Introduction / Context:
This critical reasoning problem asks you to determine what must be true, given three short facts about Robert’s vehicles. The test of necessity is strict: a statement must follow in every possible arrangement consistent with the facts, not just in some convenient scenario.
Given Data / Assumptions:
- Robert owns exactly four vehicles.
- Exactly two of the four vehicles are red.
- At least one vehicle type is identified: one vehicle is a minivan.
- We do not know the types of the other vehicles or the colors beyond “two are red.”
Concept / Approach:
Test each proposed statement against multiple consistent cases. If you can create even one valid case that makes a statement false, then that statement is not a necessary fact. Only a statement true in all valid cases can be marked as “must be true.”
Step-by-Step Solution:
Evaluate I: “Robert has a red minivan.” The facts allow the minivan to be either red or not red. For example, two red sedans + one blue minivan + one blue truck fits all facts without a red minivan. So I is not necessary.Evaluate II: “Robert has three cars.” The facts never mention cars. He could have one minivan, one motorcycle, one SUV, one pickup; or many other combinations. So II is not necessary.Evaluate III: “Robert’s favorite color is red.” Preference is never discussed. Not necessary.Since none of I, II, or III must be true, the correct choice is that none is a known fact.
Verification / Alternative check:
Construct two contrasting valid scenarios (with and without a red minivan) to confirm that I is not forced. Similar constructions show II and III are unfounded.
Why Other Options Are Wrong:
“I only”, “II only”, “II and III only”, or “I and II only” all assert something not guaranteed by the original facts.
Common Pitfalls:
Assuming typical real-world distributions (e.g., most vehicles are cars) or inferring preferences (favorite color) from counts.
Final Answer:
None of the statements is a known fact.
Discussion & Comments