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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 521 · 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 42 children, 21 play cricket, 23 play football and 4 play both. How many play only cricket?
  2. 2.In a group of 33 children, 21 enjoy drawing, 12 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  3. 3.In a group of 28 children, 16 like mangoes, 13 like bananas and 8 like both. How many like at least one of the two?
  4. 4.In a group of 26 children, 15 play chess, 13 play carrom and 10 play both. How many play only carrom?
  5. 5.In a group of 47 children, 21 play chess, 30 play carrom and 10 play both. How many play neither of the two?
  6. 6.In a group of 51 children, 25 play cricket, 30 play football and 11 play both. How many play only football?
  7. 7.In a group of 38 children, 15 sing Hindi songs, 27 sing English songs and 9 sing both. How many sing only Hindi songs?
  8. 8.In a group of 28 children, 18 enjoy drawing, 19 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 27 children, 10 sing Hindi songs, 19 sing English songs and 4 sing both. How many sing exactly one of the two?
  10. 10.In a group of 35 children, 10 play chess, 23 play carrom and 3 play both. How many play only carrom?
  11. 11.In a group of 44 children, 15 play chess, 31 play carrom and 12 play both. How many play neither of the two?
  12. 12.In a group of 50 grown-ups, 23 drink tea, 20 drink coffee and 6 drink both. How many drink exactly one of the two?
  13. 13.In a group of 35 children, 24 play cricket, 15 play football and 8 play both. How many play at least one of the two?
  14. 14.In a group of 31 children, 14 like mangoes, 9 like bananas and 4 like both. How many like at least one of the two?
  15. 15.In a group of 22 children, 6 like mangoes, 11 like bananas and 3 like both. How many like neither of the two?
  16. 16.In a group of 36 children, 13 play chess, 20 play carrom and 8 play both. How many play neither of the two?
  17. 17.In a group of 17 grown-ups, 7 drink tea, 13 drink coffee and 4 drink both. How many drink at least one of the two?
  18. 18.In a group of 33 children, 11 play chess, 16 play carrom and 4 play both. How many play only chess?
  19. 19.In a group of 54 children, 24 like mangoes, 27 like bananas and 9 like both. How many like at least one of the two?
  20. 20.In a group of 41 children, 21 play cricket, 21 play football and 6 play both. How many play only football?
  21. 21.In a group of 25 children, 9 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  22. 22.In a group of 48 children, 21 play chess, 30 play carrom and 11 play both. How many play neither of the two?
  23. 23.In a group of 41 children, 22 sing Hindi songs, 24 sing English songs and 9 sing both. How many sing neither of the two?
  24. 24.In a group of 28 children, 16 like mangoes, 13 like bananas and 9 like both. How many like at least one of the two?
  25. 25.In a group of 43 children, 20 sing Hindi songs, 26 sing English songs and 10 sing both. How many sing only English songs?
  26. 26.In a group of 33 children, 5 play cricket, 17 play football and 2 play both. How many play only football?
  27. 27.In a group of 36 children, 24 play chess, 17 play carrom and 7 play both. How many play exactly one of the two?
  28. 28.In a group of 46 children, 22 play cricket, 11 play football and 2 play both. How many play only football?
  29. 29.In a group of 26 children, 20 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing neither of the two?
  30. 30.In a group of 43 children, 18 play cricket, 31 play football and 11 play both. How many play exactly one of the two?
  31. 31.In a group of 49 children, 18 enjoy drawing, 30 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  32. 32.In a group of 39 children, 15 play cricket, 17 play football and 3 play both. How many play only cricket?
  33. 33.In a group of 25 children, 17 play cricket, 9 play football and 3 play both. How many play only football?
  34. 34.In a group of 23 children, 18 play cricket, 9 play football and 6 play both. How many play at least one of the two?
  35. 35.In a group of 24 children, 15 play chess, 7 play carrom and 4 play both. How many play only carrom?
  36. 36.In a group of 21 children, 14 play cricket, 12 play football and 8 play both. How many play only cricket?
  37. 37.In a group of 33 children, 14 sing Hindi songs, 20 sing English songs and 9 sing both. How many sing neither of the two?
  38. 38.In a group of 44 children, 14 sing Hindi songs, 20 sing English songs and 5 sing both. How many sing only English songs?
  39. 39.In a group of 19 children, 12 like mangoes, 10 like bananas and 6 like both. How many like neither of the two?
  40. 40.In a group of 40 children, 19 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?

Answer key

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

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