Logical reasoning test practice
Logical reasoning questions state a few premises and ask which conclusion follows with certainty. The premises are often abstract or unfamiliar so that prior knowledge cannot help. Only a conclusion that must be true counts; one that is merely plausible does not.
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Time pressure
Each item is quick once the structure is recognised, and slow if you argue from the content. Time is usually tight across the whole set, so recognising the pattern early matters more than care over any single item.
Heuristics that transfer
- Translate each premise into a plain form: all A are B, no A are B, if P then Q.
- From "if P then Q", only two moves are valid: P therefore Q, and not Q therefore not P.
- Affirming the consequent and denying the antecedent are the most common traps; name them when you see them.
- Draw a quick circle diagram for "all", "some" and "no" statements.
- Necessary means required; sufficient means enough. Keep the direction of the arrow straight.
Three worked examples
Try each question before opening the answer.
Example 1
No robots are sentient. All androids are robots. Which conclusion follows with certainty?
Show the answer and worked method
Correct answer: No androids are sentient
The principle
Categorical syllogism: if no B are C and all A are B, then no A are C.
Steps
- Premise 1: No robots are sentient (Robots and Sentient things are disjoint sets).
- Premise 2: All androids are robots (Androids is a subset of Robots).
- Since Androids sits entirely inside Robots, and Robots shares nothing with Sentient things, Androids can share nothing with Sentient things either.
- Therefore no androids are sentient.
Heuristic to carry forward
When a subset (androids) sits inside a set (robots) that is wholly excluded from a third set (sentient things), the subset is excluded from that third set too.
Why each other answer is wrong
- No robots are androids
- Confuses the subset relation of premise 2 with its converse; premise 2 already states all androids are robots.
- Some androids are sentient
- Contradicts the disjointness established by premise 1 combined with premise 2; this would require some robots to be sentient.
- All sentient things are androids
- Reverses the direction of the valid conclusion, an illicit conversion.
Example 2
If the alarm is faulty, the light flashes red. The light is not flashing red. What follows with certainty?
Show the answer and worked method
Correct answer: The alarm is not faulty
The principle
Modus tollens: from 'if P then Q' and 'not Q', we can validly infer 'not P'.
Steps
- The rule is: faulty alarm (P) implies red flashing light (Q).
- We are told the light is not flashing red, i.e. not Q.
- If the alarm were faulty, the light would have to flash red (by the rule); since it does not, the alarm cannot be faulty.
- Therefore the alarm is not faulty.
Heuristic to carry forward
Given 'if P then Q' and 'not Q', validly conclude 'not P' (modus tollens/contrapositive); never conclude from 'not P' alone.
Why each other answer is wrong
- The light will flash a different colour
- Introduces information about colour not supported by the rule, which only mentions red versus not-red.
- The alarm is faulty
- Directly contradicts the valid modus tollens conclusion.
- No certain conclusion can be drawn about the alarm
- Understates the certainty available; modus tollens does yield a certain conclusion here.
Example 3
If it rains, the match is postponed. It did not rain. Which conclusion follows with certainty?
Show the answer and worked method
Correct answer: No certain conclusion can be drawn
The principle
Denying the antecedent: from 'if P then Q' and 'not P', nothing certain follows about Q.
Steps
- The rule only tells us what happens if it rains; it says nothing about what happens if it does not rain.
- The match could be postponed for another reason (for example a pitch inspection) even without rain.
- It did not rain (not P) does not let us infer 'not Q'; that inference denies the antecedent, which is invalid.
- So the status of the match cannot be determined with certainty from this information alone.
Heuristic to carry forward
Denying the antecedent ('not P, so not Q') is invalid; a sufficient condition for Q does not make P necessary for Q.
Why each other answer is wrong
- The match was not postponed
- Wrongly infers 'not Q' from 'not P', the denying-the-antecedent fallacy.
- The match was postponed
- Wrongly treats rain as the only possible cause of postponement.
- It rained shortly before kick-off
- Directly contradicts the given premise that it did not rain.
Every question in the bank has a verified answer key and a worked solution.
Keep going
Related guides: Modus tollens and valid inference, The pigeonhole principle, or all worked examples.
Other test types: Numerical reasoning, Verbal reasoning, Abstract reasoning. For timed shape matching, try Shapefinder.