For A town's ice-cream sales and sunburn reports rise together; claim that ice cream causes sunburn, identify the best logical assessment.
Correct answer: A
Correlation alone does not establish direct causation.
Reasoning
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Evaluate the two proposed answers. Which are supported? I. A proposal recommends streetlights because crashes mostly occur after dark — the best logical assessment: The reasoning assumes lighting can reduce the relevant crash risk. II. A price falls from 100 to 80 and then rises to 100; claim of equal percentage changes — the best logical assessment: A single counterexample refutes the universal claim.
Correct answer: D
I is correct: A proposal recommends streetlights because crashes mostly occur after dark → The reasoning assumes lighting can reduce the relevant crash risk. The intervention must address a cause of the problem. II is incorrect: A price falls from 100 to 80 and then rises to 100; claim of equal percentage changes → The claim is false because the percentage bases differ. The fall is 20%, while the rise is 25% of 80.
Evaluate the two proposed answers. Which are supported? I. Two sets overlap, but neither contains the other — the best logical assessment: Some elements belong to both and some are exclusive to each. II. Finding rectangle area when only its perimeter is 20 cm is known — the best logical assessment: Insufficient information.
Correct answer: A
I is correct: Two sets overlap, but neither contains the other → Some elements belong to both and some are exclusive to each. Overlap does not imply complete inclusion. II is correct: Finding rectangle area when only its perimeter is 20 cm is known → Insufficient information. Different side pairs can have the same perimeter and different areas.
For A rule claims every parcel is under 2 kg; one parcel weighs 3 kg, identify the best logical assessment.
Correct answer: D
One violating instance is enough to disprove an all-statement.
Evaluate the two proposed answers. Which are supported? I. A report says 8 of 10 users improved but gives no initial selection method — the best logical assessment: Selection bias remains possible. II. An argument attacks a speaker's clothing instead of the evidence — the best logical assessment: False dilemma.
Correct answer: B
I is correct: A report says 8 of 10 users improved but gives no initial selection method → Selection bias remains possible. How participants were chosen affects generalisability. II is incorrect: An argument attacks a speaker's clothing instead of the evidence → Ad hominem diversion. The personal characteristic does not refute the claim's support.
For A conclusion repeats its premise without independent support, identify the best logical assessment.
Correct answer: C
The supposed proof assumes what it seeks to establish.
Evaluate the two proposed answers. Which are supported? I. A training group's scores improve with no comparison group — the best logical assessment: The universal conclusion exceeds the observations. II. A survey asks only gym members whether residents exercise daily — the best logical assessment: The sample may be unrepresentative.
Correct answer: B
I is incorrect: A training group's scores improve with no comparison group → Other changes could explain the improvement. A before-after change alone does not isolate the training effect. II is correct: A survey asks only gym members whether residents exercise daily → The sample may be unrepresentative. Gym members are more likely to exercise than the general population.
Evaluate the two proposed answers. Which are supported? I. Finding x from x+y=10 alone with real x and y — the best logical assessment: Insufficient information. II. Two sets overlap, but neither contains the other — the best logical assessment: Some elements belong to both and some are exclusive to each.
Correct answer: D
I is correct: Finding x from x+y=10 alone with real x and y → Insufficient information. Many ordered pairs satisfy one equation. II is correct: Two sets overlap, but neither contains the other → Some elements belong to both and some are exclusive to each. Overlap does not imply complete inclusion.
For A proposal recommends streetlights because crashes mostly occur after dark, identify the best logical assessment.
Correct answer: A
The intervention must address a cause of the problem.
Evaluate the two proposed answers. Which are supported? I. Finding the number of sides of a regular polygon from exterior angle 45 degrees — the best logical assessment: Sufficient information. II. An argument attacks a speaker's clothing instead of the evidence — the best logical assessment: Ad hominem diversion.
Correct answer: B
I is correct: Finding the number of sides of a regular polygon from exterior angle 45 degrees → Sufficient information. The number is 360/45=8. II is correct: An argument attacks a speaker's clothing instead of the evidence → Ad hominem diversion. The personal characteristic does not refute the claim's support.
For A report says 8 of 10 users improved but gives no initial selection method, identify the best logical assessment.
Correct answer: C
How participants were chosen affects generalisability.
Evaluate the two proposed answers. Which are supported? I. A witness claims no black swans exist after seeing only white swans — the best logical assessment: The universal conclusion exceeds the observations. II. A choice is presented as only A or B when C is feasible — the best logical assessment: Selection bias remains possible.
Correct answer: D
I is correct: A witness claims no black swans exist after seeing only white swans → The universal conclusion exceeds the observations. A limited sample cannot establish that no counterexample exists. II is incorrect: A choice is presented as only A or B when C is feasible → False dilemma. The argument incorrectly restricts the available alternatives.
For A price falls from 100 to 80 and then rises to 100; claim of equal percentage changes, identify the best logical assessment.
Correct answer: B
The fall is 20%, while the rise is 25% of 80.
Evaluate the two proposed answers. Which are supported? I. Two events cannot occur together but one of them must occur — the best logical assessment: They are mutually exclusive and collectively exhaustive. II. Finding a person's exact age given only that the person is older than 18 — the best logical assessment: Insufficient information.
Correct answer: D
I is correct: Two events cannot occur together but one of them must occur → They are mutually exclusive and collectively exhaustive. Exactly one of the two must occur. II is correct: Finding a person's exact age given only that the person is older than 18 → Insufficient information. Many ages satisfy the inequality.
For An argument attacks a speaker's clothing instead of the evidence, identify the best logical assessment.
Correct answer: B
The personal characteristic does not refute the claim's support.
Evaluate the two proposed answers. Which are supported? I. A training group's scores improve with no comparison group — the best logical assessment: Other changes could explain the improvement. II. Two sets overlap, but neither contains the other — the best logical assessment: Ad hominem diversion.
Correct answer: D
I is correct: A training group's scores improve with no comparison group → Other changes could explain the improvement. A before-after change alone does not isolate the training effect. II is incorrect: Two sets overlap, but neither contains the other → Some elements belong to both and some are exclusive to each. Overlap does not imply complete inclusion.
Evaluate the two proposed answers. Which are supported? I. A choice is presented as only A or B when C is feasible — the best logical assessment: False dilemma. II. A conclusion repeats its premise without independent support — the best logical assessment: Circular reasoning.
Correct answer: C
I is correct: A choice is presented as only A or B when C is feasible → False dilemma. The argument incorrectly restricts the available alternatives. II is correct: A conclusion repeats its premise without independent support → Circular reasoning. The supposed proof assumes what it seeks to establish.
For Finding the number of sides of a regular polygon from exterior angle 45 degrees, identify the best logical assessment.
Correct answer: B
The number is 360/45=8.
Evaluate the two proposed answers. Which are supported? I. A price falls from 100 to 80 and then rises to 100; claim of equal percentage changes — the best logical assessment: Sufficient information. II. A report says 8 of 10 users improved but gives no initial selection method — the best logical assessment: The claim is false because the percentage bases differ.
Correct answer: D
I is incorrect: A price falls from 100 to 80 and then rises to 100; claim of equal percentage changes → The claim is false because the percentage bases differ. The fall is 20%, while the rise is 25% of 80. II is incorrect: A report says 8 of 10 users improved but gives no initial selection method → Selection bias remains possible. How participants were chosen affects generalisability.
For Two events cannot occur together but one of them must occur, identify the best logical assessment.
Correct answer: A
Exactly one of the two must occur.
Evaluate the two proposed answers. Which are supported? I. Finding x from x+y=10 and x−y=2 together — the best logical assessment: A common cause such as hot sunny weather may explain both. II. Finding a person's exact age given only that the person is older than 18 — the best logical assessment: Insufficient information.
Correct answer: C
I is incorrect: Finding x from x+y=10 and x−y=2 together → Sufficient information. Adding gives 2x=12, so x is uniquely 6. II is correct: Finding a person's exact age given only that the person is older than 18 → Insufficient information. Many ages satisfy the inequality.
For A claim says a policy is correct solely because many people support it, identify the best logical assessment.
Correct answer: D
Popularity does not by itself establish truth or effectiveness.
Evaluate the two proposed answers. Which are supported? I. A choice is presented as only A or B when C is feasible — the best logical assessment: Selection bias remains possible. II. A training group's scores improve with no comparison group — the best logical assessment: Other changes could explain the improvement.
Correct answer: A
I is incorrect: A choice is presented as only A or B when C is feasible → False dilemma. The argument incorrectly restricts the available alternatives. II is correct: A training group's scores improve with no comparison group → Other changes could explain the improvement. A before-after change alone does not isolate the training effect.
For Finding rectangle area given length 6 cm and width 4 cm, identify the best logical assessment.
Correct answer: D
Multiplying the two dimensions uniquely determines area.
Evaluate the two proposed answers. Which are supported? I. A report says 8 of 10 users improved but gives no initial selection method — the best logical assessment: Insufficient information. II. Two events cannot occur together but one of them must occur — the best logical assessment: Other changes could explain the improvement.
Correct answer: B
I is incorrect: A report says 8 of 10 users improved but gives no initial selection method → Selection bias remains possible. How participants were chosen affects generalisability. II is incorrect: Two events cannot occur together but one of them must occur → They are mutually exclusive and collectively exhaustive. Exactly one of the two must occur.