Each new car in the lot at Rollway Motors costs more than $18,000. Any car in their lot that is ten or more years old costs less than $5,000. Thus, if a car in Rollway's lot costs between $5,000 and $18,000, it is a used car that is less than ten years old.
The pattern of reasoning in which one of the following arguments is most similar to that in the argument above?The original argument uses
two boundaries to eliminate two possibilities. A car in the middle price range cannot be new because new cars cost more than $18,000, and it cannot be ten or more years old because those cars cost less than $5,000.
The same pattern appears when a middle value eliminates categories on both sides.(A) Each apartment above the fourth floor of the building has more than two bedrooms. But all apartments below the fourth floor have fewer than two bedrooms. Thus, any apartment on the fourth floor of the building has exactly two bedrooms.
Incorrect. Nothing establishes how many bedrooms apartments on the fourth floor have. The argument wrongly infers a property from being between two locations.
(B) Each apartment above the fourth floor of the building has two or three bedrooms. But no apartment below the fourth floor has more than two bedrooms. Thus, all of the building's three-bedroom apartments are on the fourth floor or higher.
Incorrect. A three-bedroom apartment cannot be below the fourth floor, but this uses essentially one boundary to eliminate one location.
(C) No apartment above the fourth floor of the building has fewer than three bedrooms. But all apartments below the fourth floor have fewer than two bedrooms. Thus, if there are apartments in the building with exactly two bedrooms, they are on the fourth floor.
Correct. An apartment with exactly two bedrooms cannot be above the fourth floor, because those apartments have at least three bedrooms. It also cannot be below the fourth floor, because those apartments have fewer than two bedrooms. Therefore, it must be on the fourth floor. This matches the original two-boundary elimination.
(D) No apartment above the fourth floor of the building has more than two bedrooms. But only three-bedroom apartments have balconies. Thus, if any apartment in the building has a balcony, it is on the fourth floor or lower.
Incorrect. This is a chain of conditions: balcony implies three bedrooms, and three bedrooms implies not above the fourth floor. It does not use the same middle-range reasoning.
(E) Each apartment above the fourth floor of the building has more than two bedrooms. The building has no vacant apartments on or below the fourth floor. Thus, if there is any vacant apartment in the building, it will have more than two bedrooms.
Incorrect. This is also a chain: vacant implies above the fourth floor, which implies more than two bedrooms.
Answer: (C)