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On a recent trip, Cindy drove her car 290 miles, rounded to
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chetan2u
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Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink] New post  21 Dec 2019, 18:54
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jabhatta@umail.iu.edu wrote:
hi chetan2u Gladiator59 Bunuel, generis

Why is this not a following assumption one is allowed to make for this question ?

If you drive 295 miles --> you will use more fuel as compared to driving 285 miles (least amount of fuel)

Specifically if you use 294.99999999999 miles -- you use up the most fuel

which is why I assumed the answer is 295 (most distance)/12.5 (most fuel) - 285 (least distance) /11.5 (least fuel)

Where is the gap in my logic ?



The distance is between 285 and 295, and fuel consumed is 11.5 to 12.5.
We do not know whether it traveled 285 or 289 or 294 and consumed 11.5 or 12 12.4
So, we look for the extremes..Max distance in least fuel and Min distance in max fuel consumed.

In the highlighted portion what if he traveled 295 in 12 liters. It does not fall in this range
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Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink] New post  15 Apr 2020, 18:08
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.

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

What if it is \(285<m<295\) or \(11.5<g<12.5\)?
Thanks__
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Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink] New post  15 Apr 2020, 18:21
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Asad 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.

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

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


Asad

The question mentioned that the distance traveled is 290 miles rounded to nearest 10 miles

all values from 285 to 294.99 both inclusive when rounded to the nearest 10 miles become 280

that's why in equation, 285 is included but 295 is NOT included (295 when rounded to the nearest 10 mile becomes 300)

Same is the reasons for gasoline inequation too

I hope this explains now... :)
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On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink] New post  29 Apr 2020, 09:52
This one was very tricky. This is not necc because of the math, but due to understanding what that phrase "must have been between" means. Semantics.

The first thing I did was just read the problem, and without looking at the answers, came up with the following:

285/12.4 and 294/11.5

Then I looked at answers and noticed that there was neither a 294 nor a 12.4 anywhere. That threw me off.

So ... Going back to the question, the phrase is not looking for you to find exactly the range that you worked out. Rather the numbers you came up with must fall within the ranges given in the answer even if the range is much broader than your answer. (D) is the answer.

One way to check is to work things out on a calculator* to get

(a) 290/12.5 and 290/11.5 ~~~> 23.2 and 25.217
...
(d) 285/12.5 and 295/11.5 ~~~> 22.8 and 25.65
(e) 295/12.5 and 285/11.5 ~~~> 23.6 and 24.782

Now, where does 285/12.4 and 294/11.5, i.e. 22.98 and 25.565 fit in? (d)

*Not that you can use a calculator, but this is just to see whats going on.
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Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink] New post  30 Apr 2020, 08:38
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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


The Miles per gallon range will be where

Highest Miles/gallon = Highest miles/ Lowest Gallons used ~ 295 (294.999...)/ 11.5 (11.5)

Lowest Miles/ gallon = Lowest Miles/ Highest Gallons used ~ 285 / 12.5

Answer is D
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Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink] New post  30 Apr 2021, 01:05
Bunuel wrote:
prasannajeet wrote:
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.

Hope it's clear.



I was having hard time understanding the question.Now everything is clear.Thanks Bunuel
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Re: On a recent trip, Cindy drove her car 290 miles, rounded to [#permalink]
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