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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 680 · 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, 22 sing Hindi songs, 12 sing English songs and 4 sing both. How many sing only English songs?
  2. 2.In a group of 51 children, 19 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  3. 3.In a group of 37 children, 18 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing at least one of the two?
  4. 4.In a group of 34 children, 9 play chess, 21 play carrom and 2 play both. How many play only chess?
  5. 5.In a group of 38 grown-ups, 15 drink tea, 25 drink coffee and 12 drink both. How many drink exactly one of the two?
  6. 6.In a group of 43 children, 14 play chess, 21 play carrom and 3 play both. How many play at least one of the two?
  7. 7.In a group of 52 children, 18 like mangoes, 31 like bananas and 11 like both. How many like exactly one of the two?
  8. 8.In a group of 31 children, 19 play chess, 17 play carrom and 7 play both. How many play exactly one of the two?
  9. 9.In a group of 38 children, 14 play chess, 21 play carrom and 4 play both. How many play at least one of the two?
  10. 10.In a group of 37 children, 16 play chess, 20 play carrom and 6 play both. How many play only chess?
  11. 11.In a group of 17 grown-ups, 9 drink tea, 8 drink coffee and 4 drink both. How many drink only tea?
  12. 12.In a group of 30 children, 16 play chess, 23 play carrom and 11 play both. How many play only chess?
  13. 13.In a group of 45 children, 18 play cricket, 22 play football and 6 play both. How many play exactly one of the two?
  14. 14.In a group of 55 grown-ups, 23 drink tea, 23 drink coffee and 4 drink both. How many drink exactly one of the two?
  15. 15.In a group of 25 children, 13 like mangoes, 17 like bananas and 10 like both. How many like at least one of the two?
  16. 16.In a group of 27 children, 18 play cricket, 15 play football and 12 play both. How many play at least one of the two?
  17. 17.In a group of 46 children, 20 sing Hindi songs, 16 sing English songs and 2 sing both. How many sing neither of the two?
  18. 18.In a group of 43 children, 21 like mangoes, 18 like bananas and 7 like both. How many like at least one of the two?
  19. 19.In a group of 42 children, 30 sing Hindi songs, 20 sing English songs and 11 sing both. How many sing at least one of the two?
  20. 20.In a group of 32 children, 14 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  21. 21.In a group of 27 children, 9 play chess, 9 play carrom and 3 play both. How many play only chess?
  22. 22.In a group of 35 children, 18 like mangoes, 6 like bananas and 3 like both. How many like only mangoes?
  23. 23.In a group of 41 children, 25 sing Hindi songs, 23 sing English songs and 10 sing both. How many sing exactly one of the two?
  24. 24.In a group of 39 children, 16 enjoy drawing, 14 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  25. 25.In a group of 26 children, 17 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing neither of the two?
  26. 26.In a group of 46 children, 16 like mangoes, 25 like bananas and 10 like both. How many like neither of the two?
  27. 27.In a group of 25 children, 14 sing Hindi songs, 9 sing English songs and 4 sing both. How many sing only English songs?
  28. 28.In a group of 33 grown-ups, 9 drink tea, 18 drink coffee and 3 drink both. How many drink only tea?
  29. 29.In a group of 46 children, 19 enjoy drawing, 21 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  30. 30.In a group of 40 children, 20 like mangoes, 26 like bananas and 8 like both. How many like only bananas?
  31. 31.In a group of 45 children, 10 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing only Hindi songs?
  32. 32.In a group of 44 grown-ups, 21 drink tea, 17 drink coffee and 4 drink both. How many drink at least one of the two?
  33. 33.In a group of 43 children, 26 enjoy drawing, 17 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 45 grown-ups, 18 drink tea, 20 drink coffee and 6 drink both. How many drink exactly one of the two?
  35. 35.In a group of 38 children, 15 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 43 children, 20 play cricket, 21 play football and 7 play both. How many play neither of the two?
  37. 37.In a group of 30 children, 7 play cricket, 19 play football and 4 play both. How many play at least one of the two?
  38. 38.In a group of 39 children, 14 play cricket, 25 play football and 9 play both. How many play neither of the two?
  39. 39.In a group of 30 children, 6 play cricket, 19 play football and 2 play both. How many play at least one of the two?
  40. 40.In a group of 27 children, 13 play chess, 18 play carrom and 7 play both. How many play at least one of the two?

Answer key

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

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