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On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]

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18 Aug 2010, 10:56

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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 290/11.5 B. 295/12 and 285/11.5 C. 285/12 and 295/12 D. 285/12.5 and 295/11.5 E. 295/12.5 and 285/11.5

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 290/11.5

b) 295/12 and 285/11.5

c) 285/12 and 295/12

d) 285/12.5 and 295/11.5

e) 295/12.5 and 285/11.5

My approach is;

a)for miles x must be = 284< x < 295 b)for gasoline x must be = 11,4< x <12,5

then the answer has to be D or E

I chose E because of order like a/b = 284/11,5<x<295/12,5

Why the answer is D? And is it 700+ question?

Cindy drove her car 290 miles, rounded to the nearest 10 miles --> \(285\leq{m}<295\); Used 12 gallons of gasoline, rounded to the nearest gallon --> \(11.5\leq{g}<12.5\);

Minimum Miles per gallon, m/g --> \(\frac{285}{12.5}<\frac{m}{g}<\frac{295}{11.5}\) (to get lower limit take min possible for nominator and max possible for denominator, and for upper limit take max possible for nominator and min possible for denominator).

I don't quite understand your question... "Why not E?" Because we calculated range for \(\frac{m}{g}\) which was the same as in option D, so D is the correct answer and not E .

Anyway:

Range for D: \(\frac{285}{12.5}=22.8<\frac{m}{g}<25.7=\frac{295}{11.5}\) (correct answer);

Range for E: \(\frac{295}{12.5}=23.6<\frac{m}{g}<24.8=\frac{285}{11.5}\), so you can see that actual \(\frac{m}{g}\) (from correct option D) can be less than 23.6 (till 22.8) and more than 24.8 (up to 25.7), so option E does not cover all possible values of \(\frac{m}{g}\). That's why E is not correct.
_________________

On a recent trip Cindy drove her car 290 miles, rounded to the nearest [#permalink]

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16 May 2011, 18:08

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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 290/11.5 b) 295/12 and 285/11.5 c) 285/12 and 295/12 d) 285/12.5 and 295/11.5 e) 295/12.5 and 285/11.5

IF the trip is rounded to the nearest 10 miles my min max = 285 to 294 IF gasoline is rounded to nearest gallon my min max =11.5 to 12.4 Do you agree ?

Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]

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22 Apr 2012, 12:16

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The biggest mistake one can make on this question is to presume that number of miles is an integer and the number of gallons is a value rounded to the tenths digit. The upper bound for gallons is not 12.4! It can be up to 12.49999(repeated) but can never be 12.5. The number of miles can be at most 294.99999(repeated) but can never be 295. I made a massive blunder for this question.

On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]

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14 Jul 2012, 00:11

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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 290/11.5 b) 295/12 and 285/11.5 c) 285/12 and 295/12 d) 285/12.5 and 295/11.5 e) 295/12.5 and 285/11.5

For the distance to be rounded to the nearest 10 miles, it should be a value in the range from 285 to 294. Similarly, for the used-up fuel to be rounded to the nearest gallon, it should be a value in the range from 11.5 to 12.4

So we have to make the possible greatest and smallest fractions from those 4 endpoints, which are 285/12.4 (the smallest) and 294/11.5 (the greatest). So D is my best answer.

On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]

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01 Dec 2012, 23:43

What values when rounded off to the nearest 10 miles will result to 290? 285 <= m < 295 What values when rounded to the nearest gallon will result to 12 gallons? 11.5 <= g < 12

Smallest possible value: 285/12 Greatest possible value: 295/11.5

Answer: D, between 285/12 and 295/11.5
_________________

Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]

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18 Apr 2013, 13:39

I understand the Min Max reasoning now. The only issue I have with the question is if you drive 295 miles you will use more fuel as compared to driving 285 miles, which is why I assumed 295/12.5 - 285/11.5.

IN GMAT : is 12.5 rounded to 12 or 13 ? . I assumes 12.4 rounded to 12 and 12.5 rounded to 13

If thats the case , the ans should be 294/11.5 and 284/12.4

correct me if Im wrong

Hi eski, don't forget that this really means in mathematical terms 11.5 < x < 12.5

Since there is no equal sign, x can get as high as 12.499999999 but never 12.5. 12.4 is too low of an endpoint because it could easily be 12.42 or 12.48.

Re: To Bunuel, there is no logic for that please help [#permalink]

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06 May 2013, 06:51

Bunuel wrote:

fatihaysu wrote:

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 290/11.5

b) 295/12 and 285/11.5

c) 285/12 and 295/12

d) 285/12.5 and 295/11.5

e) 295/12.5 and 285/11.5

My approach is;

a)for miles x must be = 284< x < 295 b)for gasoline x must be = 11,4< x <12,5

then the answer has to be D or E

I chose E because of order like a/b = 284/11,5<x<295/12,5

Why the answer is D? And is it 700+ question?

Cindy drove her car 290 miles, rounded to the nearest 10 miles --> \(285\leq{m}<295\); Used 12 gallons of gasoline, rounded to the nearest gallon --> \(11.5\leq{g}<12.5\);

Minimum Miles per gallon, m/g --> \(\frac{285}{12.5}<\frac{m}{g}<\frac{295}{11.5}\) (to get lower limit take min possible for nominator and max possible for denominator, and for upper limit take max possible for nominator and min possible for denominator).

Answer: D.

Hope it's clear.

Sorry for not making it clear at the first time. In your solution, you had mentioned "get lower limit"(the highlighted one) and since no where in question it was mentioned 'specifically' as lower limit, why not take the upper limit? If we do so, option E could be the answer..

Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]

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01 Jun 2013, 02:40

what happen to my understanding ,I just fail to understand the sentence ...."Cindy drove her car 290 miles, rounded to the nearest 10 miles"................other part is OK with me but please som1 just calify me rounded to nearest 10 mile???

what happen to my understanding ,I just fail to understand the sentence ...."Cindy drove her car 290 miles, rounded to the nearest 10 miles"................other part is OK with me but please som1 just calify me rounded to nearest 10 mile???

Rgds Prasannajeet

Cindy drove her car 290 miles, rounded to the nearest 10 miles means that \(285\leq{m}<295\) (basically this means that the closest multiple of 10 to the distance that Cindy drove is 290).

For example, Cindy could have driven say 286 miles, which rounded to the nearest 10 miles is 290 OR Cindy could have driven say 293 miles, which rounded to the nearest 10 miles is also 290.

Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]

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21 Jul 2013, 19:18

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Hi Bunuel, Could you please explain the below? Somehow I don't get why lower limit and upper limit is considered this way

"To get lower limit take min possible for nominator and max possible for denominator, and for upper limit take max possible for nominator and min possible for denominator"

Hi Bunuel, Could you please explain the below? Somehow I don't get why lower limit and upper limit is considered this way

"To get lower limit take min possible for nominator and max possible for denominator, and for upper limit take max possible for nominator and min possible for denominator"

We want to find the range of m/g.

The lower limit would be the least possible value of m/g, to minimize it maximize denominator (g) and minimize numerator (m). The upper limit would be the maximum possible value of m/g, to maximize it minimize denominator (g) and maximize numerator (m).

Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]

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02 Aug 2013, 10:14

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

"Cindy drove her car 290 miles, rounded to the nearest 10 miles" In other words, she could have drive between 285 miles and 294.9. If she had driven 284.9 miles it would be rounded down to 280 miles. If she had driven 295 miles, it would have been rounded up to 300.

285 <= D <= 294.9

"used 12 gallons of gasoline, rounded to the nearest gallon." The same logic applies here. She used anywhere between 11.5 and 12.49 gallons of gas.

11.5 <= G <= 12.49

The trick here is that the question is looking for the maximum range of possibilities (i.e. the fewest miles traveled with the most gas and the most miles traveled with the least amount of gas) It makes sense to think that the more miles traveled, the more gas used (which is why I originally said the answer was E) but the problem want's the maximum range of values.

Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]

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11 Nov 2013, 18:14

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If it's rounded to the nearest 10 she couldn't have a max mileage of 295/11.5....it would be 294/11.5. if it was 295 it would have rounded up to 300. so her mpg would be \(\frac{285}{12.4}\leq\frac{m}{g}\leq\frac{294}{11.5}\)