3.3 Figural Series

Figural (figure) series are a core Inductive Reasoning item type on the NMAT. CEM’s blueprint groups them with figure grouping and number/letter series inside the 30-item, ~35-minute subtest. On the OCBT (online computer-based test), figures appear on screen; you still solve them by perceiving relationships and inferring a general rule without being told what changes.

You do not need artistic talent. You need a descriptive vocabulary for visual change and a discipline for tracking attributes. This section uses pure-text figure descriptions so you can practice the same cognitive steps the exam demands.

How to “See” a Figure in Words

Every figure can be decomposed into attributes:

On a real item, spend the first few seconds inventorying which of these attributes actually differ across the given frames. Attributes that never change are noise—do not invent a rule for them.

Rule Extraction: One Change vs Simultaneous Changes

Strategy A — One dominant change

Many series vary only one attribute:

• Rotation only: same arrow shape, direction cycles every 90° clockwise.
• Count only: same square, interior dots increase by 1 each frame.
• Shading only: triangle empty → half → solid → empty (cycle).

Method: Hold all other attributes fixed in your mind; verify that only the target attribute’s rule is needed to move from frame 1→2→3→4.

Strategy B — Simultaneous independent changes

Harder items change two or more attributes at once, each with its own sub-rule.

Example pattern (described):

• Frame 1: empty circle at top-left, arrow pointing up
• Frame 2: shaded circle at top-right, arrow pointing right
• Frame 3: empty circle at bottom-right, arrow pointing down
• Frame 4: shaded circle at bottom-left, arrow pointing left

Sub-rules:

1. Position of the circle walks clockwise around the four corners.
2. Shading alternates empty / shaded.
3. Arrow rotates 90° clockwise each frame.

The next frame must satisfy all three sub-rules at once. Clockwise from bottom-left, the next corner is top-left; after shaded comes empty; after a left-pointing arrow comes an up-pointing arrow. So Frame 5 is an empty circle at top-left with the arrow pointing up—identical to Frame 1, because all three sub-rules happen to share a four-step cycle.

Method: Write a mini table:

If any option breaks even one column, eliminate it.

Strategy C — Dependent / compound visual rules

Sometimes one attribute’s next state depends on another (for example, “when the figure is shaded, rotate 90°; when empty, rotate 180°”). These are rarer but appear in harder inductive sets. If independent sub-rules fail to fit, test simple dependencies.

Worked Text-Described Sequences

Worked example 1 — pure rotation

Given frames:

1. Isosceles triangle pointing up
2. Same triangle pointing right
3. Same triangle pointing down
4. Same triangle pointing left
5. ?

Rule: 90° clockwise rotation each step.
Next: triangle pointing up again (full cycle), or if only four options show continuations mid-cycle, pick the one that is 90° clockwise from left → up.

Distractors: pointing down (180° error), pointing left again (no change), counterclockwise to down from left (wrong direction). Always mark a reference—“clock face”—so clockwise stays consistent.

Worked example 2 — element count + shading

Given frames (each is a square with dots inside):

1. 1 black dot
2. 2 white (empty) dots
3. 3 black dots
4. 4 white dots
5. ?

Sub-rules:

• Count increases by 1 each frame → next has 5 dots
• Shading alternates black, white, black, white → next is black

Next: 5 black dots inside the square.

Distractors: 5 white dots (count right, shading wrong); 4 black dots (shading pattern misaligned); 6 black dots (overshoot count).

Worked example 3 — reflection series

Given: a flag-like L shape of three unit squares (a tromino):

1. L opens toward the bottom-right
2. Mirror across vertical axis → opens toward the bottom-left
3. Mirror of (2) across horizontal axis → opens toward the top-left
4. Mirror of (3) across vertical axis → opens toward the top-right
5. ?

Rule: alternating vertical then horizontal reflections.
Next: mirror of (4) across horizontal axis → opens toward the bottom-right (returns toward start of a reflection cycle).

Distractors: pure 90° rotations of the L without reflection (reflection and rotation can produce similar silhouettes—track a marked end or “hook” direction carefully).

Worked example 4 — position path

Given: a single small circle inside a larger square frame divided into a 3×3 mental grid:

1. Center cell
2. Middle-right cell
3. Bottom-right cell
4. Bottom-center cell
5. ?

Rule: the circle leaves the center for the middle-right cell, then walks clockwise around the border cells. After bottom-center, clockwise continues to bottom-left.

Distractors: back to center (false reset); middle-left (skipped a border step); top-center (counterclockwise from bottom-center).

Worked example 5 — simultaneous shape morph + count

Given:

1. One empty triangle
2. Two empty squares
3. Three empty pentagons
4. Four empty hexagons
5. ?

Sub-rules:

• Number of sides of each polygon: 3, 4, 5, 6 → next polygons are heptagons (7 sides)
• Count of figures: 1, 2, 3, 4 → next five figures
• Shading stays empty

Next: five empty heptagons.

Distractors: five hexagons (froze side-count); four heptagons (froze figure count); five solid heptagons (invented a shading change).

Step-by-Step Attack Plan (Exam Day)

1. Glance all frames (including options if shown) to see what kind of figures you are dealing with.
2. List changing attributes on scratch paper in short codes: R (rotation), F (fill), N (number), P (position), M (mirror).
3. For each attribute, write the sequence of states under frames 1…n.
4. Predict frame n+1 for every attribute before looking hard at options.
5. Eliminate any option that fails one predicted attribute.
6. If two options remain, you missed an attribute—recompare those two options only.
7. Time box: figural items can run longer than simple number series; still avoid exceeding ~90 seconds before marking for review. The subtest average is about 70 seconds per item overall.

How OCBT Visual Items Map to These Skills

The OCBT interface displays graphics instead of text descriptions, but the mental operations are identical:

Practical OCBT tips:

• Align your sense of “up” with the top of the monitor; do not tilt your head for rotations—mark a vertex mentally.
• If two frames look identical at a glance, force an attribute checklist; NMAT-style items rarely repeat a frame without a subtle change elsewhere in the series logic.
• Figure series and figure grouping (covered in the next chapter) share vocabulary: the same attributes used to continue a series are used to spot the odd figure out. Building attribute fluency once pays twice.
• Do not aim to “see the answer.” Aim to state the rule. Students who verbalize “dots +1, fill alternates, rotate 90° CW” outperform students who rely on vague visual memory under stress.

Trap Summary for Figural Series

Figural series reward calm, structured perception. Describe, track, predict, match—whether the figure is on a screen in the OCBT or described in words in practice.