Reviewed 19 August 2026 by the Cognivy editorial team
Diagrammatic items are procedural: the operators are given rather than inferred, so the method is explicit rather than intuitive. The marks go to candidates who write down what each operator does in plain words and record the intermediate state, and they are lost by candidates who apply the right operators in the wrong order. This guide covers the shapes the questions take, the Saville and Aon formats you may be sent, two worked examples solved step by step — and six free questions to try the method on.
- Questions
- Depends on provider: Saville tests are fixed-length, and Aon's switchChallenge has no set number of questions
- Time limit
- 6 minutes for Aon's switchChallenge; 10 to 24 minutes for the Saville Swift batteries that include diagrammatic reasoning
- Answer format
- Multiple choice: the missing operator, the final output, the original input or an intermediate state
- Delivery
- Saville is fixed-length with a gradual increase in difficulty; Aon's switchChallenge creates a new question each time you complete one
- Scoring
- No published pass marks. Saville combination tests report one total score plus individual sub-scores
The skill
What is a diagrammatic reasoning test?
A diagrammatic reasoning test represents a process. An input — a row of shapes, a set of symbols, a figure — passes through one or more operators, each of which does a defined thing to it, and produces an output. You are shown enough of the chain to infer the rest, and asked for the missing operator, the missing output, or the input that must have started it.
The operators are the vocabulary of the test. A single symbol may rotate, reflect, invert shading, swap two positions, remove an element or reorder the whole row. Item writers combine two or three of them, and the difficulty comes from order rather than from any individual step.
Aon's switchChallenge is a clear published example of the shape. Aon describes each question as containing three elements — input, code and output — and asks you to find the code that changes the input to the given output, noting that in harder questions the numerical codes may be presented across multiple rows, where the output of the first code becomes the input for the next.
The word is used loosely, and SHL itself notes that inductive reasoning tests are sometimes called diagrammatic style tests. Cognivy keeps the narrower meaning: a diagrammatic item has operators acting in sequence, and a defined before and after. If your item is a row of figures changing on their own with no operator shown, it belongs on the inductive or abstract guide instead.
Try it before anything else
Free diagrammatic reasoning practice questions
Six original questions in the shapes above: sequences to choose, chains to run forwards and backwards, an operator to infer and an intermediate state to hold. Write the operators down as actions, commit to an answer before opening the solution, then check your choice forwards — each solution records the intermediate states and names the error behind every wrong option.
Three operators act on a row of four lettered tiles. R moves every tile one place to the right, and the last tile wraps around to the front. S swaps the two middle tiles. F reverses the whole row.
Input: W X Y Z · Output: Z W Y X
Which single sequence of two operators produces the output?
Show the worked solution
Answer: B — S then R.
- Write each operator as an action first. R shifts right with wrap-around, S swaps positions two and three, F reverses.
- Apply S to W X Y Z: the middle two swap, giving W Y X Z. Record that intermediate state.
- Apply R to W Y X Z: every tile moves one right and Z wraps to the front, giving Z W Y X, which is the output.
- Check the alternative order to be sure: R first gives Z W X Y, and S then swaps its middle two to give Z X W Y, which is not the output.
Why the other options are there. Option A applies the right two operators in the wrong order, which is what you get once both operators are correctly identified and the sequence is not. Option C reverses the row first, which does put Z at the front and makes the output look close, but leaves W and X in the wrong cells. Option D repeats one operator and moves the row two places, which no single change in the output supports.
Two operators act on a row of three shapes. T turns every shape from outline to solid, or from solid to outline. M moves the first shape to the end of the row.
Applying M and then T produced this output: solid square, outline circle, outline triangle.
Which row was the input?
Show the worked solution
Answer: A — solid triangle, outline square, solid circle.
- The chain applied M then T, so undo them in the opposite order: T first, then M.
- Undo T by flipping every fill in the output. Solid square, outline circle, outline triangle becomes outline square, solid circle, solid triangle.
- Undo M by taking the last shape back to the front. Outline square, solid circle, solid triangle becomes solid triangle, outline square, solid circle.
- Check it forwards. M on that row gives outline square, solid circle, solid triangle; T then flips every fill to give solid square, outline circle, outline triangle, which matches.
Why the other options are there. Option C undoes the fill flip and stops, forgetting the move entirely. Option D undoes the move in the wrong direction, taking the first shape to the end instead of the last shape to the front. Option B is the correct row with every fill inverted, which is what you get if you undo T twice, and it is the option that looks most convincing to a candidate who did not write the intermediate state down.
Three operators act on a row of four lettered tiles. K reverses the whole row. L swaps the first two tiles. N moves the last tile to the front.
Input: A E P X · The chain applies K, then L, then N.
What is the output?
Show the worked solution
Answer: C — A P X E.
- Write the operators as actions first: K reverses the row, L swaps positions one and two, N brings the last tile to the front.
- Apply K to A E P X: the row reverses to X P E A. Record that state before moving on.
- Apply L to X P E A: the first two tiles swap, giving P X E A. Record it again.
- Apply N to P X E A: the last tile, A, moves to the front, giving A P X E.
Why the other options are there. Option A is the row after K and L — an intermediate state offered as a final answer, and what remains when the third operator is forgotten. Option B applies N in the wrong direction, sending the first tile to the end instead of bringing the last tile to the front. Option D runs the right three operators with L before K: an order error still produces a well-formed row, and only the recorded intermediate states show where it went wrong.
The same operator acts in both rows of this question, and its rule is not given. Applied to the first row, it produced the transformation shown.
First row: B D G W becomes W D G B · Second row: E H P U becomes ?
What is the output of the second row?
Show the worked solution
Answer: B — U H P E.
- Test each hypothesis against every tile of the first row, not just the ends. A full reversal of B D G W would give W G D B, but the middle tiles kept their order, so the operator is not a reversal.
- A cycle fails the same check: moving the last tile to the front gives W B D G, and moving the first tile to the end gives D G W B. Neither matches.
- The only single action that reproduces the whole row is a swap of the first and last tiles: B and W trade places while D and G stay put.
- Apply that to E H P U: the first and last tiles swap, giving U H P E.
Why the other options are there. Option A reverses the whole second row, the reading you settle on if you check only the end tiles of the example. Option C brings the last tile to the front, which explains W arriving at the front of the example but not B arriving at the end. Option D sends the first tile to the end, the same single-feature reading taken from the other end of the row. Each of the three fails on some tile of the example — an operator has to reproduce every tile before it can be trusted.
Two operators act in order on a row of four lettered tiles. C moves every tile one place to the left, and the first tile wraps around to the end. V swaps the two middle tiles.
Input: D G H J · The chain applies C, then V.
What does the row look like after C has acted but before V?
Show the worked solution
Answer: D — G H J D.
- The question asks for the state part-way through the chain, so only the first operator acts on the input.
- Write C as an action: every tile moves one place left, and the first tile wraps to the end.
- Apply it to D G H J: G, H and J each move one place left and D wraps to the end, giving G H J D. That is the answer — V has not acted yet.
- To confirm the chain reads correctly, V would then swap the middle tiles to give G J H D. That is the final output, which this question does not ask for.
Why the other options are there. Option A is the final output — the full chain run to the end, answering a question that was not asked. Option B shifts the row right instead of left, wrapping the last tile to the front. Option C applies V to the input first, which is the intermediate state of a chain run in the wrong order.
Two operators act on rows of four lettered tiles. F reverses the whole row. S swaps the two middle tiles.
Input: B G U W · Output: B G U W — identical to the input.
Which sequence turns the input into the output?
Show the worked solution
Answer: A — F then F.
- An output identical to the input does not mean nothing happened. It means the sequence undid itself, so the question is which sequence is its own undo.
- F is its own inverse: reversing B G U W gives W U G B, and reversing again restores B G U W. F then F is the answer.
- Check the others rather than assuming. F then S gives W U G B, then W G U B. S then F gives B U G W, then W G U B. Neither restores the row.
- F then S then F traces to W U G B, then W G U B, then B U G W — the net effect of the whole sequence is S applied once, not nothing.
Why the other options are there. Options B and C each contain one reversal that nothing undoes, and both land on the same row, W G U B — a glance at the first tile eliminates them without full working. Option D looks symmetric, so it feels as if it must cancel itself out, but traced through it equals a single swap of the middle tiles and gives B U G W. A sequence is judged by tracing it, not by its shape.
A short diagrammatic reasoning set at the real per-question pace, scored server-side like the full product, with a worked solution after every answer.
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What employers are looking at
What do diagrammatic reasoning tests measure?
Employers use diagrammatic items for roles where a process has to be followed and diagnosed: engineering, operations, software, logistics and technical apprenticeships. Saville places diagrammatic reasoning inside its technical and apprentice batteries alongside spatial and mechanical reasoning for exactly that reason.
Two abilities separate here, and both are about discipline rather than flair. Inference: can you deduce what an operator does from one clean example rather than guessing from an ambiguous one. Sequencing: can you apply two or three operators in the stated order and hold the state between them, including when you are running the chain backwards.
Reading your result
How diagrammatic reasoning tests are scored
A diagrammatic result is not a mark out of ten. Neither provider on this page publishes a pass mark, and their two delivery models mean that even the number of questions you answered, or how hard they felt, is not a figure you can read anything from. What the published materials do support:
- No pass mark exists to aim at. Neither Saville nor Aon publishes a pass mark for a diagrammatic assessment. Any benchmark belongs to the hiring organisation, so if a recruiter has disclosed a target, that is the only figure worth working to — and it is worth asking whether one has been.
- On a Saville battery, the diagrammatic score stands alone. Saville reports one total score and individual sub-scores for its combination tests in a single report, so the employer sees the diagrammatic component separately from the total. A strong verbal or numerical section does not cover for a weak diagrammatic one.
- On switchChallenge, the question count is not a score. Aon states there is no set number of questions because the system creates a new one each time you complete one. How many questions you faced is a product of the delivery model, not a result, and it cannot be compared between candidates from outside the test.
- Difficulty is not feedback on either delivery model. Saville states that its fixed-length format gives a gradual increase in difficulty, so the late questions are meant to be the hardest. Aon states that switchChallenge may get more difficult as you progress. Under both models, how hard the test feels tells you nothing about how well it is going.
- The score report is the only readable output. Because the two delivery models differ this much, the only figure worth reading is the provider's own score report for your named assessment. Comparing question counts or felt difficulty with other candidates compares delivery mechanics, not ability.
Question formats
What do the questions look like?
Diagrammatic assessments use a small set of shapes, and each one has its own first move.
- Input, operator, output. The full chain is shown with one part hidden. Aon's switchChallenge is this shape: two of input, code and output are given, and the third is chosen.
- Missing operator. Both ends are visible and the operator between them is the answer. Work out what changed, then find the operator that does exactly that and nothing else.
- Sequential transformations. Two or three operators applied in a stated order. Aon notes that in its harder switchChallenge questions the output of the first code becomes the input for the next.
- Reverse operations. The output is given and the input is the answer. Undo the operators in the opposite order to the one they were applied in, because each operator has to be reversed against the state that existed before it, not after it.
- Intermediate states. The question asks what the figure looked like part-way through the chain, not at the end. Writing the state between each step turns this from a memory task into a reading task.
- Process and flow diagrams. Boxes and arrows describing a workflow, with a question about what reaches a particular point. The same discipline applies: name each step, then follow one path at a time.
A row of four shapes goes in. Two operators are shown between the input and the output: one is known from an earlier example, the other is not. The output differs from the input in two respects — the order has changed and one shape is now solid. Separating those two changes, and assigning each to the operator that could have caused it, is the whole item. Applying both changes in the wrong order produces an answer that is present among the options.
Launch coverage
Which providers use diagrammatic reasoning tests?
Two of Cognivy's launch families publish an assessment in this family, and they present it very differently.
- Diagrammatic Analysis and Diagrammatic Reasoning. Saville publishes both as single aptitude tests with their own practice tests, and places diagrammatic reasoning inside three combination batteries: the Swift Analysis Aptitude range at 18 to 24 minutes, Swift Technical Aptitude at 10 minutes with spatial and mechanical reasoning, and Swift Apprentice Aptitude at under 20 minutes across six areas. Saville states that its fixed-length format gives a gradual increase in difficulty.
- switchChallenge. Aon labels switchChallenge Deductive Reasoning, and the published task is operator-based: each question shows an input, a choice of numerical codes and an output, and you select the code that changes the input into the output. Aon lists the module at 6 minutes and states that there is no set number of questions because the system creates a new one each time you complete one.
Provider names identify the assessment format. Cognivy is independent and is not affiliated with or endorsed by these providers.
What varies, and what does not
Timing, delivery and scoring
Diagrammatic modules are short, and the two providers use opposite delivery models. Knowing which one you have changes how you pace it.
- Saville uses a fixed-length format. Saville states that its fixed-length format ensures a fairer experience for candidates with a gradual increase in difficulty. A fixed paper means the last items are the hardest, so protecting time for them is a real decision.
- Aon switchChallenge: 6 minutes, no fixed question count. Aon states that the system will continue to create questions every time you complete one, and that the test may get more difficult as you progress. There is no finish line, so a sustainable rate beats a sprint.
- Inside a battery the diagrammatic section is one part of a short total. Saville lists Swift Technical Aptitude at 10 minutes for spatial, mechanical and diagrammatic reasoning together, and the Swift Analysis Aptitude range at 18 to 24 minutes across two to three aptitudes.
- Chained codes cost time, not difficulty. Aon notes that harder switchChallenge questions present codes across multiple rows. The individual step is no harder; there are simply more of them, which is why writing the intermediate state is worth the seconds it costs.
A repeatable approach
A method that survives the clock
This is a family where writing the method down matters, because the operators have to be applied in a specific order and that order is invisible in the final answer. Five steps, and step three is the one to hold yourself to.
- 1
Find the cleanest example of each operator. Infer one operator at a time, from the example where only that operator acts. Deducing two unknown operators from one ambiguous transformation is guesswork wearing a method's clothes.
- 2
Write each operator as a short action. Turns a quarter clockwise. Swaps positions two and three. Flips solid to outline. A sentence you can reapply beats a picture you have to re-read.
- 3
Record the intermediate state. After each operator, write the row as it now stands. On a two-operator chain that is one extra line, and it stops the second operator being applied to the original row instead of to the result of the first.
- 4
For a reverse question, undo in the opposite order. If the chain applied M then T, recovering the input means undoing T first and M second. Undoing them in the order they were applied gives a row that is wrong in a way the output cannot show you.
- 5
Check the answer forwards. Run your chosen option through the operators in the original direction and confirm it produces the given output. It is a five-second check that catches an order error before you commit.
What slows progress
Common mistakes, and the fix for each
- Applying the right operators in the wrong order. Fix: write the intermediate state after every operator. An order error still produces a well-formed row, so the output gives you nothing to check it against and the recorded intermediate state is the only place it shows.
- Inferring two operators from one example. Fix: find an example where only one unknown operator acts, and solve that one first. If no such example exists, use the operator you already know to strip its effect away before you reason about the other.
- Undoing a chain in the order it was applied. Fix: on any reverse question, write the operators down and cross them off from the right. Undoing in the forward order produces an answer that is usually present among the options.
- Confusing a position swap with a rotation. Fix: check whether individual shapes changed their own orientation or only their place in the row. A swap moves shapes between cells and leaves each shape as it was; a rotation changes the shape itself and leaves the cells alone.
- Skipping the forward check. Fix: run your answer through the chain in the original direction before committing. On a two-operator item that is one pass, and it catches both errors above: an operator applied in the wrong order, and a chain undone forwards.
You have seen the method. Employers set the full battery.Every provider, every track, a worked solution on every question.
Get full accessIn practice
How do you track a row through three operators without losing it?
Write each operator down as a short action before you touch the row: reverses the whole row, swaps the first two tiles, brings the last tile to the front. A symbol has to be re-read every time you meet it; a written action is applied and reused. Within one assessment the same symbols usually keep the same meanings, so the sentence you write on the first question keeps paying on every later one.
Then record the state after every operator, not just the final answer. Sample question 3 passes through two intermediate rows on its way to the output, and every wrong option on it is a state the chain leaves behind when a step is skipped, misdirected or reordered. An order error still produces a well-formed row, so the output alone gives you nothing to check against — the recorded intermediate is the only place the error shows.
Finish with the forward check: run your chosen option through the chain in the stated order and confirm it lands on the given output. On a two- or three-operator chain that is one pass of a few seconds, and it catches the two commonest failures — operators applied in the wrong order, and a single operator applied in the wrong direction — before the answer is committed.
In practice
How do you work out what an unknown operator does?
From the cleanest example available — the transformation where only the unknown operator acts. Trying to deduce two unknown operators from one ambiguous before-and-after is guesswork wearing a method's clothes, and the habit of isolating one operator at a time is the single most valuable thing to train before test day.
Test your hypothesis against every tile, not just the striking ones. The example in sample question 4 moves its first tile to the back and its last tile to the front at once, and each of its wrong readings — a full reversal, a cycle in either direction — explains one of those features while failing on another tile. An operator description is only proven when it reproduces the entire row.
When no clean example exists, use the operator you already know to strip its effect away, and reason about what remains. Once an operator is pinned down, write it as an action and reuse it for the rest of the assessment rather than re-deriving it — inferring is the expensive step, so do it once.
In practice
What changes when you run a chain backwards?
The order reverses. A chain that applied M and then T is undone by reversing T first and M second, because each undo has to act on the state that existed just after the operator it cancels. Undoing in the forward order feels natural under time pressure, and it produces a wrong answer that is normally waiting on the option list.
Not every operator reverses the same way. A fill flip or a row reversal is its own inverse — sample question 6 turns on exactly that — while a move to the end is undone by a move to the front, and a leftward shift by a rightward one. Write the undo as its own action instead of trusting the original: the inverse of an operator is a different instruction, even when it happens to look the same.
Then check the recovered input forwards. Sample question 2 finishes by running the answer through the chain in the original direction and matching the given output, and that five-second pass is what separates a recovered input from a plausible-looking row. The most convincing wrong option on a reverse question is usually the one that undoes a step twice or not at all, and only the forward check exposes it.
A clear route
How to prepare in the days you have
The operators in this format are given rather than inferred, so preparation has a concrete checklist to work through rather than an open-ended one. Use the days you have in this order.
- 1
First, build an operator vocabulary. Rotate, reflect, invert shading, swap positions, shift with wrap-around, add, remove, reorder. Practise naming what changed between two rows before you attempt any full item.
- 2
Next, drill single operators untimed. One operator, one transformation, no clock. The aim is to stop needing to re-derive what a symbol means every time you meet it.
- 3
Then chain two, writing the intermediate state. Do not move to three operators until writing the middle row is automatic. The habit is what makes longer chains routine rather than risky.
- 4
Practise reverse questions as their own category. Forward and reverse items feel similar and fail differently. Give reverse items a separate session so that undoing in the opposite order becomes reflexive.
- 5
Add the provider's format last. Saville publishes free practice tests for its own aptitude tests under timed conditions, and Aon publishes practice tasks for switchChallenge. Use whichever matches your invitation once the method is reliable.
Cognivy uses your assessment date to choose the route rather than asking you to predict a study schedule. When you sit down to practise, you choose the session length that fits that day.
Pace
Getting faster without losing accuracy
Speed here is almost entirely about not repeating work. Four habits remove the most.
- Note the operator once, reuse it all test. Within one assessment the same symbols usually keep the same meanings. Writing them down on the first item you meet them makes every later item shorter.
- Compare only what changed. Do not re-describe the whole row. Identify the differences between input and output first, then ask which operators could account for exactly those differences.
- Eliminate on one feature. If a single operator fixes the position of one shape, apply that alone to all four options. It usually removes two before you do any full working.
- Keep a pace rule for an open-ended module. Aon's switchChallenge keeps generating questions, so there is nothing to finish. Set a per-item ceiling before you start and accept an educated choice when you reach it.
Direct answers
Diagrammatic reasoning test FAQs
It is an assessment built around operators. An input passes through one or more defined transformations to produce an output, and the question asks for the missing operator, the missing output or the original input. Aon's switchChallenge is a published example: each question shows an input, a code and an output.
A diagrammatic item shows a process with a defined before and after, so you can name what each operator does. An abstract item shows figures that change with no operator displayed, so the rule has to be inferred from the pattern itself. The terms are used loosely in job adverts, and SHL notes that inductive tests are sometimes called diagrammatic style tests.
It depends on whether it is a single test or part of a battery. Aon lists switchChallenge at 6 minutes. Saville lists Swift Technical Aptitude at 10 minutes for spatial, mechanical and diagrammatic reasoning together, and the Swift Analysis Aptitude range at 18 to 24 minutes. Use the time stated in your own invitation.
Employers use it in technical, engineering, operations and apprenticeship hiring, and also for graduate and management roles. Saville places diagrammatic reasoning in its technical and apprentice batteries alongside spatial and mechanical reasoning, and in its analysis range alongside verbal and numerical reasoning for graduate and management roles.
Undo the operators in the opposite order to the one they were applied in, and write the row down after each step. If the chain applied M then T, you undo T first and M second. Reversing that order produces a wrong answer that is normally offered as an option.
It depends on the provider. Saville states that its fixed-length format gives a gradual increase in difficulty, which is not adaptive delivery. Aon states that switchChallenge may get more difficult as you progress and has no set number of questions. Under either model you cannot read your score from how hard the items feel, so treat rising difficulty as normal behaviour rather than as feedback. Check what your own assessment says before deciding how to pace it.
Neither Saville nor Aon publishes a pass mark. On a Saville combination test the employer receives one total score plus individual sub-scores, so the benchmark is set by the hiring organisation rather than by the test. Ask the recruiter whether a target has been disclosed.
No. Cognivy is independent and is not affiliated with or endorsed by any assessment provider. Every question is original material written to teach the operator vocabulary, the sequencing method and the pacing of a named style.