Venn Diagrams Quiz: Reasoning Practice

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. Which diagram best represents Animals, Dogs and Cats?

   • Two separate circles inside a bigger circle
   • Three separate circles
   • Three concentric circles
   • Two overlapping circles inside a bigger circle

   Answer: Two separate circles inside a bigger circle. Dogs and cats are both animals, but no dog is a cat, so two separate circles sit inside the big Animals circle.

2. Which diagram best represents Mothers, Women and Doctors?

   • Three concentric circles
   • Women inside Mothers, with Doctors separate
   • Mothers inside Women, with Doctors overlapping both
   • Three separate circles

   Answer: Mothers inside Women, with Doctors overlapping both. Every mother is a woman, so Mothers sits inside Women. Some doctors are mothers, some are women who are not mothers and some are men, so Doctors overlaps both.

3. Which diagram best represents Delhi, India and Asia?

   • Two separate circles inside a bigger circle
   • Three concentric circles
   • Three intersecting circles
   • One circle inside another, with a third separate

   Answer: Three concentric circles. Delhi is in India and India is in Asia: each lies wholly inside the next, giving concentric circles.

4. In a group of 60 students, 35 play cricket, 30 play football and 10 play both. How many play neither?

   • 10
   • 15
   • 0
   • 5

   Answer: 5. Students playing at least one = 35 + 30 − 10 = 55. So 60 − 55 = 5 play neither.

5. In a class of 50, 28 like tea and 30 like coffee. Every student likes at least one. How many like both?

   • 8
   • 12
   • 6
   • 10

   Answer: 8. Both = 28 + 30 − 50 = 8. The overlap is counted twice when the two groups are added.

6. Of 100 people, 50 read paper A, 40 read B and 30 read C; 15 read A and B, 10 read B and C, 12 read A and C, and 5 read all three. How many read none?

   • 15
   • 10
   • 12
   • 8

   Answer: 12. At least one = 50 + 40 + 30 − 15 − 10 − 12 + 5 = 88. None = 100 − 88 = 12.

7. Of 80 people, 45 speak Hindi, 50 speak English and 5 speak neither. How many speak only English?

   • 25
   • 30
   • 20
   • 35

   Answer: 30. At least one language = 75. Both = 45 + 50 − 75 = 20. Only English = 50 − 20 = 30.

8. Which diagram best represents Tigers, Carnivores and Herbivores?

   • Three separate circles
   • Three concentric circles
   • Two overlapping circles with a third inside their overlap
   • One circle inside a second, with a third circle separate from both

   Answer: One circle inside a second, with a third circle separate from both. Tigers are carnivores, so Tigers sits inside Carnivores. Herbivores share no members with either, so that circle is separate.

9. Which diagram best represents Even numbers, Prime numbers and Natural numbers?

   • Two overlapping circles inside a bigger circle
   • Two separate circles inside a bigger circle
   • Three concentric circles
   • Three separate circles

   Answer: Two overlapping circles inside a bigger circle. Both even and prime numbers are natural numbers, and they overlap in exactly one number, 2. So two overlapping circles sit inside Natural numbers.

10. Circle P = people who play chess, circle Q = people who play carrom. Inside P only: 18; overlap: 7; inside Q only: 12. How many play carrom?

    • 25
    • 19
    • 12
    • 37

    Answer: 19. Everyone in circle Q plays carrom: Q-only (12) plus the overlap (7) = 19.