# GMAT Challenge Series (700+): Q20

Question:

A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5 hrs, rounded to the nearest hour, then his average speed must be between:

A. 38 and 50 mph

B. 40 and 50 mph

C. 40 and 51 mph

D. 41 and 50 mph

E. 41 and 51 mph

$$\text{The length of the bike path is 225 miles, rounded to the nearest mile, therefore:}$$ $${224.5} \geq \textit{distance} < {225.5}$$ $$\text{The trip took 5 hrs, rounded to to the nearest hour, therefore:}$$ $${4.5} \geq \textit{time} < {5.5}$$  $$\text{Lowest average speed occurs with the lowest distance and the highest time}$$ $$\textit{Lowest average speed} \approx {{224.5} \over {5.5}} \approx {40.8}$$  $$\text{Highest average speed occurs with the highest distance and the lowest time}$$ $$\textit{Highest average speed} \approx {{225.5} \over {4.5}} \approx {50.1}$$  $${40.1} < \textit{average speed} < {50.1}$$ $${40} < {40.1} < \textit{average speed} < {50.1} < {51}$$  $$\text{Range: } {40} < \textit{average speed} < {51}$$