Free logical reasoning test

What logical reasoning is

In psychology, deductive reasoning is reasoning in which a conclusion is shown to follow necessarily from premises (APA Dictionary: deductive reasoning). It is the kind of thinking that says “if these things are true, this other thing must be true,” and it is how scientists derive predictions from general theories. Our explainer on logical reasoning goes through the theory. This page is the hands-on side: a test, worked examples and a practice plan.

The classic lab task is the syllogism: two premises that share a term, leading to a conclusion. Each statement takes one of four forms (All A are B, Some A are B, No A are B, Some A are not B) (Khemlani & Johnson-Laird, 2012), and only 24 of the possible combinations are formally valid (APA Dictionary: syllogism). People find this harder than it sounds. On the standard abstract version of the Wason selection task, where you choose which cards to turn over to test a rule, only around 10% of people pick the correct pair (Sperber, Cara & Girotto, 1995); most fail by not checking the cards that could break the rule (APA Dictionary: Wason selection task). Belief bias adds another trap: people tend to accept conclusions because they sound believable rather than because they follow (APA Dictionary: belief bias).

In the Cattell-Horn-Carroll model, deductive reasoning is a narrow ability called general sequential reasoning, part of fluid reasoning (Gf) (McGrew, 2023). Dual-process accounts hold that the system we use for abstract and hypothetical thinking is limited by working memory capacity and correlates with general intelligence (Evans, 2003). That link has limits, though: across seven studies, many classic thinking biases, such as framing and anchoring, were uncorrelated with cognitive ability, while avoiding a few others, including belief bias, was (Stanovich & West, 2008).

So why does this test use pictures? Nonverbal logic items check the same habit, exact rule-following, without depending on reading speed or vocabulary. Figure analogies (A is to B as C is to ?) are one of the most typical formats in reasoning tests (Primi et al., 2013). Strictly, they mix two kinds of thinking: you induce the change from the first pair, then apply it to the second with no room for approximation. The page on inductive vs deductive reasoning explains the difference in more detail.

How logical reasoning is measured

Clinical batteries fold logical reasoning into fluid reasoning. The WAIS-5 has a Fluid Reasoning index measured by Matrix Reasoning and Figure Weights (Pearson: WAIS-5 overview). The Stanford-Binet 5 lists Fluid Reasoning first among its five factors (PRO-ED: SB5). On the Woodcock-Johnson, deductive reasoning is measured by the Analysis-Synthesis test (McGrew, 2023). The ETS kit of reference tests measures a Logical Reasoning factor with a Nonsense Syllogisms Test, Diagramming Relationships, an Inference Test and Deciphering Languages (ETS: Kit of Factor-Referenced Cognitive Tests).

Nonverbal tests use analogies directly. The CTONI-2 measures analogical reasoning, categorical classification and sequential reasoning with pictures and geometric designs (PRO-ED: CTONI-2), and the UNIT2 has an Analogic Reasoning subtest (PRO-ED: UNIT2). Matrix tests such as Raven's Progressive Matrices use the same skill across rows and columns.

Logic is also a staple of hiring tests. The CCAT has math and logic questions alongside verbal and spatial ones (Criteria: CCAT prep). The PI Cognitive Assessment covers simple math, basic logic and language comprehension in 50 questions and 12 minutes, and reports an Abstract Reasoning subscore (Predictive Index: Cognitive Assessment). The Wonderlic timed section has 50 questions in 12 minutes (Wonderlic: FAQ). The overview of types of IQ tests shows where each one fits.

The ten questions above are seven figure analogies and three 3x3 matrices, easy to hard. The analogies use turns, flips, fill changes, shape swaps, and small parts added, removed or moved. The matrices use a row rule, a rule where each shape and fill appears once per row and column, and, in the hardest grid, lines that combine or cancel.

Worked examples: easy, medium and hard

In the easy analogy only one thing changes between the first two panels. Name it in words before you look at the options. A flip is not a turn: in a left-right flip, a shape pointing left ends up pointing right, and nothing else moves.

The medium analogy has two changes at once, a turn of the whole figure and a new fill on the large shape. Find both before you choose. Watch the small shape too: a half turn of the whole figure carries it to the opposite side, so an option that turns the large triangle but leaves the small diamond where it was is wrong.

The hard analogy combines removing parts with flipping the whole figure upside down. Do the steps in order on the third panel: take away what was removed, then flip what is left. Check that “nothing else changes” really holds for the size and fill.

Common mistakes on logic puzzles

• Stopping after one change. Medium and hard analogies combine two changes. An option that applies only the turn, or only the fill, is built to catch you.
• Confusing a flip with a turn. A half turn and an upside-down flip can look alike on a symmetric shape but differ on anything with a marked side. Check where the small parts end up.
• Describing the change loosely. “It got different” is not a rule. “The large shape turned a half turn and became hatched” is. Vague rules let wrong options through.
• Looking for confirmation instead of counterexamples. This is the selection-task error in picture form. Once you pick an option, ask what would make it wrong, and check that.
• Applying the change to the wrong part. If the small circles disappear between A and B, remove the small circles from C, not the shape that happens to sit in the same place.
• Reading matrices in one direction only. On the grids, a rule that fits the rows must also fit the columns. Check both before you commit.
• Trusting what looks right. Belief bias has a visual cousin: the option that looks neat and balanced is not always the one that follows the rule.

Pacing is the other half. Each question has its own 30-second ring and an unanswered question counts as missed. A workable rhythm is about ten seconds to name the change between A and B, ten to apply it to C in your head, and the rest to find the option that matches and rule out the near misses. If you are still unsure at about 20 seconds, pick the option that applies the most changes you found. A guess has a chance of being right; a blank does not.

One more habit helps on every format here: say the rule as a short sentence before you choose, such as “the whole figure turns a half turn and the large shape becomes hatched.” If you cannot say it, you have not found the rule yet, and any option you pick is a guess dressed up as an answer.

How to practice logical reasoning

Feedback is the best tool here. When people did repeated Wason selection tasks with feedback, they switched from picking cards that confirm the rule to picking possible counterexamples (Ragni, Kola & Johnson-Laird, 2018). Training also helps on analogy-style items: Klauer's model of inductive reasoning is assessed with item types including analogies and matrices, and a game-based program built on it for fifth graders produced a corrected effect size of .38 (Pásztor et al., 2022). A plan:

1. Learn to name changes. Work through the easy analogy puzzles and say the single change out loud before you check the answer.
2. Move to two-change items. The medium analogies use shape swaps or a turn plus a fill change. Write every change down for the first few.
3. Drill the hard set under time. The hard analogies combine two changes, such as removed or moved parts with a flip or turn, or a shape swap with a turn. Give yourself 30 seconds each.
4. Read the method. The figure analogies guide walks through every change type, and the analogy library has worked answers for all of them.
5. Cover the matrices too. Three of the ten questions here are grids. The matrix library and the abstract reasoning test drill them.
6. Mix formats. The cognitive ability test mixes number series, sequences, matrices, analogies and a rotation, closer to what a hiring test feels like.

Keep expectations honest. Retaking a cognitive test raises scores by about a quarter of a standard deviation on average, more with the same form (Hausknecht et al., 2007), and gains stop after about the third sitting (Scharfen, Peters & Holling, 2018). That is mostly familiarity with the format, which is useful before a real test but is not a change in reasoning ability. Reviews of chess, music and working memory training conclude that far transfer to general ability rarely occurs (Sala & Gobet, 2017).

Logical reasoning on the full IQ Octopus test

The full test has 25 items in five sections: Pattern Recognition (5), Abstract Reasoning (9), Spatial Reasoning (5), Quantitative Reasoning (3) and Logical Reasoning (3). The Logical Reasoning section uses figure analogies like the ones above. The matrix grids you practiced belong to the Abstract Reasoning section, the largest one, so the habit of checking rows and columns pays off there. In matrix research, item difficulty depends on both the type of rule and the number of rules (Lozano, Embretson & Revuelta, 2025), which is why harder items stack changes the way the hard analogy did.

A practice score out of ten is not an IQ. IQ is a deviation score that compares you with people your own age on a scale with a mean of 100 and a standard deviation of 15 (Wikipedia: Intelligence quotient). The full test generates fresh items for every attempt, scores all 25 answers with a Rasch model and reports an estimated IQ with a confidence range. Take the full IQ test when you are ready.