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There are only 3 quantities in every mileage question:
The below bold part is enough to answer any question on GMAT
Distance (miles)
Fuel (gallons)
Efficiency (miles per gallon)
They are always related by:
Distance = MPG x Gallons
or
Gallons = Distance / MPG
Everything comes from these two equations.
GMAT Drill
Step 1: Read the question slowly
A delivery truck traveled three times as many miles on highways as on city roads.
On highways, it averaged 24 miles per gallon.
On city roads, it averaged 12 miles per gallon.
On the entire trip, what was the truck's average miles per gallon?
Stop. Don't calculate yet.
Step 2: Ask yourself one question
What is fixed?
Is it:
Gallons? No.
Time? No.
Distance? Yes.
The problem compares miles traveled.
Whenever distance is given, think:
Fuel = Distance / MPG
Step 3: Choose easy numbers
The ratio is:
Highway : City = 3 : 1
Pick:
Highway = 72 miles
City = 24 miles
Total = 96 miles
Why?
Because 72 is divisible by 24, and 24 is divisible by 12.
GMAT loves easy numbers.
Step 4: Convert each leg into gallons
Highway:
Distance = 72
MPG = 24
Fuel = 72 / 24 = 3 gallons
City:
Distance = 24
MPG = 12
Fuel = 24 / 12 = 2 gallons
Notice what happened.
Although city driving is only one-fourth of the distance, it used almost as much fuel.
This is why averaging 24 and 12 makes no sense.
Step 5: Compute overall MPG
Total distance = 72 + 24 = 96 miles
Total fuel = 3 + 2 = 5 gallons
Overall MPG = 96 / 5 = 19.2
Done.
Now let's make it harder.
A car traveled from A to B using 20 gallons at 15 MPG.
It returned from B to A using 30 gallons at 20 MPG.
What was the average MPG for the round trip?
Read carefully.
Many people immediately think:
(15 + 20) / 2
Wrong.
Because gallons are given, not distance.
Step 1
Find each distance.
Trip 1:
Distance = 20 x 15 = 300 miles
Trip 2:
Distance = 30 x 20 = 600 miles
Total distance = 900 miles
Step 2
Total fuel = 20 + 30 = 50 gallons
Step 3
Average MPG = 900 / 50 = 18
Notice something interesting.
The return trip had higher MPG, but because it also used more gallons, it covered much more distance.
One more (700+ style)
A truck spends:
40% of its fuel driving uphill at 10 MPG.
The remaining fuel driving downhill at 30 MPG.
Find the overall MPG.
Read carefully.
Most people think:
"Need distances."
No.
Fuel percentages are given.
Fuel is fixed.
Assume total fuel = 100 gallons.
Uphill:
Fuel = 40 gallons
Distance = 40 x 10 = 400 miles
Downhill:
Fuel = 60 gallons
Distance = 60 x 30 = 1800 miles
Total distance = 2200 miles
Overall MPG = 2200 / 100 = 22
Mental decision tree
Whenever you read an MPG problem, ask one question first:
Case 1: Distance is given
Examples:
Twice the distance
Equal distance
60 miles then 90 miles
40% of the trip
Think:
Compute gallons.
Use:
Gallons = Distance / MPG
Case 2: Gallons are given
Examples:
Used 15 gallons
First half of the fuel
40% of the fuel
Think:
Compute distance.
Use:
Distance = Gallons x MPG
Case 3: Time is given
Examples:
Drove for 2 hours
Half the time
Neither distance nor fuel is fixed.
First compute distance.
Distance = Speed x Time
Then continue normally.
The one sentence that prevents almost every mistake
Do not average rates like MPG or km/L.
If distance is given, convert each segment to gallons, then compute the overall MPG.
If gallons are given, convert each segment to distance, then compute the overall MPG.
GMAT takeaway
Whenever you see mileage or fuel-efficiency questions, first identify what is fixed.
If distance is fixed, convert everything to gallons.
If gallons are fixed, convert everything to distance.
Only after combining totals should you calculate the overall MPG.
This single habit eliminates the vast majority of mistakes on these questions.
The below bold part is enough to answer any question on GMAT
Distance (miles)
Fuel (gallons)
Efficiency (miles per gallon)
They are always related by:
Distance = MPG x Gallons
or
Gallons = Distance / MPG
Everything comes from these two equations.
GMAT Drill
Step 1: Read the question slowly
A delivery truck traveled three times as many miles on highways as on city roads.
On highways, it averaged 24 miles per gallon.
On city roads, it averaged 12 miles per gallon.
On the entire trip, what was the truck's average miles per gallon?
Stop. Don't calculate yet.
Step 2: Ask yourself one question
What is fixed?
Is it:
Gallons? No.
Time? No.
Distance? Yes.
The problem compares miles traveled.
Whenever distance is given, think:
Fuel = Distance / MPG
Step 3: Choose easy numbers
The ratio is:
Highway : City = 3 : 1
Pick:
Highway = 72 miles
City = 24 miles
Total = 96 miles
Why?
Because 72 is divisible by 24, and 24 is divisible by 12.
GMAT loves easy numbers.
Step 4: Convert each leg into gallons
Highway:
Distance = 72
MPG = 24
Fuel = 72 / 24 = 3 gallons
City:
Distance = 24
MPG = 12
Fuel = 24 / 12 = 2 gallons
Notice what happened.
Although city driving is only one-fourth of the distance, it used almost as much fuel.
This is why averaging 24 and 12 makes no sense.
Step 5: Compute overall MPG
Total distance = 72 + 24 = 96 miles
Total fuel = 3 + 2 = 5 gallons
Overall MPG = 96 / 5 = 19.2
Done.
Now let's make it harder.
A car traveled from A to B using 20 gallons at 15 MPG.
It returned from B to A using 30 gallons at 20 MPG.
What was the average MPG for the round trip?
Read carefully.
Many people immediately think:
(15 + 20) / 2
Wrong.
Because gallons are given, not distance.
Step 1
Find each distance.
Trip 1:
Distance = 20 x 15 = 300 miles
Trip 2:
Distance = 30 x 20 = 600 miles
Total distance = 900 miles
Step 2
Total fuel = 20 + 30 = 50 gallons
Step 3
Average MPG = 900 / 50 = 18
Notice something interesting.
The return trip had higher MPG, but because it also used more gallons, it covered much more distance.
One more (700+ style)
A truck spends:
40% of its fuel driving uphill at 10 MPG.
The remaining fuel driving downhill at 30 MPG.
Find the overall MPG.
Read carefully.
Most people think:
"Need distances."
No.
Fuel percentages are given.
Fuel is fixed.
Assume total fuel = 100 gallons.
Uphill:
Fuel = 40 gallons
Distance = 40 x 10 = 400 miles
Downhill:
Fuel = 60 gallons
Distance = 60 x 30 = 1800 miles
Total distance = 2200 miles
Overall MPG = 2200 / 100 = 22
Mental decision tree
Whenever you read an MPG problem, ask one question first:
Case 1: Distance is given
Examples:
Twice the distance
Equal distance
60 miles then 90 miles
40% of the trip
Think:
Compute gallons.
Use:
Gallons = Distance / MPG
Case 2: Gallons are given
Examples:
Used 15 gallons
First half of the fuel
40% of the fuel
Think:
Compute distance.
Use:
Distance = Gallons x MPG
Case 3: Time is given
Examples:
Drove for 2 hours
Half the time
Neither distance nor fuel is fixed.
First compute distance.
Distance = Speed x Time
Then continue normally.
The one sentence that prevents almost every mistake
Do not average rates like MPG or km/L.
If distance is given, convert each segment to gallons, then compute the overall MPG.
If gallons are given, convert each segment to distance, then compute the overall MPG.
GMAT takeaway
Whenever you see mileage or fuel-efficiency questions, first identify what is fixed.
If distance is fixed, convert everything to gallons.
If gallons are fixed, convert everything to distance.
Only after combining totals should you calculate the overall MPG.
This single habit eliminates the vast majority of mistakes on these questions.
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