Avg. Speeds

[Priester]

Hi Guys,

I came across the following question when I was doing a practice GMAT today:

A certain car averages 25 miles per gallon 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 drive 10 miles in the city and then 50 miles on the highway?

A. 28
B. 30
C. 33
D. 36
E. 38

I have tried numerous ways to work out this solution but I keep getting an answer that isn't listed (37.5). And rounding 37.5 to the nearest mile, 38, gives you the wrong solution. The correct answer is D 36.

Please help.
Thanks.

[Stuart@KaplanGMAT]

Hi Guys,

I came across the following question when I was doing a practice GMAT today:

A certain car averages 25 miles per gallon 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 drive 10 miles in the city and then 50 miles on the highway?

A. 28
B. 30
C. 33
D. 36
E. 38

I have tried numerous ways to work out this solution but I keep getting an answer that isn't listed (37.5). And rounding 37.5 to the nearest mile, 38, gives you the wrong solution. The correct answer is D 36.

Please help.
Thanks.

If you try using weighted averages, you get 37.5.

Tot Avg = weight1*avg1 + weight2*av2 + weight3*avg3...

Here, we're getting 25mpg for 1/6 of the distance and 40mpg for 5/6 of the distance. So:

Tot Avg = (1/6)25 + (5/6)40 = 25/6 + 200/6 = 225/6 = 75/2 = 37.5

However, if we actually calculate:

25mpg for 10 miles = 10/25 = 2/5 of a gallon used.
40mpg for 50 miles = 50/40 = 5/4 gallons used.

So, we've used up 33/20 gallons and travelled 60 miles.

Therefore, our mpg = 60/(33/20) = (60*20)/33 = 400/11 = approx 36 1/3

Clearly, the weighted average formula gives us the wrong answer... not sure why though!

[Priester]

Thanks so much Stuart,

I completely understand the way you solved it, and hopefully I will be able to figure it out during the exam. I'm just worried, that if I had used the weighted averaged formula during the exam, and one of the answer choices was 37.5, would I be wrong?!?!?! Hopefully, I don't come across that!