Official Guide Problem Solving 129

[gregmh48]

In the explanation for problem 129, the range of possibilities resulting in 290 miles is given as 284 to 295, and the range for gallons is given as 11.4 to 12.5. I might be missing something simple here, but wouldn't 284 round down to 280, not 290, and 11.4 round down to 11 and not 12? I believe the possible values would be 285 to 294 for miles and 11.5 to 12.4 for gasoline. Can someone help me understand why the explanation thinks differently? Thanks.

[manulath]

please post the question

[gregmh48]

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 290/11.4

B. 295/12 and 284/11.4

C. 284/12 and 295/12

D. 284/12.5 and 295/11.4

E. 295/12.5 and 284/11.4

[permafrost2125]

In the explanation for problem 129, the range of possibilities resulting in 290 miles is given as 284 to 295, and the range for gallons is given as 11.4 to 12.5. I might be missing something simple here, but wouldn't 284 round down to 280, not 290, and 11.4 round down to 11 and not 12? I believe the possible values would be 285 to 294 for miles and 11.5 to 12.4 for gasoline. Can someone help me understand why the explanation thinks differently? Thanks.

Because the questions states "between" you know that the range of numbers is non-inclusive. You are not trying to solve for the actual maximum and minimum. You need to pick the value that definitely includes all possible mpg values.

You are correct that 11.4 and 284 round down while 12.5 and 295 round up, but by using those values it insures that anything within that range is accounted for.

Hopefully that makes sense.

[stop@800]

You have written wrong answer choices
Pl vfy

[gregmh48]

You have written wrong answer choices
Pl vfy

I just checked and they are all the same as in the book.

[praneeth]

I think this is one of the questions that the OG has a wrong answer. The answer explanation goes on to say that the range of values for miles is 284 to 295 which makes no sense since correct range should be 285 to 294 for it to round to 290.

That's how it gets to the answer.

Same issue with the gallon count.

[Ian Stewart]

I think this is one of the questions that the OG has a wrong answer. The answer explanation goes on to say that the range of values for miles is 284 to 295 which makes no sense since correct range should be 285 to 294 for it to round to 290.

That's how it gets to the answer.

Same issue with the gallon count.

The explanation in the OG is not good, but the answer is certainly correct, for the reasons permafrost gave above. While we can actually be certain that the miles per gallon was between

285/12.5 and 295/11.5

since that's the case, we can be absolutely certain that the miles per gallon was between

284/12.5 and 295/11.4

because 284/12.5 is less than 285/12.5, and 295/11.4 is greater than 295/11.5. The question does *not* ask, "what range of values gives the *only* possible values for Cindy's miles per gallon?". Instead it asks "The number of miles per gallon must have been between..." If there had been an answer choice which said "0.1 and 1000", it would be correct, because we can be completely sure that Cindy's miles per gallon was larger than 0.1 and less than 1000. In the same way, answer D is correct here, even if the range includes some values that could not possibly be equal Cindy's mileage per gallon.

[praneeth]

Ian,

Thank you for the very detailed and helpful reply.