SSC Venn Diagram Questions with Answers and Tricks

Venn Diagram questions are a standard part of the SSC reasoning section. They come in two types: choosing the diagram that shows the relationship between given words, and solving counting problems based on overlapping sets. One or two questions appear in most shifts of CGL, CHSL, MTS and GD. This practice paper gives you 30 Venn diagram questions with answers and explanations, using text descriptions of the diagrams.

Practice Paper at a Glance

What Is a Venn Diagram? Basic Concept in Simple Words

A Venn diagram uses circles to show how groups of things are related. Each circle stands for one group (set), and the overlap shows what the groups have in common.

• One circle inside another: every member of the smaller group belongs to the bigger group (for example, Dogs inside Animals).
• Two separate circles: the groups have nothing in common (for example, Dogs and Cats).
• Two overlapping circles: some members belong to both groups (for example, Doctors and Women).
• Two separate circles inside a larger circle: both are parts of the larger group (for example, Boys, Girls and Students).

Rules and Shortcut Tricks for SSC Venn Diagram Questions

• Find the relationship between each pair of words: is one a part of the other, do they share some members, or are they completely different?
• Concentric circles show a chain of parts: Delhi inside India inside Asia.
• Two groups of the same kind (lion and tiger) are shown as separate circles inside a common group (animals).
• Two groups that can overlap (doctors and women) are drawn as intersecting circles.
• Union formula for two sets: n(A or B) = n(A) + n(B) - n(A and B).
• Union formula for three sets: n(A or B or C) = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(A and C) + n(A and B and C).
• Only A = n(A) - n(A and B) for two sets. For three sets, only A = n(A) - n(A and B) - n(A and C) + n(A and B and C).
• Neither = Total - n(A or B).
• Exactly two in a three-set problem = sum of pairwise overlaps - 3 x n(all three).

Set 1: Relationship Between Given Words (Which Diagram Fits?) (Q1–Q10)

Q1. Which Venn diagram best represents Dogs and Animals?
Answer: One circle (Dogs) completely inside the other circle (Animals)
Solution: Every dog is an animal, so the dogs circle lies inside the animals circle.

Q2. Which Venn diagram best represents Lion, Tiger and Animals?
Answer: Two separate circles (Lion and Tiger) inside a bigger circle (Animals)
Trick: Lions and tigers are different animals, but both are animals.

Q3. Which Venn diagram best represents Doctors and Women?
Answer: Two intersecting circles
Solution: Some doctors are women and some women are doctors, but neither group is wholly inside the other.

Q4. Which Venn diagram best represents Pen, Pencil and Stationery?
Answer: Two separate circles (Pen and Pencil) inside a bigger circle (Stationery)
Solution: Pens and pencils are different items, and both are stationery.

Q5. Which Venn diagram best represents Triangle, Square and Polygon?
Answer: Two separate circles (Triangle and Square) inside a bigger circle (Polygon)
Solution: A triangle and a square are different polygons.

Q6. Which Venn diagram best represents Boys, Girls and Students?
Answer: Two separate circles (Boys and Girls) inside a bigger circle (Students)
Solution: Boys and girls are different groups, and both are students.

Q7. Which Venn diagram best represents Rose, Flower and Plant?
Answer: Three concentric circles: Rose inside Flower inside Plant
Trick: A rose is a flower and a flower is a plant.

Q8. Which Venn diagram best represents Apple, Fruit and Vegetable?
Answer: A small circle (Apple) inside a circle (Fruit), and a separate circle (Vegetable)
Solution: An apple is a fruit, and fruits and vegetables are different groups.

Q9. Which Venn diagram best represents Teachers, Males and Females?
Answer: Two separate circles (Males and Females), each intersected by a circle (Teachers)
Trick: Teachers can be male or female, but no person is both male and female.

Q10. Which Venn diagram best represents Delhi, India and Asia?
Answer: Three concentric circles: Delhi inside India inside Asia
Solution: Delhi is in India and India is in Asia.

Set 2: Two-Set Counting Questions (Q11–Q20)

Q11. In a class of 40 students, 25 like tea and 20 like coffee. If 5 like neither, how many like both?
Answer: 10
Trick: At least one = 40 - 5 = 35. Both = 25 + 20 - 35 = 10.

Q12. Of 100 people, 60 read Hindi and 50 read English. If each person reads at least one of them, how many read both?
Answer: 10
Solution: Both = 60 + 50 - 100 = 10.

Q13. In a group, 70 play cricket, 50 play football and 20 play both. How many people are in the group (assuming everyone plays at least one)?
Answer: 100
Solution: Total = 70 + 50 - 20 = 100.

Q14. Out of 200 students, 120 study maths, 90 study science and 30 study both. How many study only maths?
Answer: 90
Solution: Only maths = 120 - 30 = 90.

Q15. In the same group, how many students study only science?
Answer: 60
Solution: Only science = 90 - 30 = 60.

Q16. In the same group of 200 students, how many students study neither maths nor science?
Answer: 20
Solution: At least one = 120 + 90 - 30 = 180. Neither = 200 - 180 = 20.

Q17. In a village of 300 families, 150 own a TV, 100 own a radio and 50 own both. How many families own neither?
Answer: 100
Solution: At least one = 150 + 100 - 50 = 200. Neither = 300 - 200 = 100.

Q18. Of 80 students, 45 like cricket and 40 like football. If 10 like neither, how many like both?
Answer: 15
Solution: At least one = 70. Both = 45 + 40 - 70 = 15.

Q19. In a survey, 60% like tea, 50% like coffee and 20% like neither. What percentage like both?
Answer: 30%
Solution: At least one = 80%. Both = 60 + 50 - 80 = 30%.

Q20. Out of 50 students, 30 passed in maths, 28 passed in English and 10 failed in both. How many passed in both?
Answer: 18
Solution: At least one = 40. Both = 30 + 28 - 40 = 18.

Set 3: Three-Set Counting and Mixed Questions (Q21–Q30)

Q21. In a group of 100 students, 50 study A, 40 study B and 30 study C. 15 study A and B, 10 study B and C, 8 study A and C and 5 study all three. How many study at least one subject?
Answer: 92
Trick: Total = 50 + 40 + 30 - 15 - 10 - 8 + 5 = 92.

Q22. In the same group, how many students study none of the subjects?
Answer: 8
Solution: 100 - 92 = 8.

Q23. In the same group, how many study only A?
Answer: 32
Solution: Only A = 50 - 15 - 8 + 5 = 32.

Q24. In the same group, how many study only B?
Answer: 20
Solution: Only B = 40 - 15 - 10 + 5 = 20.

Q25. In the same group, how many study only C?
Answer: 17
Solution: Only C = 30 - 10 - 8 + 5 = 17.

Q26. In the same group, how many study exactly two subjects?
Answer: 18
Trick: Exactly two = (15 + 10 + 8) - 3 x 5 = 33 - 15 = 18.

Q27. Which Venn diagram best represents Brothers, Sisters and Siblings?
Answer: Two separate circles (Brothers and Sisters) inside a bigger circle (Siblings)
Solution: Brothers and sisters are different groups, and both are siblings.

Q28. Which Venn diagram best represents Politicians, Doctors and Writers?
Answer: Three intersecting circles
Solution: A person can be a politician, a doctor and a writer at the same time, so all the circles overlap.

Q29. Which Venn diagram best represents Square, Rectangle and Quadrilateral?
Answer: Three concentric circles: Square inside Rectangle inside Quadrilateral
Solution: A square is a rectangle and a rectangle is a quadrilateral.

Q30. Which Venn diagram best represents Water, Liquid and Solid?
Answer: A small circle (Water) inside a circle (Liquid), and a separate circle (Solid)
Solution: Water is a liquid, and liquids and solids are different.

Common Mistakes in Venn Diagram

• Using two intersecting circles for groups that are completely different.
• Putting a smaller part outside the bigger group.
• Forgetting to subtract the overlap in the union formula.
• Counting people twice in the overlapping region.
• Mixing "at least one" with "exactly one".
• Not checking whether the groups can overlap in real life (for example, a person can be a doctor and a writer).

How to Practice These 30 Questions

1. Make a small drawing for every question on rough paper.
2. Find the relationship between each pair of words first.
3. For counting problems, fill the overlap region first and then the remaining parts.
4. Solve Set 1 in 6 minutes, Set 2 in 10 minutes and Set 3 in 12 minutes.
5. Check that the total of all regions equals the total number given.

Related Topics to Study Next

• SSC Syllogism Questions
• Classification (Odd One Out) Questions
• Ranking and Order Questions
• SSC Previous Year Papers

Frequently Asked Questions

What is a Venn diagram in reasoning?

A Venn diagram uses circles to show the relationships between groups. In the SSC exam, you choose the diagram that represents the given words or solve counting problems about overlapping groups.

How many Venn diagram questions come in SSC exams?

Usually one or two Venn diagram questions are asked in the reasoning section of SSC CGL, CHSL and MTS.

How do I solve Venn diagram questions on relationships?

Find how each pair of words is related (part of, partly common or different) and choose the diagram that matches those relationships together.

What is the formula for two overlapping sets?

n(A or B) = n(A) + n(B) - n(A and B). Neither = total - n(A or B).

What is the formula for three overlapping sets?

n(A or B or C) = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(A and C) + n(A and B and C).

How do I find the number of people in only one set?

Subtract the overlaps from the total of that set. For two sets, only A = n(A) - n(A and B).

What does "neither" mean in a Venn diagram question?

Neither means outside all the circles. It is calculated as total - n(at least one).

What is the difference between "at least one" and "exactly one"?

"At least one" includes people in two or three sets. "Exactly one" includes only the people in just one region.

How is a Venn diagram related to syllogism?

Both use circles to show relationships. Syllogism uses statements and conclusions with the same type of diagrams.

How should I prepare Venn diagram questions for SSC exams?

Learn the common diagram patterns, practise the union formulas and solve one set daily with a timer.