Most abstract reasoning questions are built from a small set of formats and an even smaller list of transformation rules. This guide covers the method for each format, and the rules that make up almost every question.
Practise the real thing: every format below appears in our free abstract reasoning test, with a worked solution for every question. No sign-up.
How to spot the rule in a shape sequence
Work through one element at a time rather than staring at the whole frame. A frame that looks chaotic is almost always two or three simple rules running independently, and the mistake most people make is trying to read them all at once.
A reliable method:
- Pick one element and track only it across every frame. Does the circle rotate, move, change size, change shading, or appear on a cycle?
- Repeat for the next element. Treat each shape as its own separate rule until you have accounted for everything that changes.
- Check the things that stay the same. A shape that never moves is still information, and it rules out options that alter it.
- Apply every rule to predict the next frame, then find that frame in the options. Predicting first stops you being talked into a wrong answer by a plausible looking distractor.
Distractors are built from the common errors: an option that gets the rotation right but the shading wrong, or the movement right but one step too far. Predicting the answer before you look protects you from all of them.
How matrix questions work
Read a matrix along the rows and down the columns separately, because the rule almost always works in one direction and sometimes in both. Matrix questions, a three by three grid with the bottom-right cell missing, are one of the most common formats in graduate testing and in the UCAT, so they are worth drilling.
Look for how each shape changes as you move across a row: it may rotate a fixed amount, gain or lose an element, or swap colour. Then check whether the same or a different rule runs down the columns. When both directions carry a rule, the missing cell has to satisfy both, which usually narrows the options to one.
If a row rule and a column rule seem to disagree, you have misread one of them. Go back to the corner cell that both a row and a column pass through and check your rule against it, since that cell is the easiest place to catch the error.
The common transformation rules
Almost every abstract reasoning question is built from a short list of transformations, and learning them turns the test from guesswork into recognition.
- Rotation. A shape turns by a fixed angle each step, usually 45 or 90 degrees, clockwise or anti-clockwise.
- Reflection. A shape flips to its mirror image. A reflection can never be reproduced by rotation alone, which is often the key to an odd-one-out.
- Translation. An element moves a set distance or around the frame on a fixed path.
- Alternation. Something switches on and off, or between two states, on a regular cycle across the frames.
- Number. The count of sides, dots or shapes rises or falls by a constant amount.
- Shading and size. Fill and scale change on their own cycle, independent of position.
Real questions layer two or three of these at once. Once you can name them, you stop trying to see the whole answer in one glance and instead check the shapes off against a mental list.
More on abstract reasoning tests
Go back to the full abstract reasoning tests guide, or try the closely related inductive reasoning and diagrammatic reasoning tests.
