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Venn Diagrams Questions for SSC CGL

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Why this topic matters · 6 min read
Venn Diagrams appear in almost every SSC CGL Reasoning section, typically 2-4 questions per paper. The exam tests two things: (1) given a set of entities, pick the diagram that best represents their relationship, and (2) given a diagram with numbers, find the count of elements in specific regions. Both question types are fast scoring if you know the five standard relationship patterns cold.

Five Core Relationship Patterns

Every Venn Diagram question in SSC CGL is built on one of five relationships between two or three groups. Recognise the real-world logic first, then match it to the shape. The five patterns are: (1) Completely Separate — no overlap at all. (2) Completely Inside — one group is a subset of the other. (3) Partial Overlap — the groups share some but not all members. (4) One inside another which is inside a third — three nested circles. (5) Two separate groups both inside a third — two circles side by side inside a bigger circle.

  • Completely Separate: Dog, Fish, Bird — no animal belongs to more than one group.
  • Completely Inside (Subset): Roses, Flowers — all roses are flowers, so small circle sits inside big circle.
  • Partial Overlap: Teachers, Women, Mothers — a woman can be a teacher and a mother, so three circles each overlapping the others partially.
  • Three Nested: Living beings, Animals, Dogs — dogs inside animals, animals inside living beings.
  • Two inside One: Cricket Players, Football Players, Indians — both sets are subsets of Indians but not of each other, so two separate circles inside one big circle.
  • Always ask: Can A be B? Can B be A? Can neither be the other? That determines the shape.

Reading Numbers in a Diagram (Region-Based Questions)

This type gives you a diagram with numbers written in each region and asks questions like: how many students study only Maths? How many study both Maths and Science but not English? You must identify exactly which region the question is pointing to and read or calculate that value. The trick is to understand that a number written inside a region that belongs to only one circle means ONLY that subject. A number in the intersection of two circles but outside the third means BOTH those subjects and NOT the third.

  • Only A = number in A's region that does not overlap with B or C.
  • A and B but not C = number in the region where A and B overlap but C does not reach.
  • All three = number at the dead center where all three circles meet.
  • At least two = (A and B only) + (B and C only) + (A and C only) + (all three).
  • Total in A = Only A + A and B only + A and C only + all three.
  • Draw a quick rough diagram and label each region before answering — takes 20 seconds and saves errors.
Key formulas
Union of Two Sets
n(A union B) = n(A) + n(B) - n(A intersection B)
When: Use when total count of combined group is asked and overlap is given.
Union of Three Sets
n(A union B union C) = n(A) + n(B) + n(C) - n(A inter B) - n(B inter C) - n(A inter C) + n(A inter B inter C)
When: Use when total count across three groups is asked. Memorise this formula — it appears directly.
Only A (in three-set diagram)
Only A = n(A) - n(A inter B) - n(A inter C) + n(A inter B inter C)
When: Use when you need count of A members who belong to no other group.
Worked examples

In a class of 60 students: 30 play Cricket, 25 play Football, 10 play both. How many play neither? Step 1: n(C union F) = 30 + 25 - 10 = 45. Step 2: Neither = 60 - 45 = 15. Answer: 15.

A diagram shows three circles P, Q, R. Regions: Only P = 5, Only Q = 8, Only R = 6, P and Q only = 3, Q and R only = 4, P and R only = 2, All three = 7. How many are in Q? n(Q) = Only Q + PQ only + QR only + all three = 8 + 3 + 4 + 7 = 22.

Choosing the Right Diagram for Given Words

SSC CGL gives you three words and four diagram options (A, B, C, D). You must select the diagram that correctly shows their relationship. Speed trick: test each word-pair separately. Ask — is the first word a type of the second? Is there any possible overlap? Are they completely unrelated? This two-step check gets you to the answer in under 30 seconds.

  • Mammals, Whales, Animals — Whales inside Mammals inside Animals. Three nested circles.
  • Doctors, Fathers, Pilots — all three can partially overlap. Three mutually overlapping circles.
  • Squares, Rectangles, Quadrilaterals — Squares inside Rectangles inside Quadrilaterals. Nested.
  • Boys, Girls, Students — Boys and Girls are separate but both are inside Students.
  • Always eliminate impossible options first — if two words can never overlap, any diagram showing overlap is wrong.
  • Watch out for trick combinations like Nurse, Mother, Teacher — these always partially overlap with each other.
⚠ Common mistakes to avoid
  • Confusing the intersection number with the total of a circle. If 10 is written in the overlap of A and B, it means 10 belong to BOTH, not that A or B has only 10 members.
  • In the three-set union formula, forgetting to ADD back the all-three intersection after subtracting pairwise intersections. This single error costs the mark every time.
  • Treating partial-overlap relationships as subset relationships. Doctors and Women can overlap but neither is fully inside the other — do not draw a nested diagram.
  • For word-based diagram selection, not checking ALL three pairs. Checking only one or two pairs and then guessing leads to wrong diagram choice.
  • In region-count questions, when a question says 'only Maths', aspirants often pick the total Maths circle value instead of the region that excludes all overlaps.
🧠 Memory aids
  • SPIN mnemonic for the five diagram types: Separate, Partial, Inside (subset), Nested-three, Side-by-side-in-one. Run through SPIN when you see the question.
  • For three-set formula remember: Add singles, Subtract pairs, Add triple back. Think: Plus Minus Plus at each stage.
  • Dead Center = All three. Ring only = That subject alone. Think of a target board — bull's eye is all three, outer ring is just that circle.
  • Word-pair test: Ask two questions — CAN the first be the second? CAN the second be the first? Yes-Yes means overlap or subset. No-No means separate. Asymmetric yes means subset.
🎯 SSC CGL exam tips
  • SSC CGL typically asks 2-3 word-relationship diagram questions and 1-2 number-region questions per paper. Total expected time per question: 30-45 seconds for word type, 60-90 seconds for number type.
  • Recent papers (2023-2024 Tier 1) heavily favour three-word combinations where at least one pair has a partial overlap and one pair has a subset relationship — the mixed pattern is a favourite trap.
  • Number-in-region questions in recent papers provide the diagram with all regions labelled and ask for 'at least two' or 'exactly one' — practise these specific phrasings as they have predictable calculation patterns.
  • For competitive speed: in word-based questions, immediately eliminate any option where two clearly unrelated categories (like Cats and Buses) are shown overlapping. This cuts options to 1-2 instantly.
  • Do not skip Venn Diagram questions. They are among the safest marks in Reasoning if you know the five patterns. Even without formula recall, logic and elimination can get you to the answer.

Sample questions

Q1 · medium · AI-verified
In a Venn diagram, Set A has 20 elements, Set B has 30 elements, and A∩B has 8 elements. What is |A∪B|?
  1. 38
  2. 58
  3. 42
  4. 50
Q2 · medium · AI-verified
In a Venn diagram with sets P and Q, |P| = 25, |Q| = 18, |P∪Q| = 35. What is |P∩Q|?
  1. 12
  2. 7
  3. 10
  4. 8
Q3 · hard · AI-verified
In a survey, 60% of people read newspaper A, 50% read newspaper B, and 20% read both. What percentage reads neither newspaper?
  1. 30%
  2. 20%
  3. 10%
  4. 15%
Q4 · medium · AI-verified
In a survey of 100 people, 60 like tea, 50 like coffee, and 30 like both. How many like only tea?
  1. 60
  2. 30
  3. 40
  4. 20
Q5 · medium · AI-verified
In a town, 200 people were surveyed. 120 read newspaper A, 80 read newspaper B, and 40 read both. How many read neither?
  1. 60
  2. 40
  3. 80
  4. 20
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