4.1 Figure Grouping

Figure grouping is the second major figural skill in NMAT Inductive Reasoning, alongside figure series. CEM’s Part 1 Inductive Reasoning subtest has 30 items with about 35 minutes recommended total. Within that block you will see series (number, letter, figural) and grouping / classification tasks. Induction here means the same thing it means for series: infer a general rule from incomplete information. Nobody labels the rule “odd one out by number of sides.” You extract it.

Where series ask “what comes next under a transformation rule,” grouping asks “which items share a rule?” Formats vary slightly, but the cognitive job is classification:

1. Odd-one-out — four or five figures; three or four follow one rule; identify the outsider.
2. Which belong together — select the subset that forms a coherent class.
3. Which belongs with the set — a stem set of figures is given; choose the option that fits the same rule.

On the OCBT, figures appear on screen. In this section every figure is text-described so you can practice attribute discipline without images. The exam-day process is identical: name what you see, test rules, eliminate.

Attribute Checklist (Memorize and Use Every Time)

Do not start by asking “which ones look alike?” Start by inventorying attributes. The same vocabulary used in figural series pays off again here.

Method on every grouping item:

1. List attributes that actually differ among the given figures (ignore attributes that are identical for all—they cannot define a subgroup).
2. Propose a simple rule that would put most figures in one class.
3. Test the rule on every figure — membership must be yes/no with no exceptions for the “in” group.
4. Name the outsider or the matching option only after the rule survives the full set.
5. If two rules both work, prefer the simplest consistent rule (fewest conditions, no special pleading).

Why “Looks Similar” Fails

Distractors are built from shared surface features that do not define a clean class. Example: three shaded triangles and one shaded square share “shaded,” but if the intended rule is “triangles,” the square is out—or if the intended rule is “shaded polygons of any shape,” a different figure is out. You must find the rule that exam designers used to separate one figure, not the feature that merely appears most often.

Surface-feature trap pattern:

• Many figures are black → students pick the white one, but the true rule is “all have curved edges” and a black square is the real odd one out.
• Many figures are triangles → students ignore that three triangles are equilateral and one is right-angled when the rule is equilateral vs not.
• Two figures point up → orientation feels salient, but count of interior dots is the actual classifier.

Always finish with: “Rule R puts A, B, C in and D out” stated in one sentence.

Worked Classification Problems

Worked problem 1 — odd one out by side count

Figures:

• A: equilateral triangle (3 sides), empty fill
• B: square (4 sides), empty fill
• C: regular pentagon (5 sides), empty fill
• D: regular hexagon (6 sides), empty fill
• E: circle (curved boundary, not a polygon with straight sides)

Candidate rules:

• “Empty fill” — fits all five; cannot produce an odd one out.
• “Straight-edged regular polygons” — A–D fit; E (circle) is out.
• “Odd number of sides” — only A and C; too small a group for a five-figure odd-one-out.

Answer: E is the odd one out (not a straight-sided polygon).

Distractor analysis: Students who fixate on “all are outlines” find no outsider. Students who count only “pointy shapes” might wrongly exclude the square. The cleanest rule that isolates exactly one figure is polygon with straight sides vs circle.

Worked problem 2 — odd one out by symmetry

Figures (all solid black, so fill cannot be the classifier):

• A: square — 4 lines of mirror symmetry
• B: rectangle, not a square — 2 lines
• C: equilateral triangle — 3 lines
• D: isosceles triangle pointing up — 1 line
• E: scalene right triangle — 0 lines

Rule test:

• “Solid black fill” — fits all five, so it produces no outsider and cannot be the rule.
• “Is a straight-sided polygon” — also fits all five; again no outsider.
• “Has at least one line of mirror symmetry” — fits A–D and fails only for E.

Answer: E (scalene right triangle) is the odd one out.

Rule-arbitration lesson: a valid rule must isolate exactly one figure. If B were a circle instead of a rectangle, two different single-attribute rules would each isolate a different figure (“is a polygon” → the circle; “has mirror symmetry” → the scalene triangle) and the item would be ambiguous. When two rules both produce a clean partition, re-read the stem and the option set—the exam intends one attribute, and the options usually reveal which.

Worked problem 3 — which option belongs with the set

Stem set:

1. Empty circle with one solid dot at its center
2. Empty square with one solid dot at its center
3. Empty equilateral triangle with one solid dot at its center

Options:

• W: Empty pentagon with one solid center dot
• X: Empty circle with two solid dots inside
• Y: Solid-filled square with one center dot
• Z: Empty hexagon with no interior dot

Attribute table:

Rule: empty outer polygon/circle with exactly one centered solid dot. Shape identity may vary; fill and count may not.

Answer: W.

Distractor analysis:

• X shares empty circle with stem item 1 (surface match) but breaks count.
• Y shares “square + one dot” structure but breaks outer fill.
• Z varies shape acceptably but breaks dot presence.

Surface similarity to one stem figure is not membership in the class.

Worked problem 4 — enclosure and count

Figures:

• A: large empty circle containing a small empty square fully inside (no touching)
• B: large empty square containing a small empty triangle fully inside
• C: large empty triangle containing a small empty circle fully inside
• D: large empty circle beside a small empty square (separate, no enclosure)
• E: large empty hexagon containing a small empty pentagon fully inside

Rule: a smaller closed shape is strictly enclosed by a larger closed shape. D fails enclosure.

Distractor analysis: Students may pick E because “hexagon and pentagon look complex,” but complexity is not the rule—enclosure is. Or they pick C because the inner shape is a circle “different family,” while the structural relation still holds.

Worked problem 5 — orientation class

Figures (identical isosceles triangle otherwise):

• A: points up
• B: points up
• C: points up
• D: points down
• E: points up

Rule: same orientation (up). D is odd.

Trivial—but under time pressure with busier figures, orientation is easy to skip. Always include orientation on the checklist when shapes are congruent.

Worked problem 6 — competing rules (pick simplest consistent)

Figures:

• A: solid black pentagon
• B: solid black heptagon (7 sides)
• C: solid black triangle
• D: empty black-outline nonagon (9 sides)
• E: solid black square

Candidate rule 1: “solid fill” → D is out.
Candidate rule 2: “odd number of sides” → A (5), B (7), C (3) in; E (4) out; D (9) would be in—so if odd-one-out expects one outsider among five, rule 2 does not isolate a unique outsider without dropping D’s fill difference.

If only one figure should be odd and D is the only empty figure, rule 1 (solid vs empty) is simplest and unique. Rule 2 needs extra clauses (“odd sides and solid”) to force a different answer—more complex, usually wrong when a single attribute already partitions cleanly.

Principle: Prefer the lowest-complexity rule that yields exactly the required partition (one outsider, or one matching option).

Distractor Analysis Playbook

Exam-Day Micro-Routine for Grouping (~45–75 s)

1. Scan all figures once (5–10 s) — what varies?
2. Write 2–4 attribute codes on scratch paper: S (sides), F (fill), O (orientation), N (count), Y (symmetry), E (enclosure).
3. Test the most obvious varying attribute first (often fill or side count).
4. Verify the candidate isolates the right partition.
5. If stuck at ~60 s, mark for review and move on—series items may be faster points in the same 35-minute Inductive block.

Bridge to Series Vocabulary

Grouping and series share attributes; they differ in question form:

Training one attribute checklist serves both item types inside the same CEM Inductive Reasoning subtest.

Master classification by rule, not by vibe. Name the attribute, test every figure, distrust partial matches, and when two rules compete, keep the simplest rule that still separates the group cleanly.