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A scientist invented a Lamp that can give light

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Schools: HBS '16, Stanford '16
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A scientist invented a Lamp that can give light [#permalink] New post 14 Nov 2012, 09:58
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Difficulty:

  25% (medium)

Question Stats:

65% (02:11) correct 35% (01:23) wrong based on 40 sessions
A scientist invented a Lamp that can give light for about 130 hours, rounded to the nearest 10 hours, and used 10 gallons of oil, rounded to the nearest gallon. The actual number of hours per gallon that the lamp lighted must have been between

A. \frac{125}{10.5} and \frac{135}{9.5}

B. \frac{135}{10} and \frac{125}{9.5}

C. \frac{125}{9.5} and \frac{135}{10.5}

D. \frac{130}{10.5} and \frac{130}{9.5}

E. \frac{135}{10.5} and \frac{125}{9.5}

I don't understand why the correct answer should be: \frac{125}{10.4} and \frac{134}{9.5}.

If the actual number of hours is 10.5, it should be rounded to 11. And if the actual number of galons is 135, it should be rounded to 140.

Please, your comments.

Source: grockit.com
[Reveal] Spoiler: OA
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Re: A scientist invented a Lamp that can give light [#permalink] New post 14 Nov 2012, 10:37
Please read the answer. It says between 125/10.5 and 135/9.5. I had a second thought why the answer is not 125/9.5 and 135/10.5. But on close observation, I realized that with 125/10.5 and 135/9.5, the left and right boundary or the range value actually increases and so it satisfies the condition. The answer should be A) between 125/10.5 and 135/9.5.
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Re: A scientist invented a Lamp that can give light [#permalink] New post 14 Nov 2012, 13:47
danzig wrote:
A scientist invented a Lamp that can give light for about 130 hours, rounded to the nearest 10 hours, and used 10 gallons of oil, rounded to the nearest gallon. The actual number of hours per gallon that the lamp lighted must have been between

A. \frac{125}{10.5} and \frac{135}{9.5}

B. \frac{135}{10} and \frac{125}{9.5}

C. \frac{125}{9.5} and \frac{135}{10.5}

D. \frac{130}{10.5} and \frac{130}{9.5}

E. \frac{135}{10.5} and \frac{125}{9.5}

I don't understand why the correct answer should be: \frac{125}{10.4} and \frac{134}{9.5}.

If the actual number of hours is 10.5, it should be rounded to 11. And if the actual number of galons is 135, it should be rounded to 140.

Please, your comments.

Source: grockit.com
I expect you to be asking why answer shouldn't be \frac{125}{10.4} and \frac{134}{9.6}
You did analyse it correctly but what if gallons consumed is 9.51? Mathematics say that 9.59 is rounded to 9.6 which is again as per question rounded to 10 gallons.... you are missing set of solutions between 9.55-9.59 and 10.41-10.44..... you cannot loose any answer solutions....
also the question was "have been between" so your range doesn't include all solutions. Hope it is clear.
Re: A scientist invented a Lamp that can give light   [#permalink] 14 Nov 2012, 13:47
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A scientist invented a Lamp that can give light

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