Equations, Inequalities, & VICs (3rd ed) Chapter 6 #17

[john.cappuccitti]

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 hours, rounded to the nearest hour, then his average speed must be between:

A. 38-50 mph
B. 40-50 mph
C. 40-51 mph
D. 41-50 mph
E. 41-51 mph

My problem does not have to do with actually solving the question in any way. My question arises from the solution presented within the strategy guide.

In order to find the range of possible speeds the cyclist is traveling, we need to use the extreme values for the distance of his trip as well as the extreme values for the time he travels.

Given that the distance traveled, rounded to the nearest mile, is 225 miles, the corresponding extreme values are 224.5 miles and 225.4 miles. Similarly, the travel time would be between 4.5 hours and 5.4 hours. This is where my problem lies. The solution in the strategy guide suggests that the upper bound for the distance is 225.5 miles (not 225.4), and the upper bound for travel time is 5.5 hours (not 5.4). Isn't it convention to round down when the number in the tenths position is between 0-4 and round up when said number is between 5-9? What standard does the GMAT go by? I know that it may seem silly to squabble over 0.1, but in a question such as this, the answers are so close together that the 0.1 makes an enormous difference in your final solution.

Thank you for your time.

[Ben Ku]

You are assuming that the actual length can be measured to the tenths, and the hours can also be measured to the tenths. However, the range for the length is 224.5 <= d < 225.5 miles, and the range for the time is 4.5 <= t < 5.5 hours. In this case, 225.49 miles and 55.49 miles will also fit the bill. So we need to include all values of distance UP TO 225.5, and time UP TO 5.5 hours (even though we know the actual values don't include them).

I hope that helps.