Mechanical, Spatial and Social Abilities

6 min read

1. Mechanical reasoning

Most mechanical-ability questions reduce to three machines: levers, pulleys and gears. Memorise their behaviour, and you can answer almost any item by inspection.

Levers

A lever has three parts: load, effort, fulcrum. Three classes:

First-class lever (fulcrum in the middle) — see-saw, scissors, pliers.
Second-class lever (load in the middle, fulcrum at one end) — wheelbarrow, nutcracker.
Third-class lever (effort in the middle) — tweezers, your forearm.

Equilibrium rule: load × distance from fulcrum = effort × distance from fulcrum.

Worked Example 1 — See-saw

A 60 kg boy sits 2 m to the left of the pivot of a see-saw. Where should a 40 kg girl sit on the right to balance it?

60 × 2 = 40 × d → 120 = 40d → d = 3 m to the right of the pivot.

A fixed pulley changes the direction of force but doesn't change its magnitude. A single movable pulley halves the effort needed (you pull twice the rope, but with half the force). Adding pulleys in a block-and-tackle further reduces effort.

Gears

In a gear pair:

The smaller gear rotates faster than the larger gear.
Adjacent meshing gears rotate in opposite directions.
In a chain (like a bicycle), gears connected by the same chain rotate in the same direction.

Worked Example 2 — Gear ratio

A driver gear of 20 teeth meshes with a driven gear of 60 teeth. If the driver turns at 90 rpm, what is the speed of the driven gear?

Gear-tooth product is constant: 20 × 90 = 60 × x → x = 30 rpm. The larger gear turns slower.

Key Points

Mechanical advantage = load ÷ effort. A lever or pulley with MA > 1 reduces the force needed.
Energy is conserved — what you save in force, you pay in distance.
For gears: product of teeth × rpm is constant on both sides.

2. Spatial reasoning

These questions test the ability to mentally manipulate shapes.

Mirror images

A vertical mirror swaps left and right but preserves up and down. A horizontal mirror (water reflection) swaps up and down but preserves left and right.

The mirror image of the letter b in a vertical mirror is d. The mirror image of the digit 3 is a reversed three (like the letter "E" minus the middle bar in some fonts).

Paper folding and cutting

The standard pattern: a square sheet is folded once or twice and then cut. The question shows the cut piece; you choose the pattern that appears when it is unfolded.

Trick: each fold doubles the cuts. If you fold a square once and cut a triangle, you get two mirror-image triangles on unfolding. Fold twice and you get four.

Cube counting

When small cubes are stacked into a larger cube and the outside is painted:

A cube of side n is made of n³ small cubes.
Corner cubes: 8 (painted on 3 faces).
Edge cubes: 12(n − 2) (painted on 2 faces).
Face cubes: 6(n − 2)² (painted on 1 face).
Interior cubes: (n − 2)³ (no paint).

Worked Example 3

A 4 × 4 × 4 cube is painted on all faces and then cut into 64 small cubes. How many small cubes have paint on exactly two faces?

Edge cubes (excluding corners) = 12 × (4 − 2) = 12 × 2 = 24.

Social-judgement items describe a workplace or community situation and ask which response is best. There is rarely a single "correct" answer, but examiners look for responses that are:

Respectful of all stakeholders.
Lawful and ethical.
Practically effective, not merely satisfying.
Proportionate to the problem.

You are the chief of a small office. One of your senior officers persistently arrives late and disrupts morning meetings. Three junior staff have complained informally. What is the best initial response?

(a) Issue a formal written warning immediately. (b) Ignore it — he is senior and will resent intervention. (c) Have a private one-to-one conversation to understand the cause and set clear expectations. (d) Announce a new attendance rule at the next meeting without naming him.

(c) is the most reasonable first step. It is respectful (private), proportionate (informal before formal), and diagnostic (he may have a genuine reason). (a) escalates too quickly; (b) ignores a real problem; (d) is passive-aggressive.

For these questions, eliminate two options first: usually the most aggressive and the most passive. Then choose between the two reasonable middle options based on which one actually solves the underlying problem.

Putting it together

The CSS mental-ability section rewards calm pattern recognition. Don't memorise puzzles — train your eye to spot relationships, arithmetic shortcuts, and the structure of social situations. Three to five minutes of daily practice on each type compounds rapidly over a few weeks.

Try Yourself

Quiz: Mental Abilities