Question 1
Which argument is most similar to the flaw of inferring broad conclusions from a small, unrepresentative sample?
Correct Answer:
Concluding a country will have a large population increase because a city observed one-time growth.
Explanation:
Hasty generalization is at play here: drawing a broad conclusion from a small, unrepresentative sample. Concluding that the country will have a large population increase based on growth seen in a single city takes a one-off, local observation and extends it to a national scale without enough data from other cities or longer time periods. The city could be experiencing temporary factors that don’t apply nationwide, so this leap to a global claim relies on insufficient evidence. The other scenarios involve more limited or different kinds of evidence. A pilot study showing positive results is a preliminary step; it’s understood that findings from a small study need to be tested with larger, more representative samples before making wide claims. A single patient with a side effect is anecdotal and signals a possible issue, not a definitive rule about all drugs. And a product well-rated at one retailer only shows popularity within that retailer’s audience, not across all markets. All of those involve small samples or limited contexts, but the clearest, most sweeping leap to a broad conclusion from a tiny, nonrepresentative sample is the country example.
Question 2
If P ∨ Q and Q ∨ R, what can be concluded about P and R?
Correct Answer:
P and R have the same truth value
Explanation:
This question tests how chaining biconditionals works. If P is true exactly when Q is true, and Q is true exactly when R is true, then P is true exactly when R is true. In other words, P and R share the same truth value, so P ∨ R holds. That means both directions are true: P implies R and R implies P. An example helps: if P is true, Q is true, and R is true; if P is false, Q is false, and R is false. Therefore, the correct conclusion is that P and R have the same truth value.
Question 3
Two fair coins are flipped. What is P(at least one head)?
Correct Answer:
0.75
Explanation:
When two fair coins are flipped, each flip has two equally likely outcomes, and the flips are independent, so there are four equally likely result pairs: heads-heads, heads-tails, tails-heads, and tails-tails. The event “at least one head” occurs in the first three pairs, but not in tails-tails. That’s 3 favorable outcomes out of 4 total, giving a probability of 3/4, which is 0.75. Another way to see it is the complement: the only way to have no heads is tails-tail, which has probability 1/4, so at least one head is 1 − 1/4 = 3/4 = 0.75.
Question 4
All A are B; No B are C. What is necessarily true about A and C?
Correct Answer:
No A are C
Explanation:
Understanding how set relationships translate to what must be true is key here. “All A are B” means A is entirely inside B (A ∨ B). “No B are C” means B has no elements in common with C (B ∨ C = ∨). Since A is a subset of B and B has no elements in C, A cannot have any elements in C either. Put another way, there’s no overlap between A and C. So the only necessarily true statement is that no A are C. Because A lies within B and B doesn’t touch C, any claim that some A are C, or that all A are C, or that A and C share elements, would contradict the given conditions.
Question 5
Which of the following, if true, would most weaken the apparent conflict in the described system?
Correct Answer:
The system's parameter changes over time.
Explanation:
The key idea is that if the system changes over time, its behavior at one moment may differ from its behavior at another, so what looks like a contradiction under a fixed set of parameters can actually be a reflection of evolving conditions. If a parameter drifts, results obtained at different times aren’t testing the same situation, which means the apparent conflict isn’t a true mismatch in the model but a result of not accounting for time dependence. That makes the conflict weaken because it suggests the system isn’t stationary rather than that the conclusions are wrong. The other options don’t address this time-varying aspect: different collection conditions can create differences, but they don’t inherently reconcile a conflict; relying on a single experiment weakens confidence rather than the contradiction; and noisy but consistent data still supports a stable relationship rather than dissolving a contradiction.
Question 1
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Prepare with the Logical Reasoning STEM Practice Test practice quiz. This question bank includes 10 questions covering argument, reasoning, program, logical, and stem. Use it to review important concepts, identify knowledge gaps, and build confidence for the related exam, course, or assessment.

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Logical Reasoning STEM Practice Test

This practice set contains 10 questions from the matching question bank and focuses on argument, reasoning, program, logical, and stem. Work through each question carefully, review the provided solutions, and revisit topics that need more study before your next attempt.

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