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OG 11; problem solving; 129

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OG 11; problem solving; 129

by Pugalenthi » Tue May 22, 2012 12:11 pm
OG 11; problem solving; 129) 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 290/11.4
(b) 295/12 and 284/11.4
(c) 284/12 and 295/12
(d) 284/12.5 and 295/11.4
(e) 295/12.5 and 284/11.4

The answer is D. I am looking for reasoning behind miles and gallons range...why 284 to 295 instead of 285 to 294? What am I missing?
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by aneesh.kg » Tue May 22, 2012 12:46 pm
Pugalenthi wrote:OG 11; problem solving; 129) 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 290/11.4
(b) 295/12 and 284/11.4
(c) 284/12 and 295/12
(d) 284/12.5 and 295/11.4
(e) 295/12.5 and 284/11.4

The answer is D. I am looking for reasoning behind miles and gallons range...why 284 to 295 instead of 285 to 294? What am I missing?
Hi,

Good doubt. This would've escaped most people's attention.

285 < no. of miles < 295
or
285/12.5 < no. of miles per gallons < 295/11.5

The key words in the question are 'must have been'. If the 'no. of miles' is between 285/12.5 and 295/11.5 then it also be between a value little smaller than 285/12.5 (say 284/12.5) and a value little larger than 295/11.5 (say 295/11.4).
No Harm done!

Since option (D) envelops the entire range for (no. of miles per gallon), it is acceptable.
Aneesh Bangia
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by mdavidm_531 » Thu May 24, 2012 3:24 am
aneesh.kg wrote:
Pugalenthi wrote:OG 11; problem solving; 129) 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 290/11.4
(b) 295/12 and 284/11.4
(c) 284/12 and 295/12
(d) 284/12.5 and 295/11.4
(e) 295/12.5 and 284/11.4

The answer is D. I am looking for reasoning behind miles and gallons range...why 284 to 295 instead of 285 to 294? What am I missing?
Hi,

Good doubt. This would've escaped most people's attention.

285 < no. of miles < 295
or
285/12.5 < no. of miles per gallons < 295/11.5

The key words in the question are 'must have been'. If the 'no. of miles' is between 285/12.5 and 295/11.5 then it also be between a value little smaller than 285/12.5 (say 284/12.5) and a value little larger than 295/11.5 (say 295/11.4).
No Harm done!

Since option (D) envelops the entire range for (no. of miles per gallon), it is acceptable.
Hi, Aneesh,

Great job with the calculation. But don't you think the more important takeaway is the use of intuitive thinking when it comes to fractions?

See, if we want to get the range we need the least and the greatest number.

If we want to "drive down" the fraction with form a / b then we could do that by assigning a small "a" and a big "b"

As such the least number in the range would be
numerator = 285 while denominator = 12.5 (see how the "partnering" was done)

Consequently, the greatest number in the range would be
numerator = 295 while denominator = 11.5

:) Just my two cents
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by [email protected] » Fri May 25, 2012 3:25 am
Yes, what
mdavidm_531
said is also correct. But remember that what range we have calculated is the approximate. In these sort of questions, the GMAT has the habit of changing the options.

The option D could have been: 285/11.5 and 295/12.5

So focus on the concept of Miles per Gallon and that you have to calculate the range. Then start listing out the options very carefully. You will come down to D as the answer choice.

Hence the correct answer is D.
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by aneesh.kg » Fri May 25, 2012 7:52 am
mdavidm_531 wrote: Hi, Aneesh,

Great job with the calculation. But don't you think the more important takeaway is the use of intuitive thinking when it comes to fractions?

See, if we want to get the range we need the least and the greatest number.

If we want to "drive down" the fraction with form a / b then we could do that by assigning a small "a" and a big "b"

As such the least number in the range would be
numerator = 285 while denominator = 12.5 (see how the "partnering" was done)

Consequently, the greatest number in the range would be
numerator = 295 while denominator = 11.5

:) Just my two cents
Hi Dave,

I remember the (p1/r1 > p2/r2) problem that you had posted and this is on the same concept. Your approach is the best way to solve this problem. However, here, I was just trying to answer a very specific doubt.
Aneesh Bangia
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by mdavidm_531 » Sun May 27, 2012 9:59 pm
aneesh.kg wrote:
mdavidm_531 wrote: Hi, Aneesh,

Great job with the calculation. But don't you think the more important takeaway is the use of intuitive thinking when it comes to fractions?

See, if we want to get the range we need the least and the greatest number.

If we want to "drive down" the fraction with form a / b then we could do that by assigning a small "a" and a big "b"

As such the least number in the range would be
numerator = 285 while denominator = 12.5 (see how the "partnering" was done)

Consequently, the greatest number in the range would be
numerator = 295 while denominator = 11.5

:) Just my two cents
Hi Dave,

I remember the (p1/r1 > p2/r2) problem that you had posted and this is on the same concept. Your approach is the best way to solve this problem. However, here, I was just trying to answer a very specific doubt.
No problem, Aneesh. Until our next BTG problem :)
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