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.
Reasoning
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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.
For Two sets overlap, but neither contains the other, identify the best logical assessment.
Correct answer: C
Overlap does not imply complete inclusion.
Evaluate the two proposed answers. Which are supported? I. A claim says a policy is correct solely because many people support it — the best logical assessment: Appeal to popularity. 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 claim says a policy is correct solely because many people support it → Appeal to popularity. Popularity does not by itself establish truth or effectiveness. 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 training group's scores improve with no comparison group, identify the best logical assessment.
Correct answer: C
A before-after change alone does not isolate the training effect.
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: Insufficient information. II. Finding rectangle area given length 6 cm and width 4 cm — the best logical assessment: They are mutually exclusive and collectively exhaustive.
Correct answer: D
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 incorrect: Finding rectangle area given length 6 cm and width 4 cm → Sufficient information. Multiplying the two dimensions uniquely determines area.
For Finding a person's exact age given only that the person is older than 18, identify the best logical assessment.
Correct answer: B
Many ages satisfy the inequality.
Evaluate the two proposed answers. Which are supported? I. Finding rectangle area given length 6 cm and width 4 cm — the best logical assessment: A single counterexample refutes the universal claim. II. Two events cannot occur together but one of them must occur — the best logical assessment: The universal conclusion exceeds the observations.
Correct answer: D
I is incorrect: Finding rectangle area given length 6 cm and width 4 cm → Sufficient information. Multiplying the two dimensions uniquely determines area. 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.
For A choice is presented as only A or B when C is feasible, identify the best logical assessment.
Correct answer: A
The argument incorrectly restricts the available alternatives.
Evaluate the two proposed answers. Which are supported? I. A rule claims every parcel is under 2 kg; one parcel weighs 3 kg — the best logical assessment: Other changes could explain the improvement. II. Finding rectangle area given length 6 cm and width 4 cm — the best logical assessment: Sufficient information.
Correct answer: C
I is incorrect: A rule claims every parcel is under 2 kg; one parcel weighs 3 kg → A single counterexample refutes the universal claim. One violating instance is enough to disprove an all-statement. II is correct: Finding rectangle area given length 6 cm and width 4 cm → Sufficient information. Multiplying the two dimensions uniquely determines area.
For Finding x from x+y=10 alone with real x and y, identify the best logical assessment.
Correct answer: D
Many ordered pairs satisfy one equation.
Evaluate the two proposed answers. Which are supported? I. Finding a person's exact age given only that the person is older than 18 — the best logical assessment: The sample may be unrepresentative. II. A price falls from 100 to 80 and then rises to 100; claim of equal percentage changes — the best logical assessment: Sufficient information.
Correct answer: C
I is incorrect: Finding a person's exact age given only that the person is older than 18 → Insufficient information. Many ages satisfy the inequality. 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.
For Finding rectangle area when only its perimeter is 20 cm is known, identify the best logical assessment.
Correct answer: A
Different side pairs can have the same perimeter and different areas.
Evaluate the two proposed answers. Which are supported? I. Finding rectangle area when only its perimeter is 20 cm is known — the best logical assessment: They are mutually exclusive and collectively exhaustive. II. A conclusion repeats its premise without independent support — the best logical assessment: Circular reasoning.
Correct answer: C
I is incorrect: 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. II is correct: A conclusion repeats its premise without independent support → Circular reasoning. The supposed proof assumes what it seeks to establish.
For Finding x from x+y=10 and x−y=2 together, identify the best logical assessment.
Correct answer: D
Adding gives 2x=12, so x is uniquely 6.
Evaluate the two proposed answers. Which are supported? I. Finding rectangle area when only its perimeter is 20 cm is known — the best logical assessment: Sufficient information. II. Finding the number of sides of a regular polygon from exterior angle 45 degrees — the best logical assessment: Other changes could explain the improvement.
Correct answer: B
I is incorrect: 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. II is incorrect: Finding the number of sides of a regular polygon from exterior angle 45 degrees → Sufficient information. The number is 360/45=8.