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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 462 · 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 46 children, 28 play chess, 15 play carrom and 10 play both. How many play at least one of the two?
  2. 2.In a group of 31 children, 18 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 35 children, 14 play chess, 20 play carrom and 6 play both. How many play only carrom?
  4. 4.In a group of 40 children, 19 like mangoes, 19 like bananas and 3 like both. How many like only mangoes?
  5. 5.In a group of 33 children, 17 sing Hindi songs, 8 sing English songs and 2 sing both. How many sing only Hindi songs?
  6. 6.In a group of 31 children, 21 play cricket, 10 play football and 5 play both. How many play at least one of the two?
  7. 7.In a group of 41 children, 17 enjoy drawing, 26 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  8. 8.In a group of 37 children, 31 play cricket, 15 play football and 11 play both. How many play exactly one of the two?
  9. 9.In a group of 41 children, 24 enjoy drawing, 17 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  10. 10.In a group of 22 children, 8 like mangoes, 14 like bananas and 2 like both. How many like at least one of the two?
  11. 11.In a group of 37 children, 23 play cricket, 19 play football and 6 play both. How many play only football?
  12. 12.In a group of 33 children, 15 enjoy drawing, 17 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 33 children, 11 play cricket, 17 play football and 6 play both. How many play only football?
  14. 14.In a group of 33 children, 20 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  15. 15.In a group of 35 children, 15 enjoy drawing, 12 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  16. 16.In a group of 32 children, 11 play chess, 22 play carrom and 6 play both. How many play neither of the two?
  17. 17.In a group of 35 children, 13 like mangoes, 12 like bananas and 2 like both. How many like at least one of the two?
  18. 18.In a group of 36 children, 17 play cricket, 19 play football and 2 play both. How many play only cricket?
  19. 19.In a group of 33 children, 22 play chess, 19 play carrom and 11 play both. How many play only carrom?
  20. 20.In a group of 37 children, 21 sing Hindi songs, 12 sing English songs and 2 sing both. How many sing neither of the two?
  21. 21.In a group of 46 children, 30 play chess, 15 play carrom and 10 play both. How many play at least one of the two?
  22. 22.In a group of 23 children, 13 like mangoes, 9 like bananas and 4 like both. How many like at least one of the two?
  23. 23.In a group of 34 children, 17 enjoy drawing, 17 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 29 children, 7 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  25. 25.In a group of 42 children, 23 enjoy drawing, 26 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 24 children, 16 play chess, 8 play carrom and 4 play both. How many play at least one of the two?
  27. 27.In a group of 20 children, 6 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  28. 28.In a group of 41 children, 21 like mangoes, 24 like bananas and 12 like both. How many like only mangoes?
  29. 29.In a group of 35 children, 24 play cricket, 15 play football and 11 play both. How many play at least one of the two?
  30. 30.In a group of 28 children, 13 play cricket, 16 play football and 2 play both. How many play only cricket?
  31. 31.In a group of 25 children, 13 play chess, 8 play carrom and 2 play both. How many play only chess?
  32. 32.In a group of 39 children, 15 play chess, 27 play carrom and 10 play both. How many play at least one of the two?
  33. 33.In a group of 45 children, 29 play cricket, 14 play football and 10 play both. How many play only football?
  34. 34.In a group of 37 children, 20 play cricket, 11 play football and 4 play both. How many play only cricket?
  35. 35.In a group of 33 children, 26 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing only English songs?
  36. 36.In a group of 33 children, 13 like mangoes, 26 like bananas and 10 like both. How many like at least one of the two?
  37. 37.In a group of 47 children, 25 enjoy drawing, 22 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 37 children, 16 enjoy drawing, 22 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 19 children, 8 like mangoes, 7 like bananas and 2 like both. How many like neither of the two?
  40. 40.In a group of 46 children, 24 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?

Answer key

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

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