Crossover Aptitude Test Logical Reasoning: Syllogisms 5

Question 1

All diamonds are precious. Some precious things are rare. Some rare things are expensive. What can be concluded about diamonds?

Accepted Answer

Diamonds may or may not be expensive.

Answer

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:

Accepted Answer

The project is not over budget.

Answer

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?

Accepted Answer

Susan reports to a manager.

Answer

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:

Accepted Answer

Some parts of speech are not nouns.

Answer

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:

Accepted Answer

It may or may not have rained.

Answer

Affirming the consequent ('ground is wet') does not confirm the antecedent ('it rained') — other causes could wet the ground.

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