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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 180 · 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 22 children, 13 like mangoes, 8 like bananas and 2 like both. How many like only mangoes?
  2. 2.In a group of 34 children, 21 enjoy drawing, 6 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 35 children, 11 play chess, 22 play carrom and 4 play both. How many play exactly one of the two?
  4. 4.In a group of 19 children, 9 play cricket, 10 play football and 5 play both. How many play at least one of the two?
  5. 5.In a group of 44 children, 24 play chess, 24 play carrom and 8 play both. How many play neither of the two?
  6. 6.In a group of 33 children, 17 like mangoes, 21 like bananas and 10 like both. How many like exactly one of the two?
  7. 7.In a group of 50 children, 22 like mangoes, 18 like bananas and 5 like both. How many like only bananas?
  8. 8.In a group of 32 children, 11 play chess, 13 play carrom and 5 play both. How many play only chess?
  9. 9.In a group of 36 grown-ups, 20 drink tea, 16 drink coffee and 2 drink both. How many drink only tea?
  10. 10.In a group of 41 children, 20 play cricket, 29 play football and 12 play both. How many play only football?
  11. 11.In a group of 30 children, 14 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  12. 12.In a group of 48 grown-ups, 27 drink tea, 28 drink coffee and 10 drink both. How many drink exactly one of the two?
  13. 13.In a group of 51 children, 22 enjoy drawing, 18 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 43 children, 21 sing Hindi songs, 25 sing English songs and 5 sing both. How many sing only English songs?
  15. 15.In a group of 47 children, 26 like mangoes, 28 like bananas and 12 like both. How many like at least one of the two?
  16. 16.In a group of 47 children, 20 sing Hindi songs, 24 sing English songs and 11 sing both. How many sing only English songs?
  17. 17.In a group of 38 children, 16 play chess, 19 play carrom and 10 play both. How many play exactly one of the two?
  18. 18.In a group of 40 children, 18 like mangoes, 20 like bananas and 5 like both. How many like only bananas?
  19. 19.In a group of 45 children, 28 like mangoes, 20 like bananas and 8 like both. How many like exactly one of the two?
  20. 20.In a group of 37 children, 22 play chess, 20 play carrom and 10 play both. How many play exactly one of the two?
  21. 21.In a group of 25 children, 8 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing neither of the two?
  22. 22.In a group of 34 children, 21 like mangoes, 11 like bananas and 3 like both. How many like exactly one of the two?
  23. 23.In a group of 41 children, 27 play cricket, 22 play football and 11 play both. How many play only cricket?
  24. 24.In a group of 42 children, 28 sing Hindi songs, 20 sing English songs and 9 sing both. How many sing only Hindi songs?
  25. 25.In a group of 23 children, 7 play chess, 12 play carrom and 2 play both. How many play only carrom?
  26. 26.In a group of 49 children, 32 enjoy drawing, 16 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 15 children, 11 sing Hindi songs, 10 sing English songs and 7 sing both. How many sing only Hindi songs?
  28. 28.In a group of 44 children, 25 enjoy drawing, 23 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  29. 29.In a group of 50 children, 31 enjoy drawing, 20 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  30. 30.In a group of 44 children, 25 sing Hindi songs, 20 sing English songs and 6 sing both. How many sing at least one of the two?
  31. 31.In a group of 39 children, 16 play chess, 20 play carrom and 2 play both. How many play neither of the two?
  32. 32.In a group of 30 children, 19 play cricket, 15 play football and 8 play both. How many play only football?
  33. 33.In a group of 35 children, 9 like mangoes, 17 like bananas and 6 like both. How many like only mangoes?
  34. 34.In a group of 28 children, 17 enjoy drawing, 19 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  35. 35.In a group of 40 children, 11 like mangoes, 18 like bananas and 2 like both. How many like exactly one of the two?
  36. 36.In a group of 27 children, 9 sing Hindi songs, 6 sing English songs and 3 sing both. How many sing only Hindi songs?
  37. 37.In a group of 35 children, 12 like mangoes, 20 like bananas and 8 like both. How many like only mangoes?
  38. 38.In a group of 54 children, 32 play cricket, 26 play football and 12 play both. How many play at least one of the two?
  39. 39.In a group of 38 children, 9 play cricket, 22 play football and 6 play both. How many play at least one of the two?
  40. 40.In a group of 44 children, 22 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?

Answer key

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

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