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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 14 · 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, 10 like mangoes, 22 like bananas and 5 like both. How many like neither of the two?
  2. 2.In a group of 41 children, 27 sing Hindi songs, 21 sing English songs and 8 sing both. How many sing only English songs?
  3. 3.In a group of 38 children, 20 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 23 children, 11 play chess, 15 play carrom and 4 play both. How many play only chess?
  5. 5.In a group of 35 children, 16 play cricket, 16 play football and 12 play both. How many play exactly one of the two?
  6. 6.In a group of 39 children, 23 sing Hindi songs, 18 sing English songs and 3 sing both. How many sing at least one of the two?
  7. 7.In a group of 37 children, 16 like mangoes, 25 like bananas and 6 like both. How many like exactly one of the two?
  8. 8.In a group of 17 children, 6 play cricket, 12 play football and 3 play both. How many play only football?
  9. 9.In a group of 37 children, 11 play cricket, 22 play football and 8 play both. How many play neither of the two?
  10. 10.In a group of 33 children, 18 sing Hindi songs, 23 sing English songs and 12 sing both. How many sing exactly one of the two?
  11. 11.In a group of 33 children, 24 play cricket, 13 play football and 10 play both. How many play neither of the two?
  12. 12.In a group of 29 children, 17 sing Hindi songs, 17 sing English songs and 7 sing both. How many sing neither of the two?
  13. 13.In a group of 43 grown-ups, 17 drink tea, 29 drink coffee and 11 drink both. How many drink at least one of the two?
  14. 14.In a group of 41 children, 16 sing Hindi songs, 26 sing English songs and 9 sing both. How many sing at least one of the two?
  15. 15.In a group of 34 children, 13 play chess, 15 play carrom and 6 play both. How many play at least one of the two?
  16. 16.In a group of 43 children, 25 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  17. 17.In a group of 27 children, 10 like mangoes, 6 like bananas and 3 like both. How many like at least one of the two?
  18. 18.In a group of 41 children, 16 play cricket, 16 play football and 6 play both. How many play neither of the two?
  19. 19.In a group of 38 children, 18 sing Hindi songs, 22 sing English songs and 12 sing both. How many sing neither of the two?
  20. 20.In a group of 55 children, 30 play chess, 29 play carrom and 10 play both. How many play only carrom?
  21. 21.In a group of 23 children, 9 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  22. 22.In a group of 37 children, 22 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 47 children, 19 play chess, 17 play carrom and 3 play both. How many play at least one of the two?
  24. 24.In a group of 31 children, 14 like mangoes, 24 like bananas and 9 like both. How many like exactly one of the two?
  25. 25.In a group of 30 children, 16 play cricket, 14 play football and 6 play both. How many play neither of the two?
  26. 26.In a group of 25 grown-ups, 10 drink tea, 12 drink coffee and 2 drink both. How many drink at least one of the two?
  27. 27.In a group of 44 children, 28 enjoy drawing, 21 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  28. 28.In a group of 51 children, 29 play chess, 23 play carrom and 11 play both. How many play at least one of the two?
  29. 29.In a group of 36 children, 15 sing Hindi songs, 23 sing English songs and 7 sing both. How many sing only English songs?
  30. 30.In a group of 39 grown-ups, 19 drink tea, 22 drink coffee and 9 drink both. How many drink only tea?
  31. 31.In a group of 34 children, 15 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 32 children, 24 sing Hindi songs, 8 sing English songs and 5 sing both. How many sing exactly one of the two?
  33. 33.In a group of 29 children, 19 play chess, 18 play carrom and 11 play both. How many play only chess?
  34. 34.In a group of 35 children, 18 play cricket, 15 play football and 4 play both. How many play only cricket?
  35. 35.In a group of 37 children, 25 play cricket, 12 play football and 5 play both. How many play neither of the two?
  36. 36.In a group of 42 children, 17 sing Hindi songs, 23 sing English songs and 6 sing both. How many sing at least one of the two?
  37. 37.In a group of 33 children, 14 like mangoes, 12 like bananas and 4 like both. How many like only mangoes?
  38. 38.In a group of 20 children, 14 play chess, 13 play carrom and 8 play both. How many play only chess?
  39. 39.In a group of 35 children, 17 sing Hindi songs, 16 sing English songs and 4 sing both. How many sing exactly one of the two?
  40. 40.In a group of 58 children, 28 play chess, 32 play carrom and 12 play both. How many play only carrom?

Answer key

  1. 14
  2. 13
  3. 25
  4. 7
  5. 8
  6. 38
  7. 29
  8. 9
  9. 12
  10. 17
  11. 6
  12. 2
  13. 35
  14. 33
  15. 22
  16. 14
  17. 13
  18. 15
  19. 10
  20. 19
  21. 3
  22. 24
  23. 33
  24. 20
  25. 6
  26. 20
  27. 4
  28. 41
  29. 16
  30. 10
  31. 8
  32. 22
  33. 8
  34. 14
  35. 5
  36. 34
  37. 10
  38. 6
  39. 25
  40. 20

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