A certain car traveled twice as many miles from Town A to Town B as it

Average miles per gallon equals to total miles covered/total gallons used (miles/gallons), so if the distance from A to B is \(2x\) miles and from B to C is \(x\) miles then we'll have:
\(average \ miles \ per \ gallon=\frac{total \ miles \ covered}{total \ gallons \ used}=\frac{2x+x}{\frac{2x}{12}+\frac{x}{18}}=\frac{3x}{\frac{2x}{9}}=13.5\).

Answer: B.

Now, \(weighted \ average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}\) and as we are asked to determine average miles per gallon then exactly miles per gallon should be the weights and gallons used for 1st and 2nd parts of the trip should be the values, so in this case the weighted average formula will give the same expression as the one above.

Hope it's clear.

P.S.

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Note: Whenever you are confused what the weights should be (e.g. here should the weights be the distance traveled should they be gallons of fuel used...) look at the units.

Average required is \(\frac{miles}{gallon}\). So you are trying to find the weighted average of two quantities whose units must be \(\frac{miles}{gallon}\).

\(C_{avg} = \frac{C_1*W_1 + C_2*W_2}{{W_1 + W_2}}\)

\(C_{avg}, C_1, C_2 - \frac{miles}{gallon}\)

So \(W_1\) and \(W_2\) should be in gallon to get:

\(\frac{miles}{gallon} = (\frac{miles}{gallon}*gallon + \frac{miles}{gallon}*gallon)/(gallon + gallon)\)

Food for thought: If I sold 10 apples at a profit of 10% and 15 oranges at a profit of 20%, what was my overall profit%?

excellent explanation. Thank you.

yes thats fairly simple. the formula for avg. rate of the two rates r1 and r2 is avg= (2r1*r2)/(r1+r2). apply this to anything, speed , work done, mileage , provided the work done using the two rates is the same.

good job. thanks for that. i like these kind of questions.

Karishma,

Why is this not working
?


12*(2/3) + 18 *(1/3)
/1

14??

We need to find the average miles per gallon.

Average miles/gallon = Total miles/Total gallons

What is the distance travelled (i.e. miles)?
"traveled twice as many miles from Town A to Town B as it did from Town B to Town C"
We know that the ratio of the two distances must be 2:1 or we can say the distances must be 2d and d.
What is the total gallons used?
Fuel used to go from A to B = 2d/12
Fuel used to go from B to C = d/18

So Average miles/gallon = (2d + d)/(2d/12 + d/18)

Go back to my post above. It explains that you have to be mindful of how to use weighted averages. You need to know what the weights are going to be. Here, weights have to be the amount of fuel used i.e. in gallons because you are looking for average miles per gallon.

If we change the question and make it:
A certain car used twice as many gallons from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?

Now you can use 12*(2/3) + 18 *(1/3)/1

I hope it makes sense now.

Thanks karishma..
Guess to excel in gmat you need pay attention to every single word in the question before jumpin on answer it

Ans is B
Given d_ab = 2*d_bc
let d_ab = d and d_bc = x so d=2x

for average miles per gallon = (d+x)/((d/12)+(x/18)) = 13.5 (formula avg speed = total distance/ total time)

How about using a plugin techenique?
since we have the car gas milages (miles/gallon) are 12mpg and 18 mpg
LCM of 12 and 18=36
Let's say distance between B and C is 36 miles
Distance between A and B =72
So for traveling from A to B , the required gallons of gas is =72 miles/(12 miles per gallon)=6 gallons ( note : cancell the miles)
For travelling from B to C, the required gallons of gas is = 36 miles/ ( 18 miles per gallon) = 2 gallons
therefore avg miles per gallon for the total trip is = (total distance)/(total gallons) = (36+72) miles/(8) gallons = 108/8=13.5 miles per gallon.

Let,
Distance between Town A to Town B = D1
Distance between Town B to Town C = D2

Avg miles/gallon from Town A to Town B = p = 12
Avg miles/gallon from Town B to Town C = q = 18

Given : D1 = 2 * D2


Therefore Required Average can be found out by :

\(Req. Avg = \frac{(D1+D2)pq}{[D1*q+D2*p]}\)

\(Req. Avg = \frac{3*D2*12 * 18}{[2*D2*18 + D2*12]}\)

\(Req. Avg = \frac{12*18*3*D2}{48*D2}\)

Req Avg = 13.5 miles/gallon

Answer is B

Let distance A to B = 2, then distance B to C = 1

Overall Average \(= \frac{Total distance}{Total consumption} = \frac{2+1}{\frac{2}{12} + \frac{1}{18}} = \frac{3}{4} * 18 = 13.5\)

Answer = B

average miles per gallon=total miles/total gallons
let total miles=3m
total gallons=2m/9
3m/(2m/9)=13.5 miles per gallon

Shouldn't the weights be the distances???

No. Since you need to average miles/gallon, the weights will be in gallons (the denominator). It is obvious from the formula of weighted average:

\(Cavg = \frac{(C1*w1 + C2*w2)}{(w1 + w2)}\)

Also check this post: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/1 ... -averages/

We are given that a certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. Thus, if the car traveled d miles from Town B to Town C, it traveled 2d miles from Town A to Town B.

We are also given that from Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon.

Thus, the number of gallons used from Town A to Town B is 2d/12 = d/6 and the number of gallons used from Town B to Town C is d/18.

Let’s now determine the overall average miles per gallon, using the following formula:

average = (total distance)/(total gallons)

average = (d + 2d)/(d/6 + d/18)

average = 3d/(4d/18) = (3d x 18)/4d = 54/4 = 13.5 mpg

Answer: B
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Choosing smart numbers:
A to B = 36 miles
B to C = 18 miles
From A to B at 12mpg = 36 miles/12mpg = 3 gallons used
From B to C at 18mpg = 18 miles/18mpg = 1 gallon use
Total Gallons = 4
Average mpg = Total Miles/Total Gallons = (36+18)/4 = 54/4 = 13.5, Answer B.

Hi All,

We're told that a certain car traveled TWICE as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 12 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. We're asked for the average MILES PER GALLON that the car achieved on its trip from Town A through Town B to Town C. This question can be solved in a couple of different ways, including by TESTing VALUES.

To start, we should look to pick distances that work well with the given miles/gallon data that we have (re: 12 miles/gallon and 18 miles/gallon). Choosing 36 miles for the first part of the trip and 18 miles for the second part of the trip will make the math fairly easy.

Town A to Town B: 36 miles traveled at 12 miles/gallon --> 36/12 = 3 gallons used to travel 36 miles

Town B to Town C: 18 miles traveled at 18 miles/gallon --> 18/18 = 1 gallon used to travel 18 miles

Total miles traveled = 36 + 18 = 54 miles
Total gallons used = 3 + 1 = 4 gallons
Average miles/gallon = 54/4 = 13.5

Final Answer:

GMAT assassins aren't born, they're made,
Rich

So i plugged in here

A->B twice than B->C
10------------------5

average miles per gallon that the car achieved on its trip from
Town A through Town B to Town C = Total Distance/Gallons consumed per distance

= 15 / [10/12 + 5/18]
= 15 *12*18/{240}
= 13.5

B
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