Equations, Inequalities, & VICs: Chapter 6, Question 17

[Guest]

The questions is as follows"

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 and 50 miles per hour
B) 40 and 50 miles per hour
C) 40 and 51 miles per hour
D) 41 and 50 miles per hour
E) 41 and 51 miles per hour

The book says the answer is C, but I'm confused. The question uses the figures 224.5 to 225.5 miles and 4.5 to 5.5 hrs. But I believe it should be between 224.4 to 225.5 miles and 4.4 to 5.5 hours. The answer would then be 225.5/4.4 = 51.25 and 224.5/5.5 = 40.82. Which would be between 40 and 52 mph, wouldn't it?

Here's a similar question, #129, from the OG, 11ed.
[Moderator note: We can't discuss or post OG questions, but anyone who is interested may look this problem up themselves.]

[esledge]

Here's the rule about rounding: If the digit after the intended last digit is 5 or greater, round up. If the digit after the intended last digit is 4 or less, round down, or simply truncate.

So, 224.4 miles would be rounded down to 224 miles and 4.4 hours would be rounded down to 4 hours. Our minimums must be 224.5 miles and 4.5 hours.

At the high end, 225.499999999999 would round down to 225. Using 225.5 miles as the max is a bit of an approximation, as a distance of exactly 225.5 would be rounded up to 226. Since the question asks for a range, and 225.5 is the extreme for the distance, this is OK. Similarly for the maximum hours.

[Guest]

Sorry for posting the OG question. I understand how to round, but the problem doesn't ask for all the numbers, inclusive, but all the numbers in between x and y. Like the OG guide I used the limits, based on the rounding, which would be 224.4<x<225.5 miles, not 225.5=<x<225.5, which is an odd formation. I'm sorry to say, but I don't believe the answer is right at all.

[JonathanSchneider]

I believe that our book is correct, and that Emily's description above is correct as well. You might want to check your math; you may also have been reading Emily's post incorrectly. We are not advocating that 225.5=<x<225.5 (which would be not only strange but also impossible), but rather that 224.5=<x<225.5.

I also happen to think that answer explanation to the OG question you referenced has a major flaw. While D is still the right answer, it extends the range a bit more than is strictly necessary. (It is still the only right answer.) This is because the numerator of the first term could be 285 and the denominator of the second term could be 11.5, WITHOUT compromising the integrity of the answer choice. The values included in the printed answer, of course, only extend the given range, so the rate will of course still fall within the given parameters. This gets the book writers into trouble, however, when they move to explain the answer choice, as they include the numbers as the ACTUAL limits (which they're not). I've written to GMAC about this, but I have not yet received a reply. My hope is that the next edition will fix this error. (The problem, after all, is still a good one; only the explanation needs to be fixed.)

There are other rounding systems out there, of course. There is such a thing as banker's rounding, often used by computer programs. (Info: http://en.wikipedia.org/wiki/Rounding#R ... ven_method) However, to the best of my knowledge that system is NOT used by the GMAT, and it does not seem to be relevant here anyways.