Abstract Reasoning Tests: The Rules Behind Pattern Questions, With 12 Practice Items

What abstract reasoning tests measure

Abstract reasoning is induction stripped to the bone: see a few examples, infer the rule, apply it to a new case. No vocabulary or arithmetic is needed beyond counting. Raymond Cattell, who introduced the split between fluid and crystallized intelligence in 1943, defined the fluid kind as the ability to solve novel reasoning problems. Abstract reasoning items are built to be novel.

A 1990 Carnegie Mellon study of matrix problems by Patricia Carpenter, Marcel Just and Peter Shell identified what separates strong performers: they induce more abstract relations, and they keep more sub-goals alive in working memory while they test them. Our guide to Raven's Progressive Matrices covers the best-known test of this kind.

Five formats you will meet

Some tests add symbol codes, where each symbol stands for an operation such as rotate or reflect, and the test taker works out the result of a string of them.

The variables that carry most rules

Test writers draw on a short list of variables. Check them in this order, because the first ones are the easiest to see:

• Number: how many shapes, sides, dots or lines.
• Position: where an element sits, and how it moves from frame to frame.
• Direction: which way an arrow or a figure points, and by how many degrees it turns.
• Shape: the type of figure, or a property such as enclosed areas or symmetry.
• Shading: black, white, gray, striped.
• Size: larger, smaller, or swapped between inner and outer figures.

The rules acting on those variables are just as few: steady change, alternation, cycling, adding two frames together, and cancelling what two frames share. Hard items combine two or three of them. For rotation and folding specifically, see our spatial reasoning test guide.

12 original abstract reasoning items

All twelve items were written for this page and are described in words. None is copied or adapted from a commercial test.

1. A dot sits in a square's corners in this order: top left, top right, bottom right, ?
   Answer: bottom left. The dot moves one corner clockwise each frame.
2. XOO, OXO, OOX, ?
   Answer: XOO. The X steps right one place and wraps back to the start.
3. White triangle, black square, white pentagon, ?
   Answer: black hexagon. Sides rise by one and the shading alternates.
4. Odd one out: a triangle holding one dot, a square holding two, a pentagon holding three, a hexagon holding five.
   Answer: the hexagon. The dots equal the sides minus two, so it should hold four.
5. Every box in Set A holds an odd number of shapes. Every box in Set B holds an even number. A new box holds two circles and three triangles. Where does it belong?
   Answer: Set A. It holds five shapes; the shape types are a distraction.
6. A large circle containing a small square becomes a large square containing a small circle. Apply the same change to a large triangle containing a small star.
   Answer: a large star containing a small triangle. Inner and outer shapes swap.
7. In a code, # means rotate 90 degrees clockwise and @ means mirror left to right. An arrow points up. Apply # then @. Where does it point?
   Answer: left. The rotation turns it to point right; the mirror reverses it.
8. ABBA, CDDC, EFFE, ?
   Answer: GHHG. Each block takes the next two letters and wraps them in mirror order.
9. A row has six cells numbered 1 to 6. A black token moves one cell right per frame; a gray token moves two. Both wrap from cell 6 back to cell 1. Frame 1: black in 1, gray in 2. Frame 2: black in 2, gray in 4. Frame 3: black in 3, gray in 6. Frame 4?
   Answer: black in 4, gray in 2. Gray moves from 6 past the end to 1, then on to 2.
10. Odd one out among the capital letters A, D, O, P and B.
    Answer: B. It encloses two spaces; the others enclose one.
11. An arrow points up and is solid. Next it points up-right and is outlined. Next it points right and is solid. What comes next?
    Answer: an outlined arrow pointing down-right. It turns 45 degrees clockwise per frame, and the fill alternates.
12. Dots stacked in triangles: 1, 3, 6, 10, ?
    Answer: 15. Each frame adds a new bottom row one dot longer than the last: plus 2, plus 3, plus 4, then plus 5.

A five-step method

1. Scan for the obvious change. Count first; number rules are the most common and the quickest to confirm.
2. Separate the elements. Track each moving part on its own, as in item 9, rather than the frame as a whole.
3. Name the rule in words. A rule you can state in one sentence is a rule you can test.
4. Predict, then look. Describe the answer before reading the options, so a plausible distractor cannot steer you.
5. Check every frame. A rule that fits three frames but not the fourth is the wrong rule.

What the UCAT decision says about coaching

The University Clinical Aptitude Test, used by UK medical and dental schools, announced that Abstract Reasoning would be withdrawn from the 2025 test. Its own analysis found the section had lower predictive validity than the others and high coachability. Candidate performance on it had risen over the previous decade while response times fell.

That is a rare public admission from a test owner: pattern items reward preparation more than most item types, and scores drift up as coaching spreads. The test now runs three cognitive subtests, Verbal Reasoning, Decision Making and Quantitative Reasoning, plus a situational judgement section. For the broader question of what a practiced score is worth, read are online IQ tests accurate.

What practice can and cannot do

Learning the variable list and the method above will raise a score, sometimes sharply, on a first encounter with this format. It does not raise the reasoning ability the test was designed to sample, which is exactly the UCAT's complaint. Treat practice as a way to remove surprise, not as a route to a higher IQ.

Our free IQ test is a practice screener that mixes pattern items with other formats; it is not a clinical measurement. To see what a score such as IQ 130 means, and what counts as a high IQ, start there. The full library is in our IQ guides hub, and mixed verbal, numerical and logic items are in IQ test questions and answers.

Editorial standard: IQ figures for historical figures are retrospective estimates and are labeled as such; scores for living people appear only when the person disclosed them or a reputable outlet reported them. Corrections: contact the editors.