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Rounding question - something bothering me

This topic has 2 expert replies and 0 member replies
richewalsh Newbie | Next Rank: 10 Posts Default Avatar
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Posted:
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Rounding question - something bothering me

Post Thu Jan 29, 2015 2:51 pm

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I got the question, right but one aspect is bothering me and I'm sure it is just an oversight or rookie mistake, but any help is much appreciated.

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 correct answer is d. I understand the range of putting the furthest distance with lowest mpg and closest with highest mpg. But I thought the 295 figure should have been 294. 295 would be rounded to 300 miles, no?

Minor issue, but has been bothering me. TIA

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GMAT/MBA Expert

Post Thu Jan 29, 2015 2:55 pm
Quote:
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 to 290/11.5

B) 295/12 to 285/11.5

C) 285/12 to 295/12

D) 285/12.5 to 295/11.5

E) 205/12.5 to 285/11.5
We round UP when we reach the HALFWAY point between two values.
Any value BELOW the halfway point is rounded DOWN.

290 miles, rounded to the nearest 10 miles:
285 ≤ m < 295.
Please note that 295 is the UPPER LIMIT.
Any value below 295 -- even 294.999 -- is rounded DOWN to 290.

12 gallons of gasoline, rounded to the nearest gallon:
11.5 ≤ g < 12.5.
Please note that 12.5 is the UPPER LIMIT.
Any value below 12.5 -- even 12.499 -- is rounded DOWN to 12.

Worst miles per gallon = (lower limit for miles)/(upper limit for gas) = 285/12.5.
Best miles per gallon = (upper limit for miles)/(lower limit for gas) = 295/11.5.
Thus, miles per gallon is between 285/12.5 and 295/11.5.

The correct answer is D.

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GMAT/MBA Expert

Post Thu Mar 22, 2018 11:47 am
Hi All,

When dealing with "rounding" questions, you have to make sure that you're properly following the 'rules' of rounding.

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

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 inequality:

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.

Final Answer: D

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Rich

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