Free Logical Reasoning Test

How logical reasoning is tested, and how to read your score

Logical reasoning is the narrowest and most teachable of the reasoning skills, which is precisely why so many employers test it. It asks a single question about you: given a set of statements you have agreed to treat as true, can you say what must follow, what cannot follow, and what the statements simply leave open? Nothing on this page depends on vocabulary, general knowledge, arithmetic or cultural background. The subject matter is deliberately dull — gates, shipments, badges, cups on a shelf — because the moment an item is about something you have opinions on, your opinions start doing the work instead of your reasoning.

Conditionals and the one-way street

Roughly a third of the items are conditional statements: sentences of the form if this, then that. A conditional is a one-way street, and almost every mistake people make on this format comes from driving down it backwards. "If the alarm is armed, the door is locked" tells you that an armed alarm guarantees a locked door. It does not tell you that a locked door guarantees an armed alarm — the door might be locked for a dozen other reasons. What the statement does license is the contrapositive: if the door is not locked, the alarm cannot have been armed, because an armed alarm would have locked it. Getting comfortable with that flip is worth more on this test than any other single habit.

Two phrasings deserve special attention because they trip up even careful readers. "Only if" reverses the direction most people expect: "the gate opens only if the badge is valid" means an open gate guarantees a valid badge, not the other way round. And "unless" behaves like "if not": "unless it rains, the market stays open" tells you that no rain means an open market, so a closed market forces you back to rain. Neither phrase is a trick in the unfair sense. They are ordinary English, and the test simply refuses to let you skim them.

Negation, which is where sloppiness shows

Several items hand you a denial rather than an assertion and ask what survives. Denying a conjunction is weak: "it is not true that both the report was filed and the fee was paid" leaves you knowing only that at least one of the two failed, not which one, and certainly not that both failed. Denying a disjunction is strong: if "either Nora or Priya attended" is false, then neither of them attended, because a single attendee would have made the original sentence true. Quantifiers flip in the same asymmetric way. The denial of "all the lamps are working" is the modest claim that at least one lamp is not working — not the sweeping claim that none of them work — while the denial of "no student passed" is the equally modest claim that at least one did.

Ordering puzzles

Ordering items give you fragments of a sequence — who is taller than whom, which day follows which, which cup sits beside which — and ask for a position. The efficient method is to write the constraints as a chain rather than to reason about them one at a time in your head. Three comparisons involving four people usually collapse into a single line the moment you draw them. The important discipline is noticing when the chain has a gap in it: if you know Anna finished before Ben and Dan finished after Anna, you know nothing at all about how Dan and Ben compare, and any confident answer about second place is invented. Some ordering items on this test are fully determined and some are not, and the test scores your ability to tell the two apart as much as your ability to solve the first kind.

Set relations

The last family concerns membership: all, some, and no. The rules here are few and worth memorising. "All A are B" combined with "no B are C" gives you "no A are C". "Some A are B" combined with "all B are C" gives you "some A are C". But "all A are B" combined with "some B are C" gives you nothing whatsoever about A, because the C-ish part of B may lie entirely outside A. One genuinely useful fact is that "some" is symmetrical: if some teachers are cyclists then some cyclists are teachers, and that harmless-looking conversion is a valid inference that many test takers wrongly reject because it feels too easy to be the answer.

Reading your score

Your raw total out of twenty is mapped onto the familiar scale where 100 is average and fifteen points is one standard deviation. With twenty items each answer is worth several points, so read the number as the centre of a band rather than as a precise value.

How to score better, honestly

Unlike a matrix test, this format rewards practice for legitimate reasons: the traps are finite, and once you have seen the affirmed consequent three times you stop falling for it. Read every premise twice before looking at the options, since the options are written to sound plausible and will steer you if you meet them with an open mind. Refuse to import knowledge — if a premise says something you believe is false, accept it anyway for the length of the item. When a question resists you, check whether it is asking what must be true rather than what is likely; the gap between those two is where most wrong answers live. And answer every item, because nothing is deducted for a wrong guess. If you want a version of the same skill stripped of language entirely, the culture fair IQ test asks for pattern induction instead of deduction, and comparing the two scores tells you which half of your reasoning is doing the heavier lifting.