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Intelligence

Logical Reasoning

A 9-item logical reasoning assessment from the ICAR battery (Letter and Number Series). Measures your ability to detect patterns in sequences.

Measures 3 cognitive domains

10 min · 9 questions

Instructions

For each sequence, identify the next item in the pattern and select it from the options. If you do not know the answer, select "I don\x27t know".

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About the Logical Reasoning Test

Logical reasoning, in the sense this test measures, is inductive reasoning: you are shown a sequence that follows a hidden rule, and you have to discover the rule and apply it to find what comes next. It is the same mental move whether the sequence is built from numbers or letters - notice the regularity, formulate the rule that generates it, and project it forward one step. That act of rule discovery is a core component of general reasoning ability.

The 9 items are drawn from the Letter and Number Series of the ICAR, a well-documented public-domain cognitive battery, and the test takes about 10 minutes. Each sequence offers several options, with an explicit "I don't know" choice so you are not forced to guess. The test is free to take, and your result is placed on a normed scale against the adult population. Your free result shows your band on the population curve; the exact normed score and percentile come with the detailed report.

Items
9
Duration
~10 min
Format
Letter and number series, multiple choice with an explicit "I don't know" option
Free result
Your result band shown on the bell curve, free after completion
Full report
A detailed report interpreting your inductive-reasoning score and what it indicates about your reasoning ability ($9.99)

What it measures

The test measures inductive reasoning: the ability to infer a general rule from specific instances and extend it to new cases. Series-completion tasks are a classic and well-validated way to tap this, because each item forces the same sequence of cognitive steps - encode the elements, detect the relation between them, generalize it into a rule, and use the rule to predict the next element. Letter series add a small wrinkle over number series, since the solver works with ordinal position in the alphabet rather than direct arithmetic, but the underlying reasoning demand is the same.

Inductive, rule-based reasoning of this kind sits close to the general factor, g, and contributes to fluid intelligence, so a series-reasoning score is a meaningful narrow indicator of broad cognitive ability. It is narrow by design, however: this test covers sequence induction specifically, not the full breadth of reasoning. A strong score means you discover and apply rules efficiently; it does not, on its own, fix an overall IQ.

  • Sequence detectionSpotting the regularity in a series of numbers or letters - which elements change, and how.
  • Rule inductionFormulating the general rule that generates the sequence, from differences to alternating or nested patterns.
  • Rule applicationProjecting the inferred rule one step forward to select the element that correctly continues the series.

The science and validity

Series-completion and other inductive-reasoning tasks have a long pedigree in the measurement of intelligence; Carroll's factor-analytic survey places inductive reasoning among the well-established second-stratum abilities under general intelligence, and decades of research confirm that reasoning measures are strong, stable markers of g. The specific items here come from the ICAR, an open, publicly documented battery developed precisely so that reasoning can be measured with transparent, freely available content rather than proprietary items.

Scores here are reported on the familiar IQ metric (population mean of 100, standard deviation of 15) using norms from adult test-taker data, and like all our online tests they are capped at 160, because an unsupervised online instrument cannot certify extreme values. Keep the scope in mind: this is a single-domain test of sequence reasoning, so the result is best read as a focused indicator of inductive ability rather than a full IQ. For a broader estimate, take our multi-domain battery; for high-stakes purposes, only an individually supervised, professionally administered test is appropriate.

References

  1. Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. Cambridge University Press.
  2. Deary, I. J. (2012). Intelligence. Annual Review of Psychology, 63, 453-482.
  3. Condon, D. M., & Revelle, W. (2014). The International Cognitive Ability Resource: Development and initial validation of a public-domain measure. Intelligence, 43, 52-64.

Read more about our standards: How our tests are built and validated.

Sample items

  • Number series: 4, 7, 13, 25, 49, ... which option comes next?Illustrative number-series item (not a scored item) - each term roughly doubles and steps down by one (x2 - 1).
  • Letter series: A, C, F, J, O, ... which letter continues the pattern?Illustrative letter-series item (not a scored item) - the gap grows by one position each step (+2, +3, +4, +5).
  • Alternating series: 2, 20, 4, 17, 6, 14, ... which pair of values comes next?Illustrative interleaved-series item (not a scored item) - two sequences are woven together, one rising and one falling.

Frequently asked questions

What does a logical reasoning test measure?

This test measures inductive reasoning: your ability to discover the hidden rule behind a sequence and use it to predict what comes next. Each item makes you encode the elements, detect the relationship between them, generalize a rule, and apply it. That rule-discovery process is a core component of general reasoning ability and correlates strongly with broad cognitive ability.

Is the logical reasoning test free?

Yes. Taking the test is free, with no account required to start, and your free result shows your result band on the population curve. The optional paid report adds the exact normed score and percentile, plus an interpretation of what your inductive-reasoning score means in practice.

Are these the same as the puzzles in IQ tests?

Yes, series completion is one of the classic IQ item types, and it appears in the logical-series section of our full battery as well. This test focuses on that single format in depth using items from the public-domain ICAR. A full IQ test combines series reasoning with verbal, abstract, and spatial tasks for a broader overall estimate.

How do I solve a number or letter series?

Look first at how consecutive elements differ. If the difference is constant, the rule is a simple step; if the difference itself changes, look for a pattern in the differences, or for two interleaved sequences, or for a multiply-then-adjust rule. For letters, convert to alphabet positions and reason about the gaps. The skill the test rewards is trying these candidate rules systematically rather than guessing.

How is this different from the abstract reasoning test?

Both measure inductive rule discovery, but in different material. Logical reasoning here uses symbolic sequences - numbers and letters - while abstract reasoning uses visual matrix figures. The underlying ability overlaps heavily, so the two scores tend to agree; choose the format that suits you, or take both for a fuller picture of how you reason across symbolic and visual content.

How long does it take?

About 10 minutes for all 9 items. The series grow harder as you progress, so concentration matters; take it in one quiet sitting for the most representative result.

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