GMA Logical Reasoning 2 — Questions and Answers
Question 1: If all A are B, and all B are C, which statement must be true? (A) All C are A (B) All A are C (C) Some B are not A (D) No A are C
- All C are A
- All A are C (Correct answer)
- Some B are not A
- No A are C
Correct answer: All A are C
By transitivity: if A⊆B and B⊆C, then A⊆C. Therefore 'All A are C' must be true.
This is the fundamental syllogistic transitivity law: if all elements of set A belong to set B, and all elements of set B belong to set C, then all elements of set A must also belong to set C (A⊆B⊆C → A⊆C). Option A (All C are A) is the converse — valid only if the sets are equal, which is not given.
Question 2: A shopkeeper says: 'If it rains, I close early.' It is raining. What can you conclude? (A) It will stop raining soon. (B) The shopkeeper closes early. (C) The shopkeeper never closes early when it's sunny. (D) The shopkeeper is closed.
- It will stop raining soon.
- The shopkeeper closes early. (Correct answer)
- The shopkeeper never closes early when it's sunny.
- The shopkeeper is closed.
Correct answer: The shopkeeper closes early.
Given 'If rain then close early' and the fact that it is raining, we can apply modus ponens: the shopkeeper closes early.
This applies modus ponens (affirming the antecedent): P→Q, P, therefore Q. 'If rain (P), then close early (Q)'. It is raining (P is true), therefore the shopkeeper closes early (Q must be true). Option C commits the inverse fallacy — not raining does NOT necessarily mean the shopkeeper stays open (there could be other reasons to close early).
Question 3: Five people sit in a row: Alice, Bob, Carol, David, Eve. Alice sits to the left of Bob. Carol sits between Alice and David. Eve sits to the right of Bob. Where is Carol relative to Bob?
- To the right of Bob
- To the left of Bob (Correct answer)
- Next to Eve
- Between Bob and Eve
Correct answer: To the left of Bob
Order: Alice, Carol, David, Bob, Eve (or similar). Carol sits between Alice and David, who are both to the left of Bob, so Carol is to the left of Bob.
From the clues: Alice is left of Bob; Carol is between Alice and David; Eve is right of Bob. A consistent ordering is: Alice – Carol – David – Bob – Eve (Alice-left-of-Bob ✓, Carol between Alice and David ✓, Eve right of Bob ✓). In this arrangement, Carol is to the left of Bob.
Question 4: In a logic puzzle, exactly one of the following statements is true: (A) All cats have wings. (B) Some cats have wings. (C) No cats have wings. Which statement is true?
- Statement A
- Statement B
- Statement C (Correct answer)
- Both A and B
Correct answer: Statement C
Statement A (all cats have wings) is false. Statement B (some cats have wings) is also false — cats do not have wings. Statement C (no cats have wings) is true and is the only true statement.
Logical reasoning sometimes anchors to real-world facts. In reality, no cats have wings. Therefore: A (all have wings) = false; B (some have wings) = false; C (no cats have wings) = true. Note: if B were true, A would not necessarily be true; and if A were true, B would automatically also be true. Having exactly one true statement further confirms C is the answer.
Question 5: A code states: 'Only employees with Level 3 clearance may enter Room X.' A person enters Room X. What can you conclude? (A) They definitely have Level 3 clearance. (B) They might not have Level 3 clearance. (C) All Level 3 employees are in Room X. (D) Room X is secure.
- They definitely have Level 3 clearance. (Correct answer)
- They might not have Level 3 clearance.
- All Level 3 employees are in Room X.
- Room X is secure.
Correct answer: They definitely have Level 3 clearance.
If only Level 3 employees may enter, and someone has entered, they must have Level 3 clearance. This is modus tollens in reverse (contrapositive applied positively).
The statement 'Only X may enter' logically means 'If entered, then X'. This is equivalent to the contrapositive: 'If not X, then did not enter'. Since the person HAS entered, they must be X (Level 3). This is modus tollens: ¬Q → ¬P; the person entered (¬¬P), therefore they have clearance (Q). Option C misreads the conditional in the wrong direction.
Question 6: Which argument has a valid logical structure? (A) All politicians lie. John lies. Therefore John is a politician. (B) All birds can fly. Penguins are birds. Therefore penguins can fly. (C) No reptiles are warm-blooded. Snakes are reptiles. Therefore snakes are not warm-blooded. (D) Some dogs bark. Rex is a dog. Therefore Rex barks.
- Argument A
- Argument B
- Argument C (Correct answer)
- Argument D
Correct answer: Argument C
Argument C has valid logical structure: No reptiles are warm-blooded (P1), Snakes are reptiles (P2), therefore snakes are not warm-blooded (valid). Even though Argument B is structurally valid, its first premise is empirically false, making it sound-invalid but structurally valid too. Argument C is both structurally valid AND uses true premises.
Validity concerns logical structure; soundness concerns true premises. A: Affirming the consequent fallacy (politicians lie → John lies is not given). B: Structurally valid (All P→Q, snakes are P, ∴ Q) BUT the premise is false (penguins cannot fly). C: Valid AND sound (true premises + valid structure). D: 'Some dogs bark' + 'Rex is a dog' doesn't guarantee Rex barks. C is the best answer.
GMA Logical Reasoning 2
If all A are B, and all B are C, which statement must be true?
(A) All C are A
(B) All A are C
(C) Some B are not A
(D) No A are C