On a recent trip, Cindy drove her car 290 miles, rounded to

Question

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

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

Bunuel · Accepted Answer

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?

alphabeta1234 · Answer

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.

mehdiov · Answer

a)for miles x must be = 284< x < 295
b)for gasoline x must be = 11,5< x <12,5 ==> 1/12.5<1/x<1/11,5

then you can multiply.

Be carful you can multiply 2 enquality if every thing is positig but never devide them
furthermore you can add enequaliy but never sustract

hope it helps

Bunuel · Answer

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.

olivite · Answer

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 ?

amit2k9 · Answer

distance range 285<D< 294
gallons range 11.5<G<12.4

hence min = 285/12.4 max = 295/11.5

closest answer choice is D.

chels · Answer

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.

mbaiseasy · Answer

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

eski · Answer

This lead me to ask .

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

VeritasPrepRon · Answer

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.

Hope this helps!
-Ron

prasannajeet · Answer

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

Rgds
Prasannajeet

Bunuel · Answer

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.

Hope it's clear.

KalEl · Answer

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"

Bunuel · Answer

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) .

Hope it's clear.

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

JeffTargetTestPrep · Answer

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

smig · Answer

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.

Hope this helps.

PGTLrowanhand · Answer

Hi GMATters,

Here's my video explanation of the question. Enjoy!

FHSyTcjZaUw

Rowan

TheUltimateWinner · Answer

Bunuel 
Could you clarify the ''  ≤  '' in the highlighted part, please?

What if it is  285<m<295  or  11.5<g<12.5 ?
Thanks__

On a recent trip, Cindy drove her car 290 miles, rounded to

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On a recent trip, Cindy drove her car 290 miles, rounded to

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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