Rather difficult question on MCAS test

The following question appeared on the Spring 2000 10th grade MCAS (Massachusetts Comprehensive Assessment System) Mathematics test. Passing this test will soon be a requirement for high school graduation in Massachusetts.

What do you think of this question? Can you answer it? Do you agree with the 'official' answer, C?

(Display in Courier to make the columns line up)

Mark drives 25% of the time in the city and 75% of the time on the highway. Which of the four cars listed below will give him the greatest number of miles per gallon of gasoline?

average miles average miles per gallon per gallon in the city on the highway

A. Car #1 20 35 B. Car #2 25 30 C. Car #3 24 34 D. Car #4 26 31

This all depends on the aids allowed...

Consider 4 miles of driving, 1 in the city and 3 in highway. This is the same proportion as in this task.

So with x miles / gallon in city and y in highway this requires 1/x+3/y gallons. Now calculate which of the given x and y give the lowest value.

A. 0.1357 B. 0.1400 C. 0.1299 D. 0.1352

This is indeed C, but would be a bit boring without a calculator

I don't think this is difficult for high school with a calulator!

The question was talking of a 255 in time...

Can we postulate the same velocity in a city or on a highway?

The question was talking of a 25% in time? (15' and 45' for example)

Can we postulate the same velocity in a city or on a highway?

Are the persons taking this test of the order of 16 years old? 10th grade isn't a universal nomenclature.

My first instinct was to say 'yes', but then I had another think. The intended answer clearly is to find the car which maximises 1/(1/c + 3/h), using the obvious notation, and that is (clearly, after a little work I find easier with a calculator) car C.

But the question says 'time', not 'distance', and average speeds are somewhat higher on the highway than in the city. Therefore, Car A (which has better highway mileage) is relatively better, and it turns out that Car A becomes better than Car C if the average speed on the highway is more than about 3.3 times that in town. For some combinations of city and highway, this is eminently achievable.

So the question is unanswerable as stated, and fairly simple as I presume is intended. This doesn't mean that I would expect a high pass rate even to a better-worded question. The Youth of Today (TM) are notoriously innumerate.

Oops. I interpreted 'time' the wrong way It is still easy though!