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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 491 · 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 40 children, 22 sing Hindi songs, 12 sing English songs and 3 sing both. How many sing at least one of the two?
  2. 2.In a group of 31 children, 26 sing Hindi songs, 11 sing English songs and 8 sing both. How many sing at least one of the two?
  3. 3.In a group of 41 children, 19 play chess, 25 play carrom and 12 play both. How many play exactly one of the two?
  4. 4.In a group of 51 children, 21 enjoy drawing, 25 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  5. 5.In a group of 36 children, 14 play chess, 15 play carrom and 8 play both. How many play at least one of the two?
  6. 6.In a group of 46 children, 27 play chess, 21 play carrom and 7 play both. How many play only carrom?
  7. 7.In a group of 36 children, 25 play cricket, 17 play football and 7 play both. How many play only football?
  8. 8.In a group of 43 children, 12 play chess, 20 play carrom and 4 play both. How many play at least one of the two?
  9. 9.In a group of 50 children, 20 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 35 children, 15 like mangoes, 20 like bananas and 4 like both. How many like at least one of the two?
  11. 11.In a group of 38 children, 15 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing exactly one of the two?
  12. 12.In a group of 25 grown-ups, 8 drink tea, 16 drink coffee and 4 drink both. How many drink at least one of the two?
  13. 13.In a group of 36 children, 21 play cricket, 15 play football and 9 play both. How many play at least one of the two?
  14. 14.In a group of 16 children, 8 sing Hindi songs, 8 sing English songs and 2 sing both. How many sing neither of the two?
  15. 15.In a group of 32 children, 9 play chess, 15 play carrom and 3 play both. How many play only chess?
  16. 16.In a group of 30 children, 14 play chess, 16 play carrom and 10 play both. How many play only chess?
  17. 17.In a group of 42 children, 12 sing Hindi songs, 25 sing English songs and 9 sing both. How many sing at least one of the two?
  18. 18.In a group of 47 grown-ups, 27 drink tea, 19 drink coffee and 8 drink both. How many drink only tea?
  19. 19.In a group of 34 grown-ups, 12 drink tea, 14 drink coffee and 5 drink both. How many drink only tea?
  20. 20.In a group of 35 grown-ups, 24 drink tea, 18 drink coffee and 8 drink both. How many drink only coffee?
  21. 21.In a group of 40 children, 19 play chess, 16 play carrom and 2 play both. How many play only carrom?
  22. 22.In a group of 27 children, 12 sing Hindi songs, 8 sing English songs and 3 sing both. How many sing at least one of the two?
  23. 23.In a group of 40 children, 17 play cricket, 18 play football and 8 play both. How many play only football?
  24. 24.In a group of 39 children, 24 sing Hindi songs, 14 sing English songs and 6 sing both. How many sing at least one of the two?
  25. 25.In a group of 40 children, 17 like mangoes, 21 like bananas and 6 like both. How many like only mangoes?
  26. 26.In a group of 44 children, 21 play cricket, 14 play football and 4 play both. How many play only cricket?
  27. 27.In a group of 40 children, 19 enjoy drawing, 32 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  28. 28.In a group of 41 children, 19 like mangoes, 21 like bananas and 5 like both. How many like only mangoes?
  29. 29.In a group of 60 children, 29 play cricket, 29 play football and 12 play both. How many play exactly one of the two?
  30. 30.In a group of 37 children, 27 play chess, 15 play carrom and 11 play both. How many play only carrom?
  31. 31.In a group of 28 children, 11 enjoy drawing, 15 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  32. 32.In a group of 43 children, 23 play chess, 9 play carrom and 3 play both. How many play exactly one of the two?
  33. 33.In a group of 27 children, 20 play cricket, 11 play football and 8 play both. How many play only cricket?
  34. 34.In a group of 26 children, 15 like mangoes, 20 like bananas and 12 like both. How many like only mangoes?
  35. 35.In a group of 22 children, 14 like mangoes, 9 like bananas and 6 like both. How many like exactly one of the two?
  36. 36.In a group of 31 children, 13 play cricket, 14 play football and 10 play both. How many play at least one of the two?
  37. 37.In a group of 31 children, 10 play chess, 8 play carrom and 2 play both. How many play exactly one of the two?
  38. 38.In a group of 24 children, 7 enjoy drawing, 13 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 16 children, 10 like mangoes, 12 like bananas and 7 like both. How many like at least one of the two?
  40. 40.In a group of 18 children, 6 play cricket, 13 play football and 2 play both. How many play only cricket?

Answer key

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

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