The Gas Mileage problem is a classic example of the GMAT triggering one of our DSM’s: Our Default Solving Mechanisms for applied math. Yet there are three higher level solution paths that we can engage instead. So we are going to skip the math entirely on this one. In reading the question stimulus, there’s a signal that estimation is going to be a very strong and viable solution path and in fact for most folks estimation is the dominant solution path for this problem.

## What to Take Note Of

Notice in the first sentence here that we are given the relationship between the efficiency for Car X and the efficiency for Car Y. When comparing 25 to 11.9, 11.9 is a little bit less than half. Whenever we have a relationship that is a little less or a little more than a factor, that’s a clear signal that the GMAT wants us to estimate.

Now, we have an inverse relationship here, between the efficiency of Cars X and Y and the amount of gas they use. So if Car Y is using a little half or rather if Car Y has a little less than half efficiency it’s going to use a little more than double the amount of gas. Managing the directionality of estimation is essential to make full use of this solution path.

## Estimation Solution Path

Right off the bat, we have a sense that Car Y is going to use a little bit more than double the amount of gas. Now, all we need to do is figure out how much Car X will use. This is an exercise in mental math. Instead of dividing the 12,000 miles by 25 we want to build up from the 25 to 12,000.

Ask ourselves, in a scenario type of way, how many 25’s go into 100 — The answer is 4. 4 quarters to a $1. Then we can scale it up just by throwing some zeros on. So, 40 25’s are 1,000. How do we get from 1,000 to 12,000? We multiply by 12. So 40 times 12, 480 25’s gives us our 12,000 miles. Car X uses 480 gallons.

Therefore, Car Y is going to use a little more than double this and we point to answer C because we just need to answer the amount Y uses in addition to X. SO there is a bit of verbal play there that we also have to recognize. That’s the estimation solution path.

## Graphical Solution Path

We can see this via the graphic solution path by imaging a rectangle, where we have the efficiency of the engine on one side and the amount of gallons on the other. With Car X, 25 miles per gallon time 480 gallons is going to give us the area of 12,000 miles. That is we’ve driven the 12,000 miles in that rectangle. If we are cutting it in half on efficiency, or a little more than half, we end up with two strips and if we lay them side by side we see that we’re doubling of going a little more than double on the amount of gas that we use to maintain that 12,000 mile area.

## Logical Solution Path

Finally, we can look at this from a logical solution path which overlaps a bit with the estimation. But the moment we know that Y uses a little more than double the amount of gas of X, we can also look at and not manage that directionality and just say it uses about double. The only answer choice among our answer choices that is close but not exactly, is C — 520. 480 is our exact number and the A answer is way too low. It’s not close enough to 480 to be viable. So here is an example where, while best practices have us managing the directionality, we don’t even need to do that.

## Similar Problems

For similar problems like this take a look at the Wholesale Tool problem, The Glucose Solution Problem and for a really good treatment of the graphic solution path check out Don’s Repair Job. There should be links to all three right below and I hope that this helps you guys on your way to achieving success on the GMAT.

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