Problem Solving

okay. The question:

On a recent trip, Cindy dove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gas 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

Okay, the answer is D and the explanation on the page says that you must take the lowest miles/highest gallon for the minimum and vice versa for the maximum. That answers makes sense. My problem is how is it possible for it to be 284 if it is rounded to the nearest 10? 284 rounded to the nearest 10 is 280 and the question says that she drove 290 miles. Same thing for 12.5 which rounds to 13; 11.4 rounds to 11; and 295 to 300. I don't understand why that works. Please help me figure this out. Thanks.

mpaudena wrote:okay. The question:

On a recent trip, Cindy dove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gas 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

Okay, the answer is D and the explanation on the page says that you must take the lowest miles/highest gallon for the minimum and vice versa for the maximum. That answers makes sense. My problem is how is it possible for it to be 284 if it is rounded to the nearest 10? 284 rounded to the nearest 10 is 280 and the question says that she drove 290 miles. Same thing for 12.5 which rounds to 13; 11.4 rounds to 11; and 295 to 300. I don't understand why that works. Please help me figure this out. Thanks.

The answer choices in my OG read a bit different. Do you have older print ? I believe there were a few typos in the older one which are fixed in the latest reprint .......

Nope. Just bought this. It is the 11th edition. What do you mean read different? I was paraphrasing the book if that is what you meant. What does your book say?

The real issue I have is why is it permitted to be 284, 12.5, 11.5, and 295 when these numbers would round up either lower or higher the the specified number? Thanks.

I think question is asking for a range in which her "actual" mpg might fall under. This range doesn't have to be limited strictly by what could have been true, but must include what could have been true. Note that the range is the value after you divide 285/12.5

mpaudena wrote:Nope. Just bought this. It is the 11th edition. What do you mean read different? I was paraphrasing the book if that is what you meant. What does your book say?

The real issue I have is why is it permitted to be 284, 12.5, 11.5, and 295 when these numbers would round up either lower or higher the the specified number? Thanks.

lightbulb wrote:I think question is asking for a range in which her "actual" mpg might fall under. This range doesn't have to be limited strictly by what could have been true, but must include what could have been true. Note that the range is the value after you divide 285/12.5

mpaudena wrote:Nope. Just bought this. It is the 11th edition. What do you mean read different? I was paraphrasing the book if that is what you meant. What does your book say?

The real issue I have is why is it permitted to be 284, 12.5, 11.5, and 295 when these numbers would round up either lower or higher the the specified number? Thanks.

I understand the idea of the range but I don't why would this fall within 284/12.5 fall within that range? I don't understand what you mean by the range is the value after 285/12.5. Why is it 12.5? Why isn't after 285/12.4?

Or is that what it is saying? Is it saying that it should be the numbers directly above and below the 2 given numbers? So they are giving us numbers that are slightly lower and higher in order that the number falls in between the numbers, exclusive?

The one problem is that the books explanation says specifically that the lowest number of miles/gallon is 284/12.5 and the highest is 295/11.4.

Min MPG would be 285/12.4 = ~22.98
Max MPG would be 294/11.5 = ~25.56

so the mpg are somewhere between 22.98 and 25.56

If you solve the solutions

a 290/12.5 and 290/11.4..............23.2 and 25.44
b. 295/12 and 284/11.4................24.58 and 24.91
c. 284/12 and 295/12...................23.66 and 24.58
d. 284/12.5 and 295/11.4.............22.72 and 25.87
e.295/12.5 and 284/11.4..............23.6 and 24.91

Now you have to look and see which range includes both numbers 22.98 and 25.56.

and you can quickly see that the only possible answer choice would be D.
I don't recommend attempting to do all of that work, but I just wanted to elaborate on how the answer is D.


Hope this helps

dmateer25 wrote:Min MPG would be 285/12.4 = ~22.98
Max MPG would be 294/11.5 = ~25.56

so the mpg are somewhere between 22.98 and 25.56

If you solve the solutions

a 290/12.5 and 290/11.4..............23.2 and 25.44
b. 295/12 and 284/11.4................24.58 and 24.91
c. 284/12 and 295/12...................23.66 and 24.58
d. 284/12.5 and 295/11.4.............22.72 and 25.87
e.295/12.5 and 284/11.4..............23.6 and 24.91

Now you have to look and see which range includes both numbers 22.98 and 25.56.

and you can quickly see that the only possible answer choice would be D.
I don't recommend attempting to do all of that work, but I just wanted to elaborate on how the answer is D.


Hope this helps

Yes, it does help, however, I am interested in how you would quickly see that the only possible answer is D since I won't have time to do all the math. Thanks.

I have to agree. I thought it was just me but indeed the logic or my understanding of the question is flawed. 284 rounded to the nearest 10 should be 280, not 290. 295 rounded should be 300, not 290.

From my understanding of rounding to the nearest 10, the answer should have been:
285/12.4 and 294/11.5

OR

286/12.4 and 294/11.6

Any thoughts or suggestions?

dmateer25 wrote:Min MPG would be 285/12.4 = ~22.98
Max MPG would be 294/11.5 = ~25.56

so the mpg are somewhere between 22.98 and 25.56

If you solve the solutions

a 290/12.5 and 290/11.4..............23.2 and 25.44
b. 295/12 and 284/11.4................24.58 and 24.91
c. 284/12 and 295/12...................23.66 and 24.58
d. 284/12.5 and 295/11.4.............22.72 and 25.87
e.295/12.5 and 284/11.4..............23.6 and 24.91

Now you have to look and see which range includes both numbers 22.98 and 25.56.

and you can quickly see that the only possible answer choice would be D.
I don't recommend attempting to do all of that work, but I just wanted to elaborate on how the answer is D.


Hope this helps

even I am intrested to know , if these divisions were doen usual way(which I guess would be time consuming) , or any short cut followed to narrow down to choice D.

TIA