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Miles and gallons

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Miles and gallons

by metallicafan » Fri Jan 04, 2013 8:44 am
Andrew drove his truck 100 miles, rounded to the nearest 10 miles, and used 10 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Tom's truck got on this vacation trip must have been between

A. 100/10.5 and 100/9.5

B. 95/10.5 and 105/9.5

C. 95/9.5 and 105/10.5

D. 105/10 and 95/9.5

E. 105/10.5 and 95/9.5

OA is B.

In the correct answer, I don't understand why the upper limit for gallons is 10.5. If it is 10.5, that number would be rounded to eleven.
The same with the upper limit for milles. If it is 105, that number would be rounded to 110.
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by gander123 » Fri Jan 04, 2013 10:18 am
Hey metalli,

Agree with you, I also boiled down the problem to the following:

x: number of miles driven
y: number of gallons consumed

x/y miles per gallon

95<= X <= 104

9.5<= Y <= 10.4

Thus, 95/10.4 <= x/y <= 104/9.5.

The only plausible solution left would have been B. However, I understand your point.
Let's wait for an expert ;).

Brgds,

Tobi
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by Whitney Garner » Fri Jan 04, 2013 11:18 am
metallicafan wrote:In the correct answer, I don't understand why the upper limit for gallons is 10.5. If it is 10.5, that number would be rounded to eleven.
The same with the upper limit for milles. If it is 105, that number would be rounded to 110.
This is a great question metallicafan!

I think the thing you want to think about is the fact that decimals can get smaller and smaller and smaller (and closer and closer and closer to 10.5 without actually getting there). What I mean is the following:

Any number that is even infinitesimally smaller than 10.5 would round down (e.g. 10.49999999999999999999). This means that there are actually an infinite number of numbers that are larger than 10.4 but still smaller than 10.5. So the best way to represent this range is to just say that the highest possible value is infinitely close to 10.5 without actually equaling 10.5 (but how do we write that?? we don't, so we just say that is had to be smaller than 10.5!)

The same would be true for the 105 limit. So the actual ranges would be the following:

x: number of miles driven
y: number of gallons consumed

x/y miles per gallon

95<= X < 104

9.5<= Y < 10.4

Thus, 95/10.5 < x/y < 105/9.5.

Hope this helps!
:)
Whit
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by sana.noor » Fri Jan 04, 2013 11:30 am
10 gallons rounded to the nearest means the lower limit could be 9.5 and the upper limit could be 10.5...10.5+9.5/2 gives 10. If we take 11 and 9.5 as the two quantities the rounded number wont be 10. Similarly 100 miles rounded to nearest mean 95 or 105....95+105/2 = 100 miles..
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by gander123 » Sat Jan 05, 2013 3:22 am
Hey Whit,
Any number that is even infinitesimally smaller than 10.5 would round down (e.g. 10.49999999999999999999). This means that there are actually an infinite number of numbers that are larger than 10.4 but still smaller than 10.5. So the best way to represent this range is to just say that the highest possible value is infinitely close to 10.5 without actually equaling 10.5 (but how do we write that?? we don't, so we just say that is had to be smaller than 10.5!)
Great background knowledge. But dont we go far beyond what is introduced in the Math Section of the official guide?

Brgds,

Tobi
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by GMATGuruNY » Sat Jan 05, 2013 5:01 am
gander123 wrote:Hey Whit,
Any number that is even infinitesimally smaller than 10.5 would round down (e.g. 10.49999999999999999999). This means that there are actually an infinite number of numbers that are larger than 10.4 but still smaller than 10.5. So the best way to represent this range is to just say that the highest possible value is infinitely close to 10.5 without actually equaling 10.5 (but how do we write that?? we don't, so we just say that is had to be smaller than 10.5!)
Great background knowledge. But dont we go far beyond what is introduced in the Math Section of the official guide?

Brgds,

Tobi
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