For Two sets overlap, but neither contains the other, identify the best logical assessment.
Correct answer: C
Overlap does not imply complete inclusion.
Reasoning
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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.
A cube is divided into 3 equal segments along each edge. How many small cubes result?
Correct answer: D
There are 3 layers, each containing 3 × 3 cubes.
A person walks 3 m east and then 4 m north. What is the shortest distance from the starting point in metres?
Correct answer: C
The path forms perpendicular sides. Distance = √((3)²+(4)²).
Evaluate the two proposed answers. Which are supported? I. A person faces east and turns 270 degrees clockwise; final direction — the requested conclusion: North. II. A man points to his father's father; that person's relation to him — the requested conclusion: Paternal grandfather.
Correct answer: B
I is correct: A person faces east and turns 270 degrees clockwise; final direction → North. East→south→west→north is a 270-degree clockwise turn. II is correct: A man points to his father's father; that person's relation to him → Paternal grandfather. The relation passes through the father.
For A person moves 8 km west then 6 km south; straight-line distance from the start, identify the requested conclusion.
Correct answer: A
The distance is √(8²+6²)=10.
Evaluate the two proposed answers. Which are supported? I. K is L's wife and L is M's brother; K's relation to M — the requested conclusion: Nephew. II. F is G's son and G is H's sister; F's relation to H — the requested conclusion: 10 km.
Correct answer: D
I is incorrect: K is L's wife and L is M's brother; K's relation to M → Sister-in-law. K is married to M's sibling. II is incorrect: F is G's son and G is H's sister; F's relation to H → Nephew. F is a male child of H's sibling.
For Town P is north of Q and Q north of R; direction of P from R, identify the requested conclusion.
Correct answer: C
Both displacements point north.
Evaluate the two proposed answers. Which are supported? I. R is S's father and S is T's sister; R's relation to T, assuming S and T share both parents — the requested conclusion: Father. II. A is B's mother and B is C's father; A's relation to C — the requested conclusion: Paternal grandmother.
Correct answer: D
I is correct: R is S's father and S is T's sister; R's relation to T, assuming S and T share both parents → Father. Shared parentage makes R the father of both siblings. II is correct: A is B's mother and B is C's father; A's relation to C → Paternal grandmother. A is the mother of C's father.
For A person faces east and turns 270 degrees clockwise; final direction, identify the requested conclusion.
Correct answer: A
East→south→west→north is a 270-degree clockwise turn.
Evaluate the two proposed answers. Which are supported? I. A person moves 8 km west then 6 km south; straight-line distance from the start — the requested conclusion: 10 km. II. A person walks 4 km east then 3 km north; straight-line distance from the start — the requested conclusion: 5 km.
Correct answer: B
I is correct: A person moves 8 km west then 6 km south; straight-line distance from the start → 10 km. The distance is √(8²+6²)=10. II is correct: A person walks 4 km east then 3 km north; straight-line distance from the start → 5 km. The legs form a 3-4-5 right triangle.
Evaluate the two proposed answers. Which are supported? I. Town X is east of Y and Z is south of X; direction of Z from Y — the requested conclusion: Southeast. II. A woman points to her mother's only son; that person's relation to her — the requested conclusion: Son-in-law.
Correct answer: D
I is correct: Town X is east of Y and Z is south of X; direction of Z from Y → Southeast. The net movement from Y is east and south. II is incorrect: A woman points to her mother's only son; that person's relation to her → Brother. Her mother's only son is her male sibling.
For K is L's wife and L is M's brother; K's relation to M, identify the requested conclusion.
Correct answer: A
K is married to M's sibling.