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Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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13 Nov 2013, 02:30

Bunuel wrote:

Which previous post are you talking about? How did you eliminate options?

I am sorry I can not find that post, but it went along the lines of the following logic.... (I hope I got it right)

The largest amount she could have driven is: 295/11.5 The lease amount is: 285/12.5

We can rule out all options that do not have denominator of 11.5 or 12.5. We are left with only A, D, or E. We can see that the left side of D includes both sides of A and E (If either of them (A or E) were true, than D would also necessarily be true) so we can rule them out?

Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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05 Jan 2015, 03:33

mulhinmjavid wrote:

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.

Im sorry im unable to understand explanation; in final step you said that in order to get minimum possible value of fraction(miles per gasoline gallon) we should take maximum denominator and minimum nominator:

But minimum possible value of nominator is 12.4 because 11.5<= g <12.5.

Isnt it?

Why it cannot be 12.45 or 12.49 or 12.499999999999? Basically any number less than 12.5.
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Re: On a recent trip Cindy drove her car 290 miles, rounded to the nearest
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08 Feb 2015, 19:10

Hi All,

While it's a minor/nitpick point, I do want to point out some details about the "rounding" that is involved in this question.

Cindy's distance is rounded to the nearest 10 miles and is "called" 290 miles. This means that the actual distance is given by the following inequality:

285 <= Actual distance < 295

Both of the users in this thread wrote that the distance was < 294 and that is NOT technically correct.

In that same way, that number of gallons used is rounded to the nearest gallon and is "called" 12 gallons. This means that the actual number of gallons used is given by the following equation:

11.5 <= gallons used < 12.5

The question asks for the "range" that the actual MILES/GALLON falls into. This is ultimately a question of "ratios" and what it takes to make a ratio as "big" as possible or as "small" as possible.

To make a ratio "bigger", you can EITHER make the numerator bigger OR make the denominator smaller. To get the "biggest" ratio, you have to do BOTH.

In that same way, to make a ratio "smaller", you can EITHER make the numerator smaller OR make the denominator bigger. To get the "smallest" ratio, you have to do BOTH.

Regardless, the given answer is correct, but to score at the highest levels on Test Day, you have to be careful about the "details" involved in each question. With enough little errors, your score will drop.

Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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26 Mar 2015, 11:39

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.

Hi Bunuel,

Here my approach was to choose the solution in which the approximation 'rule' is if I add a qty to the numerator I subtract a qty to the denominator and vice versa. The only option that showed that pattern was D and that was my choice.

Now, look more in detail all the explanation provided I'm not sure if I got the right answer choice only by fluke.

Please, let me know if my approach to such questions make sense or If I'm missing something.

Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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02 Oct 2015, 23:09

Distance driven , rounded to the nearest 10 miles => 285≤m<295; Since 12 gallons of gasoline were used, rounded to the nearest gallon => 11.5≤g<12.5;

Actual number of miles per gallon , m/g =>285/12.5<m/g<295/11.5

We want to maximize the range for m/g .The minimum value for m/g will be when numerator is minimum and denominator is maximum . The maximum value for m/g will be when numerator is maximum and denominator is minimum .
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Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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16 Jun 2016, 06:12

1

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

In solving this problem we must remember that we are given a rate in miles per gallon. It follows that:

Rate = Distance/Gallons

We are given that she drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. We are being asked to determine a possible range for Cindy’s rate. Thus, we really are trying to determine the maximum value for her rate (the largest distance traveled divided by the smallest number of gallons used) and the minimum value for her rate (the smallest distance traveled divided by the largest number of gallons used).

Let’s first determine the minimum and maximum distance. We know that she drove 290 miles, rounded to the nearest ten miles. Thus, we first determine what values will round to 290 when rounded to the nearest 10 miles. This means the actual number of miles driven can be any number from 285 to a number that is almost 295.

So we can say the minimum distance is 285 miles and the maximum distance is (almost) 295 miles.

Next, we determine the minimum and maximum number of gallons used. We know that she used 12 gallons of gas, rounded to the nearest gallon. It follows that the actual number of gallons of gas used can be any number from 11.5 to a number that is almost 12.5.

So we can say the minimum number of gallons is 11.5 and the maximum number of gallons is (almost) 12.5.

Using the formula Rate = Distance/Gallons we see that the maximum rate is the maximum miles divided by the minimum gallons, which is 295/11.5.

Similarly, the minimum rate is the minimum miles divided by the maximum gallons, or 285/12.5.

We can see that our maximum and minimum rates are exactly those given in answer choice D.

Answer D
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Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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04 Dec 2016, 03:24

Great Question this one. Here the Distance (estimated )=290 Actual Distance => (285->294)

Gas(estimated)=>12 Actual Gas => (11.5->12.4)

Now Miles per gallon range is needed Firstly Consider any fraction p/q . In order to maximise it => We maximise p and minimise q In order to minimise in => We minimise p and maximise q

Hence the minimum value => 285/12.4 maximum value => 294/11.5

Hence the Range is => (\(\frac{285}{12.4} ,\frac{294}{11.4}\))

Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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14 Dec 2016, 14:35

Simply, only options "D" or 'E" has correct decimals in both numbers so that it conforms to the basic condition. It's more easier to grasp realising that the more miles you can drive the less would be the consumption rate of the car that is the key point therefore you'll get the highest range. I think that such sort of problems can be solved mostly logically. The only thing I do not completely understand in that case is rounding: should be as follows:

Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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11 Mar 2017, 15:42

1

I struggled with this question and chose answer E first, but later realized why it should be D. Sharing a detailed explanation in case someone is still struggling with it. So, the actual miles per gallon for Cindy is not 290/12 (it can be, but for now, let's assume that's not the actual answer). If you understand rounding, then the miles she drove are between 285-295 and her fuel consumption is 11.5-12.5 (as per ans choices). Cindy's miles/gallon will be somewhere between these values.

Now the her car's performance would be the best if she drove the maximum miles with the least fuel consumption, which is 295/11.5. Similarly, it will be the worst if 285/12.5. The car's actual performance or miles/gallon will lie somewhere between the best and the worst values. The role of 290 and 12 are just to indicate what could be the lowest and highest mileage and fuel consumption. The question asks the actual value will lie between what values... it doesn't ask which fractions are the closest to 290/12. Choice D seems logical because 285/11.5 is close to 290/12, which is close to 295/12.5. But that's not what is asked.

Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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13 Jul 2017, 19:56

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.

Hi my question is that in the OG question they have just asked us about the miles per gallon and the maximum miles or minimum miles. How should we assume that?

Re: On a recent trip, Cindy drove her car 290 miles, rounded to
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26 Oct 2017, 18:38

AccipiterQ wrote:

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 \(\frac{285}{12.4}\leq\frac{m}{g}\leq\frac{294}{11.5}\)

The official answer is missing the above point. (D) is still correct since the bounds of (D) are wider than the tightest correct answer. It might be easier to see if fuel is expressed as a whole number (i.e. \(gal * 10^{-1}]\)).