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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 74 · 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, 9 play cricket, 20 play football and 5 play both. How many play neither of the two?
  2. 2.In a group of 42 children, 26 sing Hindi songs, 26 sing English songs and 11 sing both. How many sing only English songs?
  3. 3.In a group of 35 children, 27 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 51 children, 24 sing Hindi songs, 21 sing English songs and 7 sing both. How many sing only English songs?
  5. 5.In a group of 48 children, 32 play cricket, 15 play football and 12 play both. How many play only football?
  6. 6.In a group of 30 grown-ups, 24 drink tea, 9 drink coffee and 5 drink both. How many drink neither of the two?
  7. 7.In a group of 38 children, 6 play cricket, 22 play football and 2 play both. How many play only football?
  8. 8.In a group of 31 children, 22 enjoy drawing, 9 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  9. 9.In a group of 32 children, 21 play cricket, 10 play football and 5 play both. How many play only cricket?
  10. 10.In a group of 45 grown-ups, 29 drink tea, 22 drink coffee and 10 drink both. How many drink only coffee?
  11. 11.In a group of 41 children, 19 sing Hindi songs, 14 sing English songs and 2 sing both. How many sing at least one of the two?
  12. 12.In a group of 33 children, 21 play chess, 19 play carrom and 11 play both. How many play neither of the two?
  13. 13.In a group of 48 children, 26 sing Hindi songs, 14 sing English songs and 7 sing both. How many sing only Hindi songs?
  14. 14.In a group of 51 children, 30 play chess, 27 play carrom and 10 play both. How many play only carrom?
  15. 15.In a group of 20 children, 8 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing exactly one of the two?
  16. 16.In a group of 41 children, 24 play cricket, 15 play football and 4 play both. How many play at least one of the two?
  17. 17.In a group of 32 children, 11 like mangoes, 21 like bananas and 3 like both. How many like neither of the two?
  18. 18.In a group of 24 children, 8 play cricket, 13 play football and 5 play both. How many play only cricket?
  19. 19.In a group of 42 children, 29 play cricket, 22 play football and 12 play both. How many play only football?
  20. 20.In a group of 38 children, 22 like mangoes, 13 like bananas and 6 like both. How many like only mangoes?
  21. 21.In a group of 27 children, 12 play cricket, 17 play football and 8 play both. How many play only cricket?
  22. 22.In a group of 25 children, 12 play chess, 15 play carrom and 3 play both. How many play only chess?
  23. 23.In a group of 41 children, 18 sing Hindi songs, 29 sing English songs and 11 sing both. How many sing only Hindi songs?
  24. 24.In a group of 53 children, 25 like mangoes, 25 like bananas and 9 like both. How many like exactly one of the two?
  25. 25.In a group of 52 children, 28 enjoy drawing, 28 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  26. 26.In a group of 23 grown-ups, 7 drink tea, 6 drink coffee and 2 drink both. How many drink neither of the two?
  27. 27.In a group of 28 grown-ups, 18 drink tea, 14 drink coffee and 9 drink both. How many drink at least one of the two?
  28. 28.In a group of 41 children, 15 enjoy drawing, 24 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  29. 29.In a group of 46 children, 27 like mangoes, 12 like bananas and 8 like both. How many like only mangoes?
  30. 30.In a group of 42 children, 16 like mangoes, 20 like bananas and 9 like both. How many like neither of the two?
  31. 31.In a group of 32 grown-ups, 22 drink tea, 16 drink coffee and 7 drink both. How many drink exactly one of the two?
  32. 32.In a group of 36 children, 21 play cricket, 16 play football and 3 play both. How many play neither of the two?
  33. 33.In a group of 39 children, 15 sing Hindi songs, 20 sing English songs and 8 sing both. How many sing at least one of the two?
  34. 34.In a group of 49 grown-ups, 22 drink tea, 18 drink coffee and 2 drink both. How many drink at least one of the two?
  35. 35.In a group of 31 children, 15 enjoy drawing, 20 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  36. 36.In a group of 42 children, 23 enjoy drawing, 21 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 41 children, 8 sing Hindi songs, 23 sing English songs and 4 sing both. How many sing only English songs?
  38. 38.In a group of 43 children, 22 play chess, 13 play carrom and 2 play both. How many play neither of the two?
  39. 39.In a group of 29 grown-ups, 7 drink tea, 21 drink coffee and 2 drink both. How many drink exactly one of the two?
  40. 40.In a group of 33 children, 22 play cricket, 13 play football and 9 play both. How many play neither of the two?

Answer key

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

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