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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 174 · 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 35 children, 29 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 52 children, 21 play chess, 21 play carrom and 5 play both. How many play at least one of the two?
  3. 3.In a group of 45 children, 22 play cricket, 14 play football and 4 play both. How many play only football?
  4. 4.In a group of 46 children, 20 sing Hindi songs, 18 sing English songs and 7 sing both. How many sing neither of the two?
  5. 5.In a group of 57 children, 28 play chess, 30 play carrom and 12 play both. How many play exactly one of the two?
  6. 6.In a group of 31 children, 15 play chess, 17 play carrom and 12 play both. How many play at least one of the two?
  7. 7.In a group of 47 children, 22 like mangoes, 27 like bananas and 7 like both. How many like at least one of the two?
  8. 8.In a group of 56 children, 27 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 45 children, 16 like mangoes, 28 like bananas and 9 like both. How many like neither of the two?
  10. 10.In a group of 32 children, 9 play chess, 18 play carrom and 2 play both. How many play only chess?
  11. 11.In a group of 24 children, 13 play cricket, 11 play football and 4 play both. How many play neither of the two?
  12. 12.In a group of 38 children, 6 play cricket, 22 play football and 3 play both. How many play only football?
  13. 13.In a group of 34 children, 6 like mangoes, 19 like bananas and 2 like both. How many like at least one of the two?
  14. 14.In a group of 31 children, 17 play cricket, 13 play football and 7 play both. How many play only cricket?
  15. 15.In a group of 23 grown-ups, 17 drink tea, 15 drink coffee and 11 drink both. How many drink exactly one of the two?
  16. 16.In a group of 28 children, 7 like mangoes, 20 like bananas and 3 like both. How many like only mangoes?
  17. 17.In a group of 49 children, 21 sing Hindi songs, 22 sing English songs and 6 sing both. How many sing exactly one of the two?
  18. 18.In a group of 46 children, 21 enjoy drawing, 19 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  19. 19.In a group of 48 children, 16 play chess, 28 play carrom and 10 play both. How many play only chess?
  20. 20.In a group of 45 children, 17 sing Hindi songs, 32 sing English songs and 12 sing both. How many sing exactly one of the two?
  21. 21.In a group of 45 children, 19 sing Hindi songs, 18 sing English songs and 5 sing both. How many sing at least one of the two?
  22. 22.In a group of 34 children, 22 enjoy drawing, 20 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  23. 23.In a group of 45 children, 19 play chess, 23 play carrom and 4 play both. How many play only chess?
  24. 24.In a group of 34 grown-ups, 17 drink tea, 22 drink coffee and 12 drink both. How many drink only tea?
  25. 25.In a group of 19 children, 12 play chess, 15 play carrom and 9 play both. How many play only carrom?
  26. 26.In a group of 32 children, 5 play cricket, 18 play football and 2 play both. How many play only football?
  27. 27.In a group of 35 children, 16 like mangoes, 21 like bananas and 6 like both. How many like only mangoes?
  28. 28.In a group of 41 children, 21 play cricket, 26 play football and 11 play both. How many play neither of the two?
  29. 29.In a group of 26 children, 8 play chess, 17 play carrom and 2 play both. How many play only carrom?
  30. 30.In a group of 44 children, 22 sing Hindi songs, 28 sing English songs and 9 sing both. How many sing exactly one of the two?
  31. 31.In a group of 50 children, 30 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing neither of the two?
  32. 32.In a group of 38 children, 24 play cricket, 20 play football and 11 play both. How many play only cricket?
  33. 33.In a group of 40 children, 24 like mangoes, 11 like bananas and 5 like both. How many like neither of the two?
  34. 34.In a group of 55 grown-ups, 22 drink tea, 29 drink coffee and 10 drink both. How many drink only coffee?
  35. 35.In a group of 33 children, 15 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing exactly one of the two?
  36. 36.In a group of 40 children, 11 play cricket, 18 play football and 4 play both. How many play only cricket?
  37. 37.In a group of 36 children, 14 play chess, 29 play carrom and 10 play both. How many play at least one of the two?
  38. 38.In a group of 34 children, 7 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  39. 39.In a group of 26 children, 8 play cricket, 9 play football and 2 play both. How many play exactly one of the two?
  40. 40.In a group of 36 children, 15 sing Hindi songs, 18 sing English songs and 3 sing both. How many sing only English songs?

Answer key

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

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