Combines non-verbal comparative deduction and anomaly detection. Questions require extracting the geometrical rule transforming Figure A to B and applying it to Figure C.
Core Skills & Cognitive Modules
Key cognitive competencies and question patterns assessed under Figure Analogy & Classification.
1
Geometric Transform Rules
Extract composite transformation morphisms (rotation + reflection + scaling) connecting analogous pairs and apply them to target figures.
Focus: Morphism operator formulation, multi-stage transformations, and structural mapping
Universal high frequency in SSC CGL, CHSL, MTS & RRB NTPC
2
Side Count & Angle Relations
Analyze changes in polygon edge counts, vertex angles, and internal sector divisions across comparative figure pairs.
Focus: Polygon side arithmetic (n -> n+1, n -> 2n), sector partitioning, and geometric scaling
Universal core topic in SSC, Railways & State PSCs
3
Inversion & Symmetry Mismatches
Identify anomalous figures in classification sets by analyzing lines of symmetry, rotational order, chirality (CW vs CCW), and open vs closed topologies.
Focus: Symmetry group classification, reflectional parity, and chirality detection
Theoretical foundations, question formats, and high-scoring exam techniques.
Conceptual Foundations of Figure Analogy & Classification
Figure Analogy & Classification evaluates non-verbal comparative deduction, relational mapping, and anomaly detection. Candidates must extract the underlying geometric transformation linking an analogous pair or identify the unique outlier violating a universal geometric invariant within a candidate set.
The 5-Stage Comparative Analogy & Classification Protocol
Deconstruct Primitives & Containment: Separate outer containers from inner elements. Count sides, vertices, lines of symmetry, and note shading states.
Formulate Morphism Operator T: Identify what happened from A to B: (a) Rotation/reflection? (b) Side count change (+1/-1)? (c) Container-element swap? (d) Shading flip?
Apply Morphism T to Target C: Execute the identical transformation on Figure C to construct the predicted blueprint of Figure D.
Execute Symmetry & Invariant Check (Classification): For Odd One Out sets: evaluate lines of symmetry, line segment counts, chirality, and open/closed topology across all options.
Eliminate Distractors by Elimination: Reject options failing on side count, orientation, or shading until exactly one mathematically sound figure remains.
Foundational Principles of Figure Analogy & Classification
1. The Formal Morphism MappingAnalogy is an isomorphism between structural relation graphs: A -> B induces an identical functor C -> D.
Key Formula: D = T_{morphism}(C) where T is uniquely defined by B = T(A).
2. The Dihedral Symmetry Group D_nPlanar shapes belong to dihedral symmetry groups possessing n reflection axes and n-fold rotational symmetry.
Key Rule: Invariant symmetry order separates normal members from anomalies.
3. Topological Euler InvariantsProperties invariant under continuous deformations (closure, number of holes/regions, vertex valence).
Key Rule: Closed shapes vs open curves represent distinct topological classes.
4. Chirality & Parity GroupsOrientation of asymmetric curves (left-handed vs right-handed) is preserved under 2D rotation but inverted under reflection.
Key Rule: Chiral curl direction must be uniform across all set members.
High-Frequency Exam Traps & Pitfalls
⚠️ Superficial Shape Similarity Trap
Selecting an option because it 'looks like' Figure C, ignoring that the transformation rule from A to B was violated.
✓ Prevention: Focus on the RULE, not the appearance. Derive Figure D logically from the rule.
⚠️ Partial Rule Execution
Applying the side count rule correctly but forgetting to invert the shading or swap inner/outer elements.
✓ Prevention: Write down a 3-part checklist: (1) Shape/Sides; (2) Orientation; (3) Shading. Check all 3.
⚠️ Confusing 2D Rotation with Reflection in Anomaly Detection
Marking a figure as odd because it is upside down, failing to notice it is simply rotated 180°.
✓ Prevention: Mentally rotate each figure to a standard upright position: if they all become identical, none is an outlier on shape.
⚠️ Ignoring Internal Line Segment Counts
Looking at outer shapes when the true anomaly lies in the number of internal cross-lines (e.g., four figures have 3 lines, one has 4).
✓ Prevention: Count total line segments when geometric shapes appear superficially similar.
Speed Benchmark: Target fast, structured deduction to bank buffer time for complex arrangement and analytical puzzles.
SSC: High RelevanceRailways: High RelevanceBanking: Low RelevanceState PSCs: Medium Relevance
Morphism templates, symmetry checklists, and anomaly detection rules.
Side Count Delta Rule
Count sides: if A has 3 sides and B has 4 sides (Delta = +1), then C (4 sides) must transform to D with 5 sides (pentagon).
Condition: Polygonal analogies.
Watch out: Assuming the outer shape is fixed instead of tracking side count progression.
Container-Element Inversion Rule
If Outer becomes Inner and Inner becomes Outer: the shape inside A becomes the big boundary of B, and the big boundary of A shrinks to sit inside B.
Condition: Nested dual-shape analogies.
Watch out: Forgetting to invert the shading texture during the swap.
Symmetry Axis Classification Checklist
To find the odd figure: Count lines of symmetry for each figure. If 4 figures have at least 1 line of symmetry and 1 figure has ZERO, that asymmetric figure is the OUTLIER.
Condition: Odd One Out classification sets.
Watch out: Guessing based on visual complexity rather than counting lines of symmetry.
Chirality (Curl Direction) Rule
If pinwheel blades or curved hooks in 4 figures bend CLOCKWISE, the one figure bending COUNTER-CLOCKWISE is the outlier.
Condition: Rotational figures with directional hooks or arrows.
Watch out: Rotating the page and confusing clockwise curls with counter-clockwise curls.
Open vs Closed Topology Filter
If 4 figures form completely closed loops (Eulerian boundaries) and 1 figure has an open gap, the open figure is the outlier.
Condition: Geometric line drawings.
Watch out: Missing a tiny gap in a line network.
2D Rotation vs Reflection Verification
Before declaring a transformation as 'reflection', check if it can be achieved by a 180° in-plane rotation. If yes, it is ROTATION, not reflection.
Condition: Inverted figure pairs.
Watch out: Confusing a 180° rotation with a mirror reflection on chiral figures.
Geometrical Analogy & Topological Symmetry Models
Internal/external boundary inversions, polygonal side increments, and rotational/reflectional symmetry classification.
Model 1: Geometrical Transformation Mapping (A : B :: C : D)
Analogy Isomorphism: The exact mathematical transformation connecting Figure A to B must be replicated identically from Figure C to D. Side Count Invariants: Watch for polygon side changes (triangle $\to$ square $\to$ pentagon $\to$ hexagon). Position Swaps: Central elements expanding to become outer containers is a classic non-verbal examination pattern.
Model 2: Symmetry Classification & Odd-One-Out
Symmetry Priority: Always check bilateral reflection axes first before rotational symmetry. Odd-One-Out Test: If four figures possess at least one line of symmetry and one is completely asymmetric, the asymmetric figure is the answer. Open vs Closed Curves: A secondary classification criterion tests whether shapes are enclosed polygons or open linework.
Modeled Problem Walkthroughs: Figure Analogy & Classification
Step-by-step cognitive deduction showing how to isolate governing rules before timed practice.
4 Modeled Walkthroughs
Exemplar Problem Statement
Problem Analogy: Figure A : Figure B :: Figure C : ?
- Figure A is an unshaded Triangle (3 sides).
- Figure B is a shaded Square (4 sides).
- Figure C is an unshaded Pentagon (5 sides).
What is the correct analogous Figure D?
AA shaded Hexagon (6 sides)Correct Answer
BAn unshaded Hexagon (6 sides)
CA shaded Heptagon (7 sides)
DA shaded Pentagon (5 sides)
Step-by-Step Cognitive Deduction
Step 1Step 1: Analyze the transformation from Figure A to Figure B:
Step 2- Side count: Figure A has 3 sides (triangle); Figure B has 4 sides (square). Delta n = +1 side.
Step 3- Shading texture: Figure A is unshaded; Figure B is completely shaded (fill texture inverted).
Step 4Step 2: Formulate the transformation operator T: T(Polygon) = Polygon with (sides + 1), with shading inverted.
Step 5Step 3: Apply operator T to Figure C:
Step 6- Figure C has 5 sides (pentagon) and is unshaded.
Step 7- Side count for D = 5 + 1 = 6 sides (Hexagon).
Step 8- Shading for D = Invert unshaded to SHADED.
Step 9Step 4: Figure D must be a SHADED HEXAGON.
Step 10Step 5: Matches Option A.
Decisive Deduction Factor:The transformation adds +1 side and inverts unshaded to shaded. Applying this to an unshaded pentagon yields a shaded hexagon.
A shaded Hexagon (Option A)
Exam Insight: Decompose analogy transformations into discrete operators (Side Delta and Shading Phase) and apply both to the third figure.
Featured Practice Set (10 Balanced MCQs)
Work through these representative solved questions covering diverse difficulty tiers and cognitive patterns. Select an option to test your deduction with instant feedback and pedagogical explanations.
10 Curated Questions
Question 1easy
Geometric Transform Rules
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: An upright L-shaped bracket composed of a vertical line segment on the left and a shorter horizontal foot extending to the right from the bottom endpoint.
[ Figure B ]: An L-shaped bracket rotated 90° clockwise, consisting of a horizontal line segment on top extending to the right, and a shorter vertical foot extending downward from its right endpoint.
[ Figure C ]: An upright T-shaped figure composed of a horizontal top crossbar and a vertical stem extending downward from the exact midpoint of the crossbar.
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
Question 2easy
Geometric Transform Rules
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: A musical eighth note glyph with a solid notehead on the bottom-left, a vertical stem rising along its right edge, and a curved flag extending to the right (East) from the top of the stem.
[ Figure B ]: A laterally reflected musical eighth note glyph (reflection across a vertical axis) with the solid notehead on the bottom-right, a vertical stem rising along its left edge, and the curved flag extending to the left (West).
[ Figure C ]: A lowercase letter-like figure 'b' consisting of a vertical stem on the left and a circular closed loop attached to the lower-right side of the stem.
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
Question 3easy
Geometric Transform Rules
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: A Greek cross '+' composed of equal-length perpendicular vertical and horizontal bars intersecting at their midpoints.
[ Figure B ]: A saltire cross 'X' (the Greek cross rotated 45° clockwise), composed of two equal-length diagonal bars intersecting at their midpoints.
[ Figure C ]: A vertical double-ended arrow pointing directly North and South.
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
Question 4medium
Geometric Transform Rules
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: A right-angled triangle with its vertical leg on the left, horizontal base at the bottom, and hypotenuse sloping from top-left to bottom-right.
[ Figure B ]: A right-angled triangle resulting from a 90° clockwise rotation followed by a reflection across the horizontal axis: vertical leg at the bottom right, horizontal base on top right, hypotenuse sloping upward and to the right.
[ Figure C ]: A right-angled triangle with its horizontal base at the bottom, vertical leg on the right, and hypotenuse sloping downward and outward from top-right to bottom-left.
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
Question 5medium
Geometric Transform Rules
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: An upright trapezoid with a narrow top edge and wide bottom base, containing an internal arrow pointing North.
[ Figure B ]: An inverted trapezoid with a wide top edge and narrow bottom base (rotated 180°), containing an internal arrow pointing South (reversed direction).
[ Figure C ]: An upright regular pentagon with a pointed apex at the top and horizontal base at the bottom, containing an internal arrow pointing East.
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
Question 6medium
Geometric Transform Rules
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: A solid-lined L-bracket with a vertical spine on the left and a horizontal foot extending East from the bottom endpoint.
[ Figure B ]: A dotted-lined L-bracket (line style changed to dotted) rotated 90° clockwise: a horizontal spine on top extending East, and a vertical foot extending downward from the right endpoint.
[ Figure C ]: A solid-lined T-figure with a vertical stem and a top horizontal crossbar.
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
Question 7medium
Side Count & Angle Relations
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: An equilateral triangle with an interior angle of 60 degrees at each vertex.
[ Figure B ]: A regular pentagon with an interior angle of 108 degrees at each vertex (side count increased by +2, from 3 to 5).
[ Figure C ]: A square with an interior angle of 90 degrees at each vertex.
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
Question 8hard
Geometric Transform Rules
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: A system of three nested concentric shapes: outermost is a square resting flat on its base, middle is a crescent moon facing North, and innermost is a straight arrow pointing East.
[ Figure B ]: The concentric system where outermost square rotates 45° clockwise into a diamond, middle crescent reflects across the horizontal axis to face South, and innermost arrow rotates 90° counter-clockwise to point North.
[ Figure C ]: A system of three nested concentric shapes: outermost is a regular octagon with a horizontal top edge, middle is a semicircle with its curved dome facing North, and innermost is a straight arrow pointing South.
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
Question 9hard
Geometric Transform Rules
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: A target divided by vertical and horizontal axes into four quadrants, comprising three concentric annular rings: in the outer ring, the top-left (TL) quadrant is shaded solid black; in the middle ring, the top-right (TR) quadrant is shaded solid black; in the inner circle, the bottom-right (BR) quadrant is shaded solid black.
[ Figure B ]: The target where the outer ring shaded quadrant advances 1 quadrant clockwise (moving to TR); the middle ring shaded quadrant advances 2 quadrants (180° shift, moving to BL); and the inner circle shaded quadrant advances 1 quadrant counter-clockwise (moving to TR).
[ Figure C ]: A target divided into four quadrants with three concentric rings: in the outer ring, the bottom-left (BL) quadrant is shaded solid black; in the middle ring, the bottom-right (BR) quadrant is shaded solid black; in the inner circle, the top-left (TL) quadrant is shaded solid black.
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
Question 10hard
Side Count & Angle Relations
Problem Figures (Figure Analogy: A : B :: C : ?)
Vector Graphic (High-DPI)
Figure A relates to Figure B following a geometric rule. Apply this exact rule to Figure C to deduce Figure D [ ? ].
Problem Figures Analogy:
[ Figure A ]: A concentric figure consisting of an outer regular hexagon (6 sides) enclosing an inner equilateral triangle (3 sides) and exactly 3 solid black dots placed in the annular space (6 - 3 = 3 dots).
[ Figure B ]: A concentric figure consisting of an outer regular heptagon (7 sides) enclosing an inner square (4 sides) and exactly 3 solid black dots placed in the annular space (7 - 4 = 3 dots).
[ Figure C ]: A concentric figure consisting of an outer regular octagon (8 sides) enclosing an inner regular pentagon (5 sides) and exactly 3 solid black dots placed in the annular space (8 - 5 = 3 dots).
Which of the following figures logically replaces the question mark (?) for [ Figure D ]?
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Frequently Asked Questions & Preparation Strategy
Decompose Figure A and B into three independent attributes: (1) Outer polygon side count; (2) Internal elements (count, position, and orientation); and (3) Shading/Texture. Note the exact change for each attribute (e.g., sides +1, rotation 90° CW, shading inverted). Then apply those exact three changes to Figure C.