing neither of the two?
  25. 25.In a group of 36 children, 24 sing Hindi songs, 17 sing English songs and 12 sing both. How many sing at least one of the two?
  26. 26.In a group of 48 children, 22 enjoy drawing, 21 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 31 children, 19 play cricket, 10 play football and 3 play both. How many play at least one of the two?
  28. 28.In a group of 29 grown-ups, 15 drink tea, 24 drink coffee and 12 drink both. How many drink neither of the two?
  29. 29.In a group of 27 children, 19 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing exactly one of the two?
  30. 30.In a group of 51 children, 25 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 25 children, 14 enjoy drawing, 9 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 44 children, 21 enjoy drawing, 20 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  33. 33.In a group of 32 children, 23 play cricket, 9 play football and 5 play both. How many play neither of the two?
  34. 34.In a group of 36 grown-ups, 13 drink tea, 26 drink coffee and 9 drink both. How many drink neither of the two?
  35. 35.In a group of 21 children, 11 like mangoes, 11 like bananas and 4 like both. How many like only bananas?
  36. 36.In a group of 44 children, 23 play chess, 14 play carrom and 4 play both. How many play only chess?
  37. 37.In a group of 34 children, 14 sing Hindi songs, 23 sing English songs and 4 sing both. How many sing exactly one of the two?
  38. 38.In a group of 33 children, 6 like mangoes, 17 like bananas and 2 like both. How many like only mangoes?
  39. 39.In a group of 37 children, 26 play cricket, 15 play football and 9 play both. How many play exactly one of the two?
  40. 40.In a group of 27 children, 21 sing Hindi songs, 6 sing English songs and 3 sing both. How many sing exactly one of the two?

Answer key

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

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