TehJay wrote:
In order to finance road repairs, the highway commission of a certain state is considering a 50 percent increase in the 10-centers-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 percent per year.
Which of the following is an assumption on which the highway commissioner's claim depends?
(A) The amount of money required annually for road repairs will not increase from its current level.
(B) The total number of trips made on the toll highway per year will not decrease from its current level.
(C) The average length of a trip made on the toll highway will not decrease from its current level.
(D) The number of drivers who consistently avoid the highway tolls by using secondary roads will not increase from its current level.
(E) The total distance traveled by vehicles on the toll highway per year will not decrease from its current level.
Okay, so the commissioner is claiming that an increase in tolls will result in a proportionate increase in revenues. So the assumption must have something to do with the increase in tolls not somehow increasing costs or decreasing the amount of money that comes in (through a decrease in traffic, for example). For a 50% increase in tolls to result in a 50% increase in revenues, the amount of traffic would have to stay similar. But every single one of the answers makes this assumption!
A - If the amount of money for road repairs increased, more money would be spent, which would cut into that 50% figure.
B - If the total number of trips made on the highway decreased, due to the increase in tolls, then the highway would generate less money than expected. (Revenues would likely still go up, but how could they hit the 50% increase?)
C - If the average length of the trips made on the highway went down, then the tolls would generate less money, because they're paid by the mile.
D - If the toll increase causes more people to avoid using the highway, then revenues won't increase as much as hoped. I picked this answer.
E - If the total distance traveled by the vehicles went down, revenues won't increase as much as hoped. This is the OA.
The official explanation is:
"The toll is charged on a per-mile basis. A 50 percent increase in the toll will bring a 50 percent increase in revenue only if the total number of miles traveled on the toll highway per year does not decrease."
But all of the answers, except A, would result in a decrease in the total number of miles traveled on the highway.
This is a tricky question. Many options look like the answer assuming everything else will remain constant. But the actual correct answer doesn't need to assume that. Let's discuss this:
Argument:
50 percent increase in toll is being considered on the 10-centers-per-mile toll for highway
Claim - the toll increase will increase the annual revenue it generates by at least 50 percent per year.
Revenue = Price*Amount
So if the toll (say Price) increases by 50%, the revenue will increase by 50% (or more) if the Amount does not decrease.
(A) The amount of money required annually for road repairs will not increase from its current level.
This is irrelevant. The target is to increase the annual revenue generated by 50%. Whether this is enough for road repairs, doesn't matter.
(B) The total number of trips made on the toll highway per year will not decrease from its current level.
On the face of it, it might seem that this is saying "Amount" should be the same or more. But it is not so. Tolls are 10 centres a mile so longer the trip, more the toll collected.
Even if the total number of trips decrease, if the trips are longer, they should cover for the reduction since tolls are 10 centres a mile. The overall toll collected may still be the same. So negating this option doesn't necessarily break the claim.
(C) The average length of a trip made on the toll highway will not decrease from its current level.
So this is complementary to option (B) above. Here, we are assuming that the length of the trip stays the same. But what about the number of trips? Even if the length decreases, if the number of trips increase, we can still maintain the Amount. So negating this option does not break the claim either.
(D) The number of drivers who consistently avoid the highway tolls by using secondary roads will not increase from its current level.
Even if fewer people take the highway, if the ones who take the highway take longer trips, the Amount can be made up. So negating this will also not break the claim. This is not n assumption either.
(E) The total distance traveled by vehicles on the toll highway per year will not decrease from its current level.
This is what we are looking for. "the total distance travelled by vehicles on the toll highway" is the "Amount". It includes the number of trips and the length of the trips. So this entire amount should not decrease. If this decreases, the revenue collected will decrease. Hence, this is an assumption made by the commissioner.
Answer (E)
for shedding some light on this question. Although, what is the meaning of a 10-centers-per-mile toll?