Logical Reasoning: Rules, Constraints and Counterexamples
Check finite rule families, alternating streams, letter-number pairs and ordering constraints without treating a short pattern record as a general intelligence score.
Read this full public learning guide before or after practice. It is identical for everyone. Your private on-page record separately shows correct, wrong and unanswered counts out of six; no percentile, employer cutoff or ability level is inferred.
Identify the stated rule family
- These original tasks use small written sequences, arithmetic rows and explicit ordering constraints. They do not reproduce a provider’s graphical item bank or adaptive test. A finite sequence can admit many imaginable continuations, so read the stated family: constant changes in differences, separate alternating streams, fixed letter steps, fixed multipliers or one operation from a specified set. The keyed answer follows those declared constraints rather than claiming a uniquely discoverable law of nature.
- This distinction matters when making new examples. If your proposed rule needs exceptions to fit early terms, check whether the prompt allows them. If two offered answers both satisfy every declared condition, the exercise needs repair rather than a story about which one feels more intelligent. In this bank, the rule families and finite answer sets make the selected continuation checkable against all supplied evidence.
Use differences only when allowed
- For a sequence whose consecutive differences increase by a fixed amount, write a second row of first differences. A fresh example is 2, 6, 12, 20: differences are 4, 6 and 8. Their constant increase of two gives the next difference ten and next term thirty. Check the same procedure at every earlier transition before using it to predict the missing term.
- Do not choose an option merely because it is close to an intuitive estimate or because one late pair happens to fit. An answer should carry a short witness: the complete difference row and the stated next operation. That witness helps separate a calculation slip from a rule-selection error. It also shows why alternative continuations outside the specified family do not invalidate the bounded exercise as written.
Split independent streams
- When odd and even positions follow separate rules, label positions before computing. For 5, 30, 9, 27, 13, 24, the odd stream rises by four and the even stream falls by three. The next odd term is seventeen. Mixing all adjacent differences would conceal the explicitly supplied two-stream structure. Write two short rows instead of holding both rules in memory while scanning the answer choices.
- The same method works for a letter stream paired with an independent number cycle. Track each feature separately and recombine at the required position. Check both components of every option; a distractor can have the right letter and wrong number. A short written position index is particularly helpful when the repeating cycles have different lengths, because the most recent whole pair need not be the unit that repeats next.
Check every component and every row
- For letter-number pairs, first specify the alphabet convention and whether wrapping is permitted. In this bank letters move forward without wrapping, while a separate fixed multiplier controls the numbers. For a fresh example, C2, F6, I18 uses a three-place letter step and multiplication by three; the next pair is L54. A rule that checks only the letters or only the numbers is incomplete.
- For arithmetic rows, test every permitted operation against every completed row. If addition alone fits two rows and the allowed set is addition, subtraction, multiplication and division, carry that same addition into the incomplete row. Do not invent powers, hidden constants or a different operation for each row. The finite operation set is part of the problem, just as important as the visible numerical values.
Build a constraint chain
- Ordering problems concern logical consequence rather than discovering a visual pattern. Translate each “left of” statement into an arrow, combine compatible arrows, and list every supplied object exactly once. With four objects in a complete strict chain, every position is fixed. Without a complete chain, some positions may remain undetermined; a plausible arrangement is not proof that it is the only permitted one.
- A useful check is to try constructing a counterexample. For example, if P must precede R and Q must also precede R, the relative order of P and Q is not fixed. Both P-Q-R and Q-P-R satisfy the statements. This fresh example contrasts with a complete chain. Checking an alternative valid arrangement protects you from assuming adjacency or an order the wording never supplied.
Practise pacing with an explicit record
- Timed mode gives six logical items four minutes, chosen by this site for this short written edition. It is not an official provider limit. A rough forty seconds per item is only a planning average. Start by identifying the permitted family, write one compact witness and check it against the earlier terms. If you cannot justify a choice, you can explicitly leave it unanswered and revisit within the active part.
- Finishing early or reaching the deadline locks that part; the next clock starts only with your explicit action. Untimed study removes the deadline while retaining the same evidence rules. Clock limits are practice conditions, not a speed norm or a certification that you worked without help. Record use of notes, fatigue and familiarity when comparing your own attempts, and follow actual invitation rules for a real assessment.
Review without turning counts into a label
- After all parts close, open each explanation and recreate its witness without relying on the option letter. For an error, ask whether you missed the family, mixed streams, checked only one component, overlooked a row or added an unstated constraint. Then build a small fresh example and one deliberate distractor. Explain why the distractor fails a stated condition, rather than merely saying it looks less regular.
- Your raw count out of six is not an IQ, calibrated reasoning level, percentile or hiring prediction. These parts have not been equated, so the smallest count does not diagnose a weakest ability. Repeated success can include memory for the fixed questions. This full public guide is identical for all readers and contains no private answer record; sharing its link shares only the learning material.