Crossover Aptitude Test Logical Reasoning: Syllogisms 5 — Questions and Answers
Question 1: All diamonds are precious. Some precious things are rare. Some rare things are expensive. What can be concluded about diamonds?
- All diamonds are expensive.
- Diamonds may or may not be expensive. (Correct answer)
- No diamonds are expensive.
- All expensive things are diamonds.
Correct answer: Diamonds may or may not be expensive.
The chain breaks at 'some precious things are rare,' so we cannot determine diamonds' relationship to expensive.
Question 2: Either the project is on time, or it is over budget. The project is on time. Therefore:
- The project is over budget.
- The project is not over budget. (Correct answer)
- The project may be over budget.
- Both conditions hold.
Correct answer: The project is not over budget.
In a disjunctive syllogism with 'either...or,' if one condition is confirmed, the other is negated (assuming exclusive or).
Question 3: All supervisors report to managers. All managers report to directors. Susan is a supervisor. What must be true?
- Susan reports to a director directly.
- Susan reports to a manager. (Correct answer)
- Susan is a manager.
- Directors report to Susan.
Correct answer: Susan reports to a manager.
Susan is a supervisor so she reports to a manager, which is the direct and necessary inference.
Question 4: Some words are nouns. All nouns are parts of speech. No verbs are nouns. Therefore:
- Some parts of speech are not nouns. (Correct answer)
- All words are parts of speech.
- Some words are verbs.
- Verbs are not parts of speech.
Correct answer: Some parts of speech are not nouns.
Since nouns are parts of speech and verbs are not nouns, verbs may be other parts of speech, meaning some parts of speech are not nouns.
Question 5: If it rains, the ground is wet. The ground is wet. Therefore:
- It rained.
- It may or may not have rained. (Correct answer)
- It did not rain.
- The ground is always wet.
Correct answer: It may or may not have rained.
Affirming the consequent ('ground is wet') does not confirm the antecedent ('it rained') — other causes could wet the ground.
Question 6: All responsible employees meet deadlines. Mark does not meet deadlines. Which conclusion is valid?
- Mark is responsible.
- Mark is not a responsible employee. (Correct answer)
- Some responsible employees miss deadlines.
- Mark never works hard.
Correct answer: Mark is not a responsible employee.
By modus tollens (contrapositive), failing to meet deadlines means Mark is not a responsible employee.
Question 7: Some G are H. Some H are I. Which conclusion is valid?
- All G are I.
- Some G are I.
- No G are I.
- We cannot determine G's relationship to I. (Correct answer)
Correct answer: We cannot determine G's relationship to I.
Two 'some' statements do not allow any definite conclusion about the relationship between the outer terms G and I.
Crossover Aptitude Test Logical Reasoning: Syllogisms 5
All diamonds are precious.
Some precious things are rare.
Some rare things are expensive.
What can be concluded about diamonds?