Crossover Aptitude Test Logical Reasoning 5 — Questions and Answers
Question 1: Which statement is the contrapositive of 'If it is a dog, then it is a mammal'?
- If it is a mammal, then it is a dog
- If it is not a dog, then it is not a mammal
- If it is not a mammal, then it is not a dog (Correct answer)
- If it is a mammal, then it is not a dog
Correct answer: If it is not a mammal, then it is not a dog
The contrapositive of 'If P then Q' is 'If not Q then not P': 'If not a mammal, then not a dog.'
Question 2: A manager evaluates candidates: candidates who score above 80 on logic AND above 70 on communication pass. Candidate A scores 85 logic, 65 communication. What happens?
- A passes — logic score is sufficient
- A fails — both conditions must be met (Correct answer)
- A is borderline — needs review
- A passes — average is above 75
Correct answer: A fails — both conditions must be met
Both conditions are required (AND logic); since communication is 65 < 70, A fails.
Question 3: A project has tasks A, B, C, D. B depends on A. C depends on A. D depends on B and C. What is the minimum number of sequential stages to complete the project?
- 2
- 3 (Correct answer)
- 4
- 5
Correct answer: 3
Stage 1: A; Stage 2: B and C (parallel); Stage 3: D — so 3 sequential stages are needed.
Question 4: Which best describes the logical flaw: 'This medicine works — my cold got better after I took it.'
- Ad hominem
- Post hoc ergo propter hoc (Correct answer)
- Straw man
- False dilemma
Correct answer: Post hoc ergo propter hoc
This is 'post hoc ergo propter hoc': assuming that because B followed A, A caused B.
Question 5: There are 4 cards on a table showing: 3, 8, A, D. Rule: 'If a card shows an even number on one side, it must show a vowel on the other.' Which cards must you flip to verify the rule?
- 8 and A
- 8 and D (Correct answer)
- 3 and A
- All four cards
Correct answer: 8 and D
Flip 8 (even, check for vowel) and D (consonant, check it doesn't hide an even number).
Question 6: A code converts numbers to letters: 1=A, 2=B, ... 26=Z. What word does 20-5-1-13 spell?
- TEST
- TEAM (Correct answer)
- TEAL
- TEAR
Correct answer: TEAM
20=T, 5=E, 1=A, 13=M — the word is TEAM.
Question 7: Premises: All X are Y. Some Y are Z. Can you conclude that some X are Z?
- Yes, always
- No, not necessarily (Correct answer)
- Only if Z is a subset of Y
- Only if X equals Y
Correct answer: No, not necessarily
The Y elements that are Z may or may not overlap with the X elements; the conclusion does not follow necessarily.
Crossover Aptitude Test Logical Reasoning 5
Which statement is the contrapositive of 'If it is a dog, then it is a mammal'?