Non-Verbal Reasoning

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Non-verbal questions replace words with figures — cubes, mirrors, patterns and shapes. They carried real weight in 2022: ten questions across the two papers were figure-based, including a five-question cluster at Q96–100 of the SI paper.

About the figures on this page. The original exam diagrams cannot be reproduced here, so the illustrations below are drawn to teach each technique. Where a paper question used a given type, it is named so you can look it up in the full papers.

Cubes & Dice

A cube has three pairs of opposite faces. On an unfolded net, faces that are one square apart in a straight line are opposite each other.

Faces separated by exactly one square in a row or column end up facing away from each other when the net is folded. Adjacent faces never are.

Painted cube. An n×n×n cube painted on all sides and cut into unit cubes gives:

3 faces painted (corners) = 8 · 2 faces (edges) = 12(n − 2)

1 face (face centres) = 6(n − 2)² · 0 faces (interior) = (n − 2)³

TS Police SI 2022 — Q95

A solid cube of 4-inch edge is painted with red, green and yellow, each colour on a pair of opposite faces, then cut into one-inch cubes. How many small cubes have only one face painted with red?
(1) 16 (2) 24 (3) 8 (4) 32

This one is worth studying because the wording admits more than one reading, and all three readings appear among the options:
• Cubes with exactly one painted face, of any colour: 6(n−2)² = 6 × 4 = 24.
• Cubes having exactly one red face, other colours permitted: all 16 on each red face, twice = 32.
• Cubes whose only painted face is red: the inner 2×2 of each red face, twice = 8.
The standard formula reading gives 24, and that is what the widely circulated key states — but no official key was published, so treat this one as contested and know the formula rather than the answer.

Mirror & Water Images

A vertical mirror reverses left and right but leaves top and bottom unchanged. A water image (horizontal mirror) does the opposite.

Mirror image — left and right swap; top and bottom stay.

Water image — top and bottom swap; left and right stay.

Letters unchanged by a vertical mirror: A, H, I, M, O, T, U, V, W, X, Y.

Letters unchanged by a water image: B, C, D, E, H, I, K, O, X.

SI Q100 was a mirror-image question with the mirror placed on a line MN beside the figure.

Counting Figures

Count in size order and keep a running tally — never count at a glance.

A 2×4 grid. Count the unit squares first, then squares made of four cells, and so on until no larger size fits.

Constable Q166 asked for triangles in a figure and SI Q99 for squares in a gridded rectangle crossed by diagonals — both reward this size-by-size method.

Venn Diagram Questions

Some questions ask which Venn diagram represents a set of categories. Decide the relationship between each pair first, then match:

One inside another — every A is a B (equilateral triangles inside triangles).

Partly overlapping — some A are B (drivers of cars and of two-wheelers).

Separate — no A is a B (cats and dogs).

Constable Q79 and SI Q51 were both of this type, and SI Q53 layered four overlapping shapes with counts in each region — there, shade the region the question names before doing any arithmetic.

These are the most skippable questions in the paper. Figure counting and paper folding can eat three or four minutes each. If a non-verbal question does not resolve within about a minute, mark it and move on — the marks are identical to the quick ones.

Also see: Syllogism · Inequalities · Analogy