Speed/Distance

vaibhav101 wrote:On a recent trip , Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between

A 290/12.5 and 290/11.5
B 295/12 and 285/11.5
C 285/12 and 295/12
D 285/12.5 and 295/11.5
E 295/12.5 and 285/11.5

If the distance of 290 miles is obtained by rounding to the nearest 10 miles, the actual distance must be between 285 miles and 295 miles. Similarly, if the number of gallons of gasoline used, 12 gallons, is obtained by rounding to the nearest gallons, the actual number of gallons must be between 11.5 gallons and 12.5 gallons. Therefore, the maximum number of miles per gallon is 295/11.5 and the minimum number of miles per gallon is 285/12.5 and the actually number of miles per gallon is some number in between these two numbers.

Note that we maximized the number of miles per gallon by making the numerator as large as possible (295) and the denominator as small as possible (11.5). Similarly, to minimize the mpg, we made the numerator as small as possible (285) and the denominator as large as possible (12.5).

Answer: D