How These Are Formatted
Twenty items across the four families that appear in almost every abstract battery: pattern series, transformations, classification, and matrices.
One difference from a real paper is worth stating up front: these items are described in words rather than drawn. Real abstract tests are entirely figural, and you will be looking at shapes rather than reading about them.
That makes these slower to read and the underlying rule far more visible — which is the point of practising. Each item carries the full reasoning and, where one exists, the trap it was built around.
Family 1: Pattern Series
Item 1
A square rotates 45° clockwise at each step. Step 1 shows it upright. What does step 5 look like?
Answer: identical to step 1. Four rotations of 45° make 180°, and a square looks the same at 180° as at 0°.
The trap. Answering "upside down". Symmetry means some rotations are invisible, so check what the shape's symmetry allows before tracking the angle.
Item 2
The sequence runs triangle, square, pentagon, hexagon. What comes next?
A heptagon — seven sides. The rule is one additional side per step, and it is a counting rule rather than a shape-recognition one.
Item 3
Now the same series with shading: black triangle, white square, black pentagon, white hexagon. What comes next?
A black heptagon. Two independent rules run at once — sides increase by one, shading alternates.
Why this is the real difficulty. Single rules are rarely hard. Items become hard when two or three rules operate simultaneously and you have to hold all of them while checking the options.
Item 4
A dot moves one corner clockwise around a square at each step. It starts at the top-left corner. Where is it after six steps?
Bottom-right. Six steps around a four-position cycle leaves a remainder of two, and two corners clockwise from top-left is bottom-right.
The method. Cycles are arithmetic, not visualisation. Divide by the cycle length and use the remainder.
Item 5
Each frame keeps everything from the previous frame and adds new lines. The counts run 1, 2, 4, 7. How many lines in the next frame?
Eleven. The differences are 1, 2, 3 — increasing by one each time — so the next difference is 4.
The trap. Looking for a rule in the numbers themselves. When a series resists, take differences; when the differences resist, take differences of those.
Family 2: Transformations and Analogies
Item 6
An arrow pointing up becomes an arrow pointing right. Apply the same transformation to an arrow pointing left.
It becomes an arrow pointing up. The operation is a 90° clockwise rotation: up to right, right to down, down to left, left to up.
Item 7
Two dots become four dots. What do three dots become — five, or six?
It cannot be determined. Two to four is equally consistent with "add two" and "multiply by two", and one pair cannot distinguish them.
Why this item exists. Real matrix items give you a whole row precisely so the rule is pinned down. If a rule you have inferred is consistent with only one example, you have not finished inferring it.
Item 8
An L-shape opening to the right becomes an L-shape opening to the left. Is the operation a rotation or a reflection?
A reflection. Rotation preserves handedness; only reflection converts a shape into its mirror image.
How to use it. When an option looks correct but subtly wrong, check mirroring first. It is the single most common constructed distractor in figural tests.
Item 9
A large circle containing a small square becomes a large square containing a small circle. Apply the same operation to a large triangle containing a small hexagon.
A large hexagon containing a small triangle. The rule is a swap of roles — outer and inner exchange shape while sizes stay put.
Item 10
Three white stars become three black stars. Apply the same operation to five black squares.
Five white squares. Shading inverts; count and shape are untouched.
The discipline. Name which dimensions change and which are held constant. An option that alters a held-constant dimension is wrong however plausible it looks.
Family 3: Classification
Item 11
Five figures: a square, a hexagon, an octagon, a decagon and a pentagon. Which is the odd one out?
The pentagon. Every other figure has an even number of sides.
The habit. Count before you look. Side counts, element counts and enclosed regions are checkable in a second and settle a large share of classification items.
Item 12
Five figures, each containing dots: a triangle with 3, a square with 4, a pentagon with 5, a hexagon with 6, a heptagon with 6.
The heptagon is the odd one out. In every other figure the number of dots equals the number of sides.
Why this is a step up. The property is a relationship between two features, not a feature. Checking each dimension separately would never find it.
Item 13
Four figures have a vertical line of symmetry; one does not. The shapes are otherwise unrelated.
The asymmetric figure is the answer, and symmetry is the dimension people check last if at all.
Add it to your list. Shape, count, shading, position, rotation, size — and symmetry.
Item 14
Five figures. Four have rotational symmetry of order two — they look identical after a 180° turn. One does not. Their shading varies with no pattern at all.
The answer is determined by the symmetry, not the shading. The shading is deliberate noise.
The lesson. Not every varying feature is part of the rule. Test writers include irrelevant variation specifically to absorb your attention.
Item 15
Five closed line figures. Four enclose exactly two separate regions; one encloses three.
The three-region figure is the odd one out. Enclosed regions — "holes" — are a standard dimension and among the least often checked.
Family 4: Matrices
Item 16
A 3 × 3 grid of dot counts. Row 1 reads 1, 2, 3. Row 2 reads 2, 3, 4. Row 3 reads 3, 4, and the last cell is missing.
Five. Counts increase by one across each row and down each column, and both readings agree.
Always check both. When a row rule and a column rule agree, your answer is confirmed twice.
Item 17
In a 3 × 3 grid, the rows are circles, squares and triangles from top to bottom. The columns are white, grey and black from left to right. The bottom-right cell is missing.
A black triangle. Rows control shape, columns control shading, and the two rules are independent.
Item 18
In each row of a 3 × 3 grid, the third cell contains the lines from the first and second cells, except that any line appearing in both is removed.
Row 3, cell 1 has a vertical and a horizontal line. Cell 2 has a horizontal and a diagonal line. What is in cell 3?
A vertical and a diagonal line. The horizontal appears in both and therefore cancels.
Learn this one by name. It is a standard matrix rule, and the "shared elements cancel" variant catches people who assume everything simply combines.
Item 19
A figure rotates 45° clockwise from each cell to the next, reading left to right and continuing onto the row below. The ninth cell is missing.
It is identical to the first cell. Eight steps of 45° make a full 360° turn.
The trap. Assuming an answer must look different from something already on the grid. Cyclic rules return to the start, and a repeat is often correct.
Item 20
Each row and each column of a 3 × 3 grid contains a circle, a square and a triangle exactly once. Row 3 shows a circle then a square. Column 3 already contains a circle and a square in the rows above.
The missing cell is a triangle — required by the row and by the column independently.
The name for it. Distribution of three: each element appears once per row and once per column. It is one of the most common matrix rules and reduces the item to elimination.
How Long Should I Take Per Question?
Divide the stated time limit by the number of items, and treat that as your ceiling rather than your target — the easy items must subsidise the hard ones.
Employer abstract tests are usually tight enough that finishing every item is not the expectation, which is by design. The length of ours is shown on its own page.
The practical rule: if two full passes through the dimensions have produced nothing, mark the item and move on. Coming back with a fresh view costs seconds; grinding costs the items you never reach.
Are These the Same as the Real Test?
No. These are teaching items chosen because they can be stated in words. A real abstract test is figural throughout, and the figures carry a lot of what these descriptions have to spell out.
The rules transfer completely. Rotation, accumulation, alternation, shared-element cancellation, distribution of three and the mirror-image distractor are the same on any paper you sit.
What if You Got Most of These Wrong?
Check which ones, because the four families fail for different reasons and only some of them are about reasoning.
- Series errors are usually a missed second rule. One rule was found, the item had two.
- Transformation errors are usually mirroring, or a rule inferred from a single example.
- Classification errors are usually an unchecked dimension — symmetry and enclosed regions above all.
- Matrix errors are usually reading rows without reading columns, when the two together would have confirmed the answer.
Format familiarity accounts for a great deal on a first attempt. A poor score the first time you meet these items is weak evidence about anything except how new they are to you.