Loading...
In order to finance road repairs, the highway commission of a certain state is considering a \(50\%\) increase in the \(10\)-cents-per-mile toll for vehicles using its toll highway. The highway commissioner claims that the toll increase will increase the annual revenue generated by the toll highway by at least \(50\%\) per year.
Which of the following is an assumption on which the highway commissioner's claim depends?
| Text from Passage | Analysis |
|---|---|
| In order to finance road repairs, the highway commission of a certain state is considering a \(50\%\) increase in the \(\$0.10\)-per-mile toll for vehicles using its toll highway. |
|
| The highway commissioner claims that the toll increase will increase the annual revenue generated by the toll highway by at least \(50\%\) per year. |
|
The argument starts by describing a proposed toll increase, then presents the commissioner's prediction about how this change will affect revenue. There's no supporting evidence provided for the commissioner's claim.
The highway commissioner claims that increasing tolls by \(50\%\) will increase annual revenue by at least \(50\%\).
This is actually a very simple argument structure - we have a proposed action (toll increase) and a predicted outcome (revenue increase). The commissioner is making a direct cause-and-effect claim without providing any supporting premises. The argument assumes that higher tolls will automatically lead to proportionally higher revenue, but doesn't explain why this would be true.
Assumption - We need to find what the highway commissioner must believe to be true for his claim to work. An assumption is something that, if false, would make the conclusion fall apart.
The commissioner's claim is very specific: a \(50\%\) toll increase will generate AT LEAST \(50\%\) more revenue. This is a quantitative claim about revenue that depends on both price per mile AND total miles driven.
For assumption questions, we look for ways the conclusion could fail while respecting the facts given. The commissioner assumes revenue will increase by at least \(50\%\), but revenue = price per mile × total miles driven. If the toll increase causes people to drive significantly less on this highway, revenue might not increase as expected. We need to find what the commissioner must assume about driver behavior and other factors.
This is about expenses, not revenue. The commissioner's claim is specifically about revenue generation from tolls increasing by at least 50%. Whether repair costs go up or down doesn't affect whether toll revenue will increase as predicted. The commissioner could be right about revenue even if repair costs change.
This focuses on number of trips, but what really matters for revenue is total distance traveled. We could have the same number of trips but with shorter distances, which would hurt revenue. Or we could have fewer trips but longer distances, which might maintain revenue. The commissioner's claim depends on total mileage, not trip count.
This only covers one component of total distance. Even if average trip length stays the same, if the number of trips drops significantly, total distance (and thus revenue) could still fall. The commissioner needs total distance to hold steady, not just average distance per trip.
This is about people who already avoid tolls continuing to avoid them. But the real concern is whether current toll-paying drivers will start avoiding the highway due to the price increase. This choice misses the main threat to the commissioner's revenue projection.
This directly addresses what the commissioner must assume. Since revenue equals price per mile times total miles traveled, and the price is going up 50%, the commissioner needs total distance to stay roughly the same for revenue to increase by at least 50%. If total distance traveled decreased significantly, it could prevent the revenue increase the commissioner predicts.