Bunuel wrote:

When an automobile is driven at 70 miles per hour, it uses 0.06 gallon of gas per mile. When the car is driven at 50 miles per hour, it uses 0.04 gallon of gas per mile. Which of the following relations are possible between the gallons of gas used per mile and the speed at which the car is driven?

I. They are directly proportional.

II. They are indirectly proportional.

III. They are linearly related.

(A) only I

(B) only II

(C) only III

(D) I and III

(E) I, II, and III

When two quantities are directly proportional, if one quantity increases (or decreases), so does the other quantity. Moreover, the ratio of the two quantities will be the same. Thus, we must check whether

70/(0.06) = 50/(0.04), or equivalently, whether 70(0.04) = 50(0.06).

We have 70(0.04) = 2.8 and 50(0.06) = 3; thus, we conclude that the two quantities are not directly proportional.

When two quantities are indirectly (inversely) proportional, if one quantity increases (or decreases), the other quantity decreases (or increases). Thus, the two quantities cannot be indirectly proportional.

Since we eliminated statements I and II, and since according to the answer choices one of the statements must be true, we conclude that only statement III is true.

Answer: C

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