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555-605 Level|   Distance and Speed Problems|   Min-Max Problems|   Word Problems|                                          
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On a recent trip, Cindy drove her car 290 miles, rounded to 15 Apr 2020, 19:21
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Asad
Bunuel
fatihaysu
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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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 29 Apr 2020, 10:52
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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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On a recent trip, Cindy drove her car 290 miles, rounded to 30 Apr 2020, 09:38
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fatihaysu
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
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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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On a recent trip, Cindy drove her car 290 miles, rounded to 04 Oct 2020, 16:14
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Video solution from Quant Reasoning:
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On a recent trip, Cindy drove her car 290 miles, rounded to 30 Aug 2025, 05:24
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hi bunuel,
i want to say that i am little confused about rounding to nearest 10 miles becoz i thought 290 become 300 miles, so please clear this and also provide some estimation problem link and link of problem based on rounding the number.
and if there is some theory regarding making estimation.
Bunuel
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

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.
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On a recent trip, Cindy drove her car 290 miles, rounded to 30 Aug 2025, 07:37
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shaliny
hi bunuel,
i want to say that i am little confused about rounding to nearest 10 miles becoz i thought 290 become 300 miles, so please clear this and also provide some estimation problem link and link of problem based on rounding the number.
and if there is some theory regarding making estimation.
Show more
290 is the value that is already rounded to its nearest 10 miles, therefore the actual value was between 285 and 294, inclusive.

Here's a post on rules for rounding numbers: https://gmatclub.com/forum/rounding-rul ... 96273.html
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