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by GmatKiss » Sun Aug 14, 2011 1:30 pm
A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?

- 28
- 30
- 33
- 36
- 38
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by sumgb » Sun Aug 14, 2011 2:33 pm
we need to find the value of (total miles / total gallons of fuel used)

if car runs of 25 miles on 1 gallon fuel in city, then for 10 miles in city car needs 10/25 = 2/5 gallons of fuel

if car run for 40 miles on 1 gallon fuel on highway, then for 50 miles on highway car needs 50/40 = 5/4 gallons of fuel

so (total miles / total gallon) = 60 / (2/5 + 5/4) = 400 / 11 = 36.33 (approx.)

so I would go with answer choice D which is 36

What is OA?

Hope this helps...
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by GMATGuruNY » Mon Aug 15, 2011 1:21 am
GmatKiss wrote:A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?

- 28
- 30
- 33
- 36
- 38
City miles:Highway miles = 10:50 = 1:5.
Any values that conform to this ratio will yield the same average miles per gallon.

Let city miles = 200 and highway miles = 1000. (200:1000 = 1:5.)
Gas used in the city = 200/25 = 8.
Gas used on the highway = 1000/40 = 25.
Total gas used = 8+25 = 33.
Total Miles/Total Gas = 1200/33 = 400/11 ≈ 36.
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by Fighting with GMAT » Mon Aug 15, 2011 7:01 am
Why can't we use the weighted average to solve this question ?

Weighted Average miles / gallon
= [(25x1)+(40x5)]/6
= 225/6
= 37.5
= 38 miles per gallon (Answer choice # E)
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by GmatKiss » Mon Aug 15, 2011 8:36 pm
OA: D
I have the same doubt! Why can't we use weighted average in this case?
Experts, pls help!
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by GMATGuruNY » Tue Aug 16, 2011 4:23 am
GmatKiss wrote:OA: D
I have the same doubt! Why can't we use weighted average in this case?
Experts, pls help!
Imagine the problem said this:
A certain car averages 25 miles PER HOUR when driven in the city and 40 miles PER HOUR when driven on the highway. According to these rates, which of the following is closest to the AVERAGE SPEED FOR THE ENTIRE TRIP when the car is driven 10 miles in the city and then 50 miles on the highway?

- 28
- 30
- 33
- 36
- 38
The problem above asks for the average speed for the entire trip.
To calculate the average speed for the entire trip, we need to determine how much weight must be given to each rate (25 miles per hour and 40 miles per hour).
The amount of weight given to each rate is the amount of TIME spent traveling at each rate.
Thus, we calculate the times, then divide the total distance by the total time.

The same holds true for the gasoline problem, which asks for the average number of miles PER GALLON.
This is no different from asking for the average number of miles PER HOUR -- the average speed -- for the entire trip.
To calculate the average number of miles per gallon for the entire trip, we need to determine how much weight must be given to each miles-per-gallon rate (25 miles per gallon and 40 miles per gallon).
The amount of weight given to each miles-per-gallon rate is the amount of GASOLINE used when traveling at each rate.
Thus, we calculate the amounts of gasoline used, then divide the total distance by the total amount of gasoline.
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by sl750 » Tue Aug 16, 2011 5:29 am
The bottom line is, in speed-distance, or work-rate problems, you have to make sure the relationship is correct.i.e speed= distance/time or rate = work/time. So multiplying 25 with 1 is wrong as that is like multiplying speed times distance
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by gmatboost » Wed Aug 17, 2011 1:34 pm
To be specific, the quantities in this question are miles, gallons, and miles/gallon.
The "RTD" equation that relates these is (Miles/Gallon) * Gallons = Miles

The question asks for overall Miles/Gallon, so you need to find total gallons and total miles. You know total miles, so you need to figure out how to find total gallons.

Let the equation be your guide:
(Miles/Gallon) * Gallons = Miles
Gallons = Miles / (Miles/Gallon)

Multiplying 25 * 10 is multiplying Miles/Gallon * Miles, which (as you can see with the equation above) isn't the right calculation.

The takeaway, in my opinion, is to always use units when you're in an unfamiliar situation.
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by jzw » Wed Mar 14, 2012 1:39 pm
would anyone be willing to do the original problem using the rate pie method please? i just need to see it applied once and i should be able to re-apply it afterward. i really appreciate it. taking the gmat next week!
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