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# Problem solving - 600 level question

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Problem solving - 600 level question [#permalink]

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23 May 2010, 09:22
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Could anyone help me with this question.

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

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Senior Manager
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Re: Problem solving - 600 level question [#permalink]

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23 May 2010, 10:17
shekar123 wrote:
Could anyone help me with this question.

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

d = 100 miles (rounded to nearest miles) so it will be
90<d<110

g = 10 g
9<g<11

miles / gallon = d/g

To maximize this we need to maximize d and minimize g = 110/9= 12.22
To minimize this we need to minimize d and maximize g = 100/11 = 9.11

9.11 < mpg < 12.22
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Re: Problem solving - 600 level question [#permalink]

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23 May 2010, 13:05
shekar123 wrote:
Could anyone help me with this question.

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

100 miles rounded t nearest 10 miles which means Andrew drove his truck in between 95 -104 miles

similarly for fuel the actual usage will be between 9.5-10.4

Now, to get actual number of miles per gallon (Mileage) we have 2 options
1. when the mileage is maximum i.e maximum miles divided by minimum number of gallons = 104/ 9.5 =10.9 ( approx)

2. When the mileage is minimum i.e when the minimum miles divided by maximum number of gallons = 95/10.4= 9.1( approx)

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Intern
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Re: Problem solving - 600 level question [#permalink]

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23 May 2010, 15:50
dimitri92 wrote:
shekar123 wrote:
Could anyone help me with this question.

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

d = 100 miles (rounded to nearest miles) so it will be
90<d<110

g = 10 g
9<g<11

miles / gallon = d/g

To maximize this we need to maximize d and minimize g = 110/9= 12.22
To minimize this we need to minimize d and maximize g = 100/11 = 9.11

9.11 < mpg < 12.22

OA is 95/10.5 and 105/9.5

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Re: Problem solving - 600 level question [#permalink]

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23 May 2010, 19:46
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Nitish has the right answer. I missed the part that when we are approximating it goes only to 5 units behind. So 100 will be in the range of 95 to 105.
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Intern
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Re: Problem solving - 600 level question [#permalink]

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24 May 2010, 10:18
Good explanations guys, could you please elaborate on the approximation? (i.e. +- 5 rather than 10)

Thanks!
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Re: Problem solving - 600 level question [#permalink]

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24 May 2010, 23:51
cgl7780 wrote:
Good explanations guys, could you please elaborate on the approximation? (i.e. +- 5 rather than 10)

Thanks!

Hope this helps

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Re: Problem solving - 600 level question   [#permalink] 24 May 2010, 23:51
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