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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 553 · 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 25 grown-ups, 17 drink tea, 17 drink coffee and 11 drink both. How many drink exactly one of the two?
  2. 2.In a group of 45 children, 14 enjoy drawing, 23 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  3. 3.In a group of 30 grown-ups, 8 drink tea, 14 drink coffee and 5 drink both. How many drink only tea?
  4. 4.In a group of 37 children, 19 play cricket, 11 play football and 4 play both. How many play only cricket?
  5. 5.In a group of 31 children, 17 play cricket, 13 play football and 5 play both. How many play at least one of the two?
  6. 6.In a group of 40 children, 18 enjoy drawing, 20 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 39 children, 17 like mangoes, 22 like bananas and 10 like both. How many like at least one of the two?
  8. 8.In a group of 32 children, 11 like mangoes, 23 like bananas and 7 like both. How many like only mangoes?
  9. 9.In a group of 51 children, 30 play cricket, 22 play football and 11 play both. How many play neither of the two?
  10. 10.In a group of 21 grown-ups, 14 drink tea, 9 drink coffee and 5 drink both. How many drink only tea?
  11. 11.In a group of 42 children, 20 like mangoes, 15 like bananas and 3 like both. How many like exactly one of the two?
  12. 12.In a group of 43 children, 22 play cricket, 20 play football and 3 play both. How many play only cricket?
  13. 13.In a group of 48 children, 13 like mangoes, 23 like bananas and 3 like both. How many like neither of the two?
  14. 14.In a group of 32 children, 12 play cricket, 12 play football and 4 play both. How many play exactly one of the two?
  15. 15.In a group of 19 children, 11 enjoy drawing, 11 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 51 children, 20 enjoy drawing, 20 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  17. 17.In a group of 26 children, 14 play cricket, 15 play football and 9 play both. How many play only cricket?
  18. 18.In a group of 37 children, 19 play chess, 9 play carrom and 2 play both. How many play exactly one of the two?
  19. 19.In a group of 44 children, 21 play chess, 23 play carrom and 9 play both. How many play neither of the two?
  20. 20.In a group of 30 children, 22 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 39 children, 14 play cricket, 20 play football and 9 play both. How many play only football?
  22. 22.In a group of 35 children, 20 play cricket, 17 play football and 9 play both. How many play at least one of the two?
  23. 23.In a group of 35 children, 24 play cricket, 15 play football and 7 play both. How many play only cricket?
  24. 24.In a group of 29 children, 19 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  25. 25.In a group of 34 children, 14 play chess, 16 play carrom and 10 play both. How many play only carrom?
  26. 26.In a group of 30 children, 14 play chess, 8 play carrom and 4 play both. How many play only carrom?
  27. 27.In a group of 26 children, 8 play chess, 16 play carrom and 5 play both. How many play only carrom?
  28. 28.In a group of 49 children, 25 play chess, 19 play carrom and 10 play both. How many play only chess?
  29. 29.In a group of 27 children, 19 sing Hindi songs, 12 sing English songs and 7 sing both. How many sing only English songs?
  30. 30.In a group of 24 children, 14 play cricket, 8 play football and 3 play both. How many play neither of the two?
  31. 31.In a group of 49 children, 16 play cricket, 27 play football and 8 play both. How many play only cricket?
  32. 32.In a group of 31 children, 14 play cricket, 18 play football and 10 play both. How many play at least one of the two?
  33. 33.In a group of 37 children, 14 play cricket, 21 play football and 3 play both. How many play only cricket?
  34. 34.In a group of 41 children, 21 play chess, 15 play carrom and 7 play both. How many play only carrom?
  35. 35.In a group of 48 children, 19 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 30 children, 13 sing Hindi songs, 24 sing English songs and 9 sing both. How many sing only English songs?
  37. 37.In a group of 39 grown-ups, 16 drink tea, 16 drink coffee and 2 drink both. How many drink neither of the two?
  38. 38.In a group of 37 grown-ups, 9 drink tea, 21 drink coffee and 3 drink both. How many drink only tea?
  39. 39.In a group of 62 children, 29 enjoy drawing, 30 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  40. 40.In a group of 39 children, 12 enjoy drawing, 24 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?

Answer key

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

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