CAT Question wrong answer?

[VictoriaF551]

I got this question on my first Prep Test:

A certain taxi driver charges a rate of r cents per person per mile. How much money, in dollars, would it cost three people to travel x miles if he gives them a 50% discount? (100 cents = 1 dollar)
A) 3xr/2
B) 3x/200r
C) 3r/200x
D) 3xr/200
E) xr/600

Reviewing the question, I came through this explanation for the correct answer:

We can solve this as a VIC (Variable In answer Choices) and plug in values for x and r.
r - cents per person per mile: 10
x - # of miles: 20
Since there are 3 people, the taxi driver will charge them 30 cents per mile.
Since they want to travel 20 miles, the total charge (no discount) would be (30)(20) = 600.
With a 50% discount, the total charge will be 300 cents or 3 dollars.
If we plug r = 10 and x = 20 into the answer choices, the only answer that yields 3 dollars is D.

The correct answer is D.

My question is, why isn't the correct answer A, which yields 300 (cents) and therefore 3 dollars? If r is given in cents then the answer should be in cents, and then converted to dollars, no?

If someone could help me that would be amazing! Thank you!

[Sage Pearce-Higgins]

Apologies for the slow response to this - it looks like our spam blocker held up your message.

To be clear, the correct answer is definitely D. If we take the Smart Numbers suggested in the explanation, we're looking for the answer of 3 dollars. The question asks "how many dollars would it cost...?". If we substitute the smart numbers into answer choice A we get the number 300. We don't have the freedom simply to say "oh, that must be 300 cents, which makes 3 dollars" as we're working in dollars. Answer choice A actually gives the answer 300 dollars, which doesn't match up.

It might help to think about this problem from another angle. We could solve it without smart numbers, by just taking simple algebraic steps. If the taxi driver charges r cents per mile, then that makes r / 100 dollars per mile. To travel x miles would be rx / 100. If there are 3 people, then that makes 3xr / 100, and if they have a 50% discount (half price), then the total is 3rx / 200.