The process side of diagrammatic reasoning asks you to deduce what a symbol does to a diagram, and to apply it. This guide covers operators, input and output questions, comparing sets, and the short list of transformations they are all built from.
Practise the real thing: these formats appear in our free diagrammatic reasoning test, with a worked solution for every question. No sign-up.
How operators work
An operator is a symbol that stands for a fixed change applied to a diagram, and your job is to deduce what each one does. A question shows you a shape passing through one or more operator boxes and coming out altered; you compare the input with the output to work out the rule each box represents.
Work one operator at a time. If a single box turns a diagram from two black circles into two white circles, that operator swaps colour. If another rotates the whole figure 90 degrees, that is its fixed job wherever it appears. Once you have decoded each operator from the examples given, you apply them in order to a new input to find the answer.
The common trap is order. When two operators act in sequence, applying them in the wrong order produces a different result, and that wrong result is usually sitting there as an option. Read left to right, exactly as the diagram lays them out.
How input and output questions work
Compare the input and the output and name every single thing that has changed, because the rule is the complete list of those changes and nothing else. It is easy to spot one change, assume you have the rule, and miss a second transformation happening at the same time.
A dependable approach:
- List what is different between input and output: position, rotation, number, colour, size.
- List what has stayed the same, which is just as much a part of the rule.
- State the rule as a full sentence, covering every change at once.
- Apply it to the new input and predict the output before you look at the options.
Predicting first is what protects you. The distractors are built to match a partial rule, so an option that gets the rotation right but ignores a colour change will look convincing until you have already worked out the full answer.
How comparing sets questions work
In a comparing sets question you find the single feature that every diagram in a set shares, then decide which set a new diagram belongs to. Set A follows one rule, Set B follows another, and your task is to identify the defining feature of each rather than to complete a sequence.
The feature is usually simpler than it looks, and it is often about one element while everything else is a decoy. In a well-known example, every Set A block contains an arrow pointing at a circle, and the size, colour and position of the other shapes are irrelevant. Once you spot that all six Set A blocks share the arrow-to-circle feature, a new block either has it, in which case it is Set A, or it does not, in which case it is Set B or neither.
Test your candidate rule against every member of the set before you trust it. A rule that fits five of six diagrams is the wrong rule, not a near miss.
The common transformation rules
Diagrammatic questions are built from a short list of transformations, and recognising them turns decoding an operator into a quick check rather than a puzzle.
- Rotation. The figure, or one element of it, turns by a fixed angle.
- Reflection. The figure flips to its mirror image.
- Addition and removal. An element is added, deleted or duplicated.
- Colour or shading swap. Black becomes white, or fills invert.
- Reordering. Elements shift position or cycle around the figure.
- Substitution. One shape is replaced by another according to a rule.
Real operators often combine two of these, so once you suspect one change, keep checking for a second before you commit.
More on diagrammatic reasoning tests
Go back to the full diagrammatic reasoning tests guide, or practise the visual side: sequencing, similar shapes and unfolded shapes.
