PwC abstract and inductive reasoning: how to find the rule

People who find the rule quickly are not seeing more than you are. They are deliberately looking at less: one attribute at a time, compared between two adjacent frames, with everything else in the picture ignored until that attribute is settled. If you are preparing for the PwC inductive reasoning test, that habit is the thing to build, because it is a search you can run rather than a knack you either have or do not. Staring at a whole sequence at once gives your eye a row of pictures and no comparison, which is why nothing arrives. Below is the search itself, not a glossary of rule names: isolate one variable, compare neighbours, write the rule as a sentence, then test that sentence against every frame including the last one.

Why staring at the whole sequence does not work

Your eye is good at similarity and poor at difference, and a shape sequence is built so that the frames look alike. Compare whole frames and you get a vague impression that something is turning. Compare a single attribute across two frames and you get an answer that is either yes or no, which is the only kind of answer you can build on.

Whole-set looking also encourages the worst habit in pattern work: glancing at the first frame, glancing at the last, and interpolating. Any attribute that alternates is invisible that way, because an alternating attribute returns to the same state every second frame, so the two ends of a sequence can match. So is any attribute that completes a cycle and returns to where it started. The information lives in the transitions, not in the frames.

How to find the rule: the six-step method

1. Name what does not change. Say out loud what is constant: the outer frame is always a square, there are always four shapes, the background is always white. Constraints narrow the search and this one is free.
2. List the attributes that could carry a rule. Shape, count, size, shading, rotation, position, the orientation of a small marker, which element is drawn on top of which.
3. Pick one attribute and read it across every frame as a list of values, ignoring everything else in the picture. Write the list down the margin: black, white, black, white.
4. Compare adjacent frames only. Frame 1 to frame 2, then 2 to 3, then 3 to 4. Never the first frame against the last.
5. Say the rule as a sentence with a verb and a quantity. "The dot moves one corner clockwise each frame", not "the dot goes round".
6. Test the sentence against every transition, including the last one, before you commit to an answer.

Read one attribute at a time

Isolating a variable sounds abstract until you have a checklist. These are the attributes that carry rules in almost every shape sequence you will meet, and what each one usually does.

The list is mechanical. That is the point. By the time you have written black, white, black, white in the margin, you have the rule. You did not have to see it.

The seven rule families in inductive reasoning tests

Rotation

A square frame contains an L-shaped arm with a small circle at one end. Frame 1 has the circle top-left, frame 2 top-right, frame 3 bottom-right, frame 4 bottom-left. Track only the circle and the list reads top-left, top-right, bottom-right, bottom-left: a quarter turn clockwise each frame. Tracking one endpoint is the whole trick, because a rotating shape as a whole is hard to hold in memory and a single point is not.

Reflection

Reflection reverses handedness; rotation never does. Picture a flag attached to the right of a vertical pole at the top. Turn the whole thing 180 degrees and the flag ends up on the left at the bottom. Reflect it in a vertical mirror and the flag is on the left at the top. Both moved the flag left, only one moved it down. When a shape is symmetrical enough that rotation and reflection produce the same picture, hunt for the asymmetric detail the setter has left in: a notch, a shaded corner, a dot slightly off centre. That detail exists precisely to separate the two, and it is usually the only thing that can.

Translation

A three by three grid with one shaded cell. Reading the cells as positions 1 to 9, the shading goes 1, 2, 3, then 4, which is the start of the second row. The rule is one cell per frame with a wrap. Most errors in this family happen at the wrap, because the eye has settled on "it moves right" and then meets a frame where the element appears to jump left.

Alternation

Shading runs black, white, black, white. Trivial once written down, and nearly invisible if you compare frame 1 with frame 3, because those two match. Alternation punishes whole-set looking harder than any other family: an attribute with an even period looks constant from every other frame. Cycles of three exist as well, such as black, grey, white, black, so once you suspect alternation, read the entire list before you commit.

Replacement

Four shapes in a row. Frame 1 is four triangles, frame 2 is three triangles and a square, frame 3 is two and two, frame 4 is one triangle and three squares. Two facts fit in one sentence: four shapes throughout, and one more of them is a square each frame. The frame after that is four squares. Notice that the constant, the total of four, did as much work here as the change did.

Counting progression

A count that moves by a fixed amount is the gentle version: sides going triangle, square, pentagon, hexagon, or dots going 1, 3, 5, 7. A count that moves by a changing amount is where this family gets dangerous, and it is the trap the doubling section below takes apart.

Two rules at once

Most questions that feel impossible are two easy rules stacked, not one hard rule. A dot moves clockwise round the corners while the number of internal lines goes 1, 2, 3, 4. Neither rule is difficult. The difficulty is entirely in trying to find a single rule that produces both. If one attribute gives you a clean rule and the picture still does not resolve, that is a signal to start a second list, not to abandon the first. Two variants are worth knowing: the attributes may run at different speeds, so one changes every frame and the other every second frame; and the rule may live in the relationship between two elements, such as an arrow that always points at the black dot wherever the dot has moved to. In that case neither the arrow nor the dot has a rule of its own, and you will not find one by staring at either.

The distractor that survives two frames and dies on the third

Here is a very common way to lose a question you could have had. Four frames, each containing black dots and nothing else: 2 dots, then 4, then 8, then 14.

You compare frame 1 with frame 2: doubled. You compare frame 2 with frame 3: doubled. Two confirmations in a row feels like certainty, and "the count doubles" is now fixed in your head. It predicts 16 for the next frame, and 16 is exactly the number this kind of question is built to produce, because it is what the person who stopped at frame 3 will answer.

Frame 4 has 14, not 16. The rule that survives all three transitions is in the gaps between the counts: 2, then 4, then 6. The next gap is 8, so the answer is 22.

The general lesson matters more than the example. Two transitions can confirm a false rule. Only a transition you have not yet checked can kill one. Two points define a line; the third tells you whether the thing was ever a line. So the final step of the method is not decoration, and if you only have time to test your sentence against one transition, make it the last one, because that is the transition sitting next to the answer you are about to give.

Is abstract reasoning the same as inductive reasoning?

In practice, near enough. Inductive reasoning means inferring a general rule from specific instances, which is exactly what a shape sequence asks for. Different publishers label the same skill differently: you will see abstract reasoning, diagrammatic reasoning, logical reasoning and inductive reasoning used for tests that look almost identical, and diagrammatic reasoning sometimes adds operator boxes that transform an input. The label on the tin varies; the method above does not. Deductive reasoning is the genuinely different one, because there you are given the rules and asked what they force, rather than given the outcomes and asked for the rule.

When the clock is running and you still cannot see it

• If the question gives you options, use them as data. Where a set of candidate answers is offered, they are competing statements about the same thing, and the attributes they disagree on tell you which attribute is being tested: if all but one share a shading, shading is load-bearing. Where you have to build the answer yourself, the equivalent move is to fix the attribute you are certain of first and let it constrain the rest.
• Settle the attribute you are sure of, even when the rest is a fog, and build your answer out from it. One attribute you have actually verified is a better foundation than a whole picture you are guessing at.
• Read count first. It is the fastest attribute to check and one of the most commonly used, so it has the best return per second.
• Decide what "too long" means before you meet it. A limit chosen in advance costs nothing to follow. A decision made halfway through a hard question costs exactly the seconds you were trying to protect.

What PwC says about the inductive reasoning test

PwC's own careers site describes the cognitive test in its online assessment as an ability test including numerical, inductive and deductive reasoning, and says the behavioural profile alongside it is not timed while the cognitive test is. That is the extent of what is publicly established about the PwC inductive reasoning test. PwC does not publish how many inductive questions there are, how long you get, or whether they are multiple choice or interactive, and preparation sites contradict one another on all three. Our guide to the PwC online assessment sets out what the published process does and does not say. We are an independent practice site and are not affiliated with PwC or SHL.

How to practise the search

Practise the search. The answer is a by-product. After each question, write the rule out as a sentence and check it against every frame, including the ones you did not need in order to reach a choice. A rule that holds for three transitions and fails on the fourth is the most useful thing you will produce in an hour of practice, because it names the exact attribute your eye skips.

Keep a short log of which family beat you, in the seven-name vocabulary above. Almost nobody is weak at all seven. Most people have one blind spot, often layering or a count that grows by a changing amount, and a log finds it inside thirty questions where unguided practice never quite does. Once the method is reliable, put a clock on it, because reading one attribute at a time is a habit that only counts if it survives time pressure.

That is also why building a pattern is better practice than picking one from a list. When you have to place the shapes or colour the zones yourself, a half-formed rule fails immediately and visibly, whereas a menu of ready-made answers will happily hand you a plausible one for a rule you never actually had. The inductive questions in our five practice tests work that way, and each explanation names the rule in the same one-sentence form, so you can hold it against whatever you wrote in the margin and see precisely where your search went wrong.