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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 512 · 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 29 children, 10 play cricket, 16 play football and 2 play both. How many play at least one of the two?
  2. 2.In a group of 50 children, 26 enjoy drawing, 25 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  3. 3.In a group of 21 children, 10 like mangoes, 9 like bananas and 4 like both. How many like only mangoes?
  4. 4.In a group of 52 grown-ups, 22 drink tea, 20 drink coffee and 5 drink both. How many drink exactly one of the two?
  5. 5.In a group of 35 children, 11 like mangoes, 24 like bananas and 6 like both. How many like at least one of the two?
  6. 6.In a group of 31 children, 19 like mangoes, 22 like bananas and 11 like both. How many like exactly one of the two?
  7. 7.In a group of 29 children, 9 play cricket, 18 play football and 3 play both. How many play only football?
  8. 8.In a group of 46 grown-ups, 21 drink tea, 17 drink coffee and 2 drink both. How many drink only tea?
  9. 9.In a group of 40 children, 26 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing neither of the two?
  10. 10.In a group of 37 children, 19 sing Hindi songs, 21 sing English songs and 6 sing both. How many sing only Hindi songs?
  11. 11.In a group of 39 children, 16 enjoy drawing, 26 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  12. 12.In a group of 40 children, 19 like mangoes, 21 like bananas and 7 like both. How many like neither of the two?
  13. 13.In a group of 35 grown-ups, 13 drink tea, 17 drink coffee and 10 drink both. How many drink neither of the two?
  14. 14.In a group of 20 grown-ups, 9 drink tea, 11 drink coffee and 3 drink both. How many drink only tea?
  15. 15.In a group of 51 children, 30 play cricket, 18 play football and 10 play both. How many play at least one of the two?
  16. 16.In a group of 37 children, 19 sing Hindi songs, 18 sing English songs and 3 sing both. How many sing exactly one of the two?
  17. 17.In a group of 37 children, 21 play chess, 21 play carrom and 7 play both. How many play neither of the two?
  18. 18.In a group of 48 children, 28 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 25 children, 11 like mangoes, 14 like bananas and 2 like both. How many like neither of the two?
  20. 20.In a group of 52 children, 27 play cricket, 31 play football and 12 play both. How many play exactly one of the two?
  21. 21.In a group of 51 children, 25 play cricket, 23 play football and 11 play both. How many play only cricket?
  22. 22.In a group of 36 children, 15 play cricket, 25 play football and 12 play both. How many play only football?
  23. 23.In a group of 50 children, 32 sing Hindi songs, 16 sing English songs and 12 sing both. How many sing at least one of the two?
  24. 24.In a group of 36 children, 20 play chess, 27 play carrom and 12 play both. How many play exactly one of the two?
  25. 25.In a group of 21 grown-ups, 10 drink tea, 15 drink coffee and 7 drink both. How many drink exactly one of the two?
  26. 26.In a group of 39 children, 24 play cricket, 17 play football and 4 play both. How many play only football?
  27. 27.In a group of 26 children, 8 play chess, 17 play carrom and 3 play both. How many play only chess?
  28. 28.In a group of 22 children, 12 like mangoes, 16 like bananas and 8 like both. How many like exactly one of the two?
  29. 29.In a group of 33 grown-ups, 6 drink tea, 22 drink coffee and 2 drink both. How many drink only tea?
  30. 30.In a group of 28 children, 8 play cricket, 22 play football and 5 play both. How many play only cricket?
  31. 31.In a group of 43 children, 11 like mangoes, 21 like bananas and 3 like both. How many like only bananas?
  32. 32.In a group of 50 children, 21 like mangoes, 25 like bananas and 7 like both. How many like neither of the two?
  33. 33.In a group of 40 children, 24 play cricket, 11 play football and 8 play both. How many play only football?
  34. 34.In a group of 38 children, 25 sing Hindi songs, 16 sing English songs and 7 sing both. How many sing neither of the two?
  35. 35.In a group of 54 children, 24 like mangoes, 27 like bananas and 11 like both. How many like only mangoes?
  36. 36.In a group of 37 children, 18 play chess, 15 play carrom and 2 play both. How many play only carrom?
  37. 37.In a group of 41 children, 9 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing at least one of the two?
  38. 38.In a group of 41 children, 26 like mangoes, 22 like bananas and 10 like both. How many like at least one of the two?
  39. 39.In a group of 44 children, 26 play cricket, 15 play football and 11 play both. How many play at least one of the two?
  40. 40.In a group of 44 children, 21 play cricket, 13 play football and 5 play both. How many play exactly one of the two?

Answer key

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

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