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Rounding numbers - OG has mistake?

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Rounding numbers - OG has mistake?

by AndreiGMAT » Sun May 01, 2016 11:20 pm
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

Image

Here is explanation from OG: Since the miles are rounded to the nearest 10 miles, the number of miles is between 285 and 295. Since the gallons are rounded to the nearest gallon, the number of gallons is between 11.5 and 12.5

Should not 290 miles rounded to the nearest 10 miles be between 285 and 294?
Should not 12 gallons rounded to the nearest gallon be between 11.5 and 12.4?

The rule of rounding states: Five or more - Raise the score.
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by GMATGuruNY » Mon May 02, 2016 2:35 am
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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by AndreiGMAT » Mon May 02, 2016 4:30 am
GMATGuruNY, this is a very good explanation that made it clear for me. Thanks.
Please note that 295 is the UPPER LIMIT.
Any value below 295 -- even 294.999 -- is rounded DOWN to 290.
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by ygcrowanhand » Tue Apr 18, 2017 5:40 am
Hi GMATters,

Here's my video explanation of the question.

Basically don't get hung up on the rounding thing. If the GMAT wants to round in a stupid way, let them--just figure out how they're thinking about it. It wouldn't be the first pointless thing that's appeared in an OG question.

Enjoy!

https://youtu.be/FHSyTcjZaUw

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by Matt@VeritasPrep » Fri Apr 28, 2017 12:21 am
I think we're missing the essential point here. If I say that x is *between* 285 and 295, that means that

285 < x < 295

If we want to include the endpoints (285 ≤ x ≤ 295), then we MUST say *between, inclusive*. The GMAT will be consistent about this.
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by Matt@VeritasPrep » Fri Apr 28, 2017 12:24 am
ygcrowanhand wrote:If the GMAT wants to round in a stupid way, let them--just figure out how they're thinking about it.
That would be extremely controversial on their part, enough to call the validity of the test into question. (I mean, they have carte blanche to pull whatever nonsense they want in SC, but in math they have to stick to math, they can't perpetrate any bizarre and arbitrary notions of rounding!)

In any event, it's a non issue, since they're rounding in the proper way. No integer between 285 and 295 can end in 5, since "between" excludes 285 and 295 from consideration.
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by Matt@VeritasPrep » Fri Apr 28, 2017 12:28 am
Of course, the GMAT isn't doing the best job of using "between" in their own explanation! If the number of gallons used is x, and x rounds to 290, then 285 ≤ x < 295.

That said, what I've posted above still holds, "between x and y" means x < ... < y, while "between x and y, inclusive" means x ≤ ... ≤ y. Any official GMAT question (though perhaps not official GMAT explanation) will be consistent about this.
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by Matt@VeritasPrep » Fri Apr 28, 2017 12:31 am
Let me also add a way to solve.

Say the number of miles driven is x. Since x, rounded to the nearest 10, is 290, we have 285 ≤ x < 295.

Say the number of gallons used is y. Since y, rounded to the nearest gallon, is 12, we have 11.5 ≤ y < 12.5.

If Cindy drove 295 miles with 11.5 gallons of gas, she'd have maximum efficiency.

If Cindy drove 285 miles with 12.5 gallons of gas, she'd have minimum efficiency.

Normally, we'd say minimum efficiency ≤ Cindy's mpg ≤ maximum efficiency. But since we must be below 295 miles and below 12.5 gallons of gas, we have to change those ≤s to <s. This gives us the inequality

285/12.5 < Cindy's mpg < 295/11.5

and her mpg is between 285/12.5 and 295/11.5.
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Re: Rounding numbers - OG has mistake?

by Scott@TargetTestPrep » Mon Apr 13, 2020 3:55 am
AndreiGMAT wrote: ↑
Sun May 01, 2016 11:20 pm
 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

Image
If the distance of 290 miles is obtained by rounding to the nearest 10 miles, the actual distance must be between 285 miles and 295 miles. Similarly, if the number of gallons of gasoline used, 12 gallons, is obtained by rounding to the nearest gallon, the actual number of gallons must be between 11.5 gallons and 12.5 gallons. Therefore, the maximum number of miles per gallon is 295/11.5 and the minimum number of miles per gallon is 285/12.5, and the actual number of miles per gallon is some number in between these two numbers.

Note that we maximized the number of miles per gallon by making the numerator as large as possible (295) and the denominator as small as possible (11.5). Similarly, to minimize the mpg, we made the numerator as small as possible (285) and the denominator as large as possible (12.5).

Answer: D

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