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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 260 · 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 41 children, 26 play cricket, 14 play football and 8 play both. How many play only cricket?
  2. 2.In a group of 35 grown-ups, 12 drink tea, 25 drink coffee and 6 drink both. How many drink neither of the two?
  3. 3.In a group of 26 children, 17 like mangoes, 12 like bananas and 5 like both. How many like only mangoes?
  4. 4.In a group of 30 children, 26 play chess, 13 play carrom and 10 play both. How many play only chess?
  5. 5.In a group of 36 grown-ups, 17 drink tea, 21 drink coffee and 9 drink both. How many drink neither of the two?
  6. 6.In a group of 44 children, 21 like mangoes, 23 like bananas and 10 like both. How many like only mangoes?
  7. 7.In a group of 24 children, 9 play cricket, 5 play football and 2 play both. How many play exactly one of the two?
  8. 8.In a group of 18 children, 7 play cricket, 13 play football and 4 play both. How many play only football?
  9. 9.In a group of 23 children, 18 play chess, 12 play carrom and 8 play both. How many play exactly one of the two?
  10. 10.In a group of 59 children, 30 play chess, 26 play carrom and 10 play both. How many play only chess?
  11. 11.In a group of 20 children, 16 like mangoes, 6 like bananas and 3 like both. How many like at least one of the two?
  12. 12.In a group of 30 children, 17 play chess, 18 play carrom and 9 play both. How many play at least one of the two?
  13. 13.In a group of 31 children, 11 play chess, 16 play carrom and 6 play both. How many play exactly one of the two?
  14. 14.In a group of 43 children, 23 play chess, 22 play carrom and 6 play both. How many play only chess?
  15. 15.In a group of 39 children, 23 enjoy drawing, 14 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  16. 16.In a group of 41 children, 25 enjoy drawing, 24 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 26 children, 12 play cricket, 16 play football and 4 play both. How many play only football?
  18. 18.In a group of 44 children, 18 play cricket, 16 play football and 5 play both. How many play neither of the two?
  19. 19.In a group of 45 children, 26 like mangoes, 24 like bananas and 12 like both. How many like at least one of the two?
  20. 20.In a group of 38 children, 16 play chess, 30 play carrom and 11 play both. How many play at least one of the two?
  21. 21.In a group of 42 children, 20 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing only Hindi songs?
  22. 22.In a group of 51 children, 24 enjoy drawing, 26 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  23. 23.In a group of 28 grown-ups, 20 drink tea, 13 drink coffee and 8 drink both. How many drink only coffee?
  24. 24.In a group of 47 children, 26 play chess, 32 play carrom and 12 play both. How many play at least one of the two?
  25. 25.In a group of 45 children, 17 enjoy drawing, 25 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 40 children, 18 enjoy drawing, 15 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 47 children, 26 sing Hindi songs, 30 sing English songs and 10 sing both. How many sing at least one of the two?
  28. 28.In a group of 36 children, 15 enjoy drawing, 25 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 38 children, 19 like mangoes, 10 like bananas and 5 like both. How many like at least one of the two?
  30. 30.In a group of 41 children, 27 sing Hindi songs, 12 sing English songs and 9 sing both. How many sing only Hindi songs?
  31. 31.In a group of 28 children, 11 like mangoes, 14 like bananas and 7 like both. How many like at least one of the two?
  32. 32.In a group of 53 grown-ups, 31 drink tea, 30 drink coffee and 11 drink both. How many drink only tea?
  33. 33.In a group of 48 children, 28 play chess, 30 play carrom and 12 play both. How many play only carrom?
  34. 34.In a group of 32 grown-ups, 18 drink tea, 25 drink coffee and 12 drink both. How many drink only tea?
  35. 35.In a group of 28 children, 19 play chess, 10 play carrom and 7 play both. How many play exactly one of the two?
  36. 36.In a group of 32 children, 11 like mangoes, 25 like bananas and 8 like both. How many like only mangoes?
  37. 37.In a group of 26 children, 13 sing Hindi songs, 8 sing English songs and 4 sing both. How many sing exactly one of the two?
  38. 38.In a group of 45 children, 27 sing Hindi songs, 23 sing English songs and 10 sing both. How many sing at least one of the two?
  39. 39.In a group of 42 children, 31 sing Hindi songs, 18 sing English songs and 11 sing both. How many sing only English songs?
  40. 40.In a group of 21 children, 8 enjoy drawing, 10 enjoy dancing and 2 enjoy both. How many enjoy only drawing?

Answer key

  1. 18
  2. 4
  3. 12
  4. 16
  5. 7
  6. 11
  7. 10
  8. 9
  9. 14
  10. 20
  11. 19
  12. 26
  13. 15
  14. 17
  15. 31
  16. 12
  17. 12
  18. 15
  19. 38
  20. 35
  21. 9
  22. 42
  23. 5
  24. 46
  25. 12
  26. 8
  27. 46
  28. 4
  29. 24
  30. 18
  31. 18
  32. 20
  33. 18
  34. 6
  35. 15
  36. 3
  37. 13
  38. 40
  39. 7
  40. 6

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